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White paper on light sterile neutrino searches and related phenomenology

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Journal of Physics G: Nuclear and Particle Physics
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M A Acero
M A Acero
M A Acero
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C A Argüelles
C A Argüelles
C A Argüelles
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M Hostert
M Hostert
M Hostert
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Figures

The LSND anomalous events as a function of both L/E ν (left) and observable electron energy (right), for the subset of total selected events with R γ > 10 and 20 < E e < 60 MeV. Note the blue shaded region is for a best fit two-neutrino oscillation fit of sin22θ=0.003 and Δm ² = 1.2 eV². Reprinted (figure) with permission from [19], Copyright (2001) by the American Physical Society.
The LSND anomalous events as a function of both L/E ν (left) and observable electron energy (right), for the subset of total selected events with R γ > 10 and 20 < E e < 60 MeV. Note the blue shaded region is for a best fit two-neutrino oscillation fit of sin22θ=0.003 and Δm ² = 1.2 eV². Reprinted (figure) with permission from [19], Copyright (2001) by the American Physical Society.
… 
The results of a two-neutrino oscillation fit performed by the LSND collaboration for all data with reconstructed electron energy 20 < E e < 200 MeV, showing the resulting 90 and 99% confidence level allowed regions for sin22θμe and Δm ². Shown also are the 90% CL limits from other contemporary experiments. Reprinted (figure) with permission from [19], Copyright (2001) by the American Physical Society.
The results of a two-neutrino oscillation fit performed by the LSND collaboration for all data with reconstructed electron energy 20 < E e < 200 MeV, showing the resulting 90 and 99% confidence level allowed regions for sin22θμe and Δm ². Shown also are the 90% CL limits from other contemporary experiments. Reprinted (figure) with permission from [19], Copyright (2001) by the American Physical Society.
… 
The final MiniBooNE allowed regions for the full fit of all neutrino and antineutrino running mode data. Reproduced from [33]. CC BY 4.0.
The final MiniBooNE allowed regions for the full fit of all neutrino and antineutrino running mode data. Reproduced from [33]. CC BY 4.0.
… 
The final MiniBooNE results corresponding to 18.75 × 10²⁰ POT in neutrino mode (top figures) and 11.27 × 10²⁰ POT in antineutrino mode (bottom figures) for both the reconstructed visible energy (left) and the reconstructed angle that the Cherenkov cone makes with respect to the neutrino beam (right). Note that as the top two figures corresponding to neutrino mode are from [33], and the bottom two for antineutrino running more are from [32], the best-fit line does not correspond to the exact same point in sterile parameter space. Reproduced from [32, 33]. CC BY 4.0.
The final MiniBooNE results corresponding to 18.75 × 10²⁰ POT in neutrino mode (top figures) and 11.27 × 10²⁰ POT in antineutrino mode (bottom figures) for both the reconstructed visible energy (left) and the reconstructed angle that the Cherenkov cone makes with respect to the neutrino beam (right). Note that as the top two figures corresponding to neutrino mode are from [33], and the bottom two for antineutrino running more are from [32], the best-fit line does not correspond to the exact same point in sterile parameter space. Reproduced from [32, 33]. CC BY 4.0.
… 
The final MiniBooNE results in neutrino mode in terms of both the timing of the events relative to the beam (right) and the reconstructed radial position of the spherical detector. By studying the excess in terms of additional distributions like these, a better understanding of the excess as well as the backgrounds has begun to emerge. In this example, both the beam timing and radial distributions heavily disfavor an underestimation of the ‘Dirt’ component normalization being the source of the excess. Reproduced from [33]. CC BY 4.0.
+125
The final MiniBooNE results in neutrino mode in terms of both the timing of the events relative to the beam (right) and the reconstructed radial position of the spherical detector. By studying the excess in terms of additional distributions like these, a better understanding of the excess as well as the backgrounds has begun to emerge. In this example, both the beam timing and radial distributions heavily disfavor an underestimation of the ‘Dirt’ component normalization being the source of the excess. Reproduced from [33]. CC BY 4.0.
… 
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Major Report
White paper on light sterile neutrino
searches and related phenomenology
M A Acero
1,119
, C A Argüelles
2,119
, M Hostert
3,4,5,119
,
D Kalra
6,119
, G Karagiorgi
6,119
, K J Kelly
7,119
,
B R Littlejohn
8,119
, P Machado
9,119
, W Pettus
10,119
,
M Toups
9,119
, M Ross-Lonergan
6,119
, A Sousa
11,119
,
P T Surukuchi
12,119
, Y Y Y Wong
13,119
, W Abdallah
14,120
,
A M Abdullahi
9,15,120
, R Akutsu
16,120
, L Alvarez-Ruso
17,120
,
D S M Alves
18,120
, A Aurisano
11,120
, A B Balantekin
19,120
,
J M Berryman
20,21,120
, T Bertólez-Martínez
22,120
,
J Brunner
23,120
, M Blennow
24,25,26,120
, S Bolognesi
27,120
,
M Borusinski
28,120
, T Y Chen
6,120
, D Cianci
6,120
, G Collin
29,120
,
J M Conrad
30,120
, B Crow
28,120
, P B Denton
31,120
,
M Duvall
28,120
, E Fernández-Martinez
25,120
, C S Fong
32,120
,
N Foppiani
2,120
, D V Forero
33,120
, M Friend
34,35,120
,
A García-Soto
2,17,120
, C Giganti
36,120
, C Giunti
37,120
,
R Gandhi
38,120
, M Ghosh
39,120
, J Hardin
30,120
,
K M Heeger
12,120
, M Ishitsuka
40,120
, A Izmaylov
41,42,120
,
B J P Jones
43,120
, J R Jordan
44,120
, N W Kamp
30,120
,
T Katori
45,120
, S B Kim
46,120
, L W Koerner
47,120
,
M Lamoureux
48,120
, T Lasserre
27,120
, K G Leach
49,120
,
J Learned
28,120
,YFLi
50,51,120
, J M Link
52,120
, W C Louis
18,120
,
K Mahn
53,120
, P D Meyers
54,120
, J Maricic
28,120
,
D Markoff
55,120
, T Maruyama
34,120
, S Mertens
56,57,120
,
H Minakata
52,120
, I Mocioiu
58,120
, M Mooney
59,120
,
M H Moulai
60,120
, H Nunokawa
61,120
, J P Ochoa-Ricoux
62,120
,
YMOh
63,120
, T Ohlsson
24,26,120
, H Päs
64,120
, D Pershey
65,120
,
R G H Robertson
66,120
, S Rosauro-Alcaraz
67,120
,
C Rott
46,68,120
, S Roy
69,120
, J Salvado
22,120
, M Scott
41,120
,
S H Seo
63,120
, M H Shaevitz
6,120
, M Smiley
20,70,120
,
J Spitz
44,120
, J Stachurska
30,120
, M Tammaro
71
,
T Thakore
11,120
, C A Ternes
37,120
, A Thompson
72,120
,
S Tseng
73,120
, B Vogelaar
52,120
, T Weiss
12,120
,
R A Wendell
74,75,120
, R J Wilson
59,120
, T Wright
52,120
,
Z Xin
50,51,120
, B S Yang
76,120
, J Yoo
76,120
, J Zennamo
9,120
,
J Zettlemoyer
9,120
, J D Zornoza
17,120
, J Zupan
11
, S Ahmad
77
,
E Arrieta-Diaz
78
, V S Basto-Gonzalez
79
, N S Bowden
80
,
B C Cañas
79
, D Caratelli
81
, C V Chang
82
, C Chen
82
,
Journal of Physics G: Nuclear and Particle Physics
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 (214pp)https://doi.org/10.1088/1361-6471/ad307f
© 2024 The Author(s). Published by IOP Publishing Ltd 1
T Classen
80
, M Convery
83
, G S Davies
84
, S R Dennis
85
,
Z Djurcic
86
, R Dorrill
8
,YDu
87
, J J Evans
88
, U Fahrendholz
57
,
J A Formaggio
30
, B T Foust
12
, H Frandini Gatti
9
,
D Garcia-Gamez
89
, S Gariazzo
37
, J Gehrlein
31
, C Grant
90
,
R A Gomes
91
, A B Hansell
92
, F Halzen
60
,SHo
93
,
J Hoefken Zink
94,95
, R S Jones
96
, P Kunkle
90
, J-Y Li
97
,
SCLi
52,98
, X Luo
81
, Yu Malyshkin
42,99
, C J Martoff
100
,
D Massaro
94,95,101
, A Mastbaum
102
, R Mohanta
39
,
H P Mumm
103
, M Nebot-Guinot
97
, R Neilson
104
,KNi
105
,
J Nieves
17
, G D Orebi Gann
20,70
, V Pandey
106
, S Pascoli
94,95
,
G Paz
107
, A A Petrov
107,108
, X Qian
31
, M Rajaoalisoa
11
,
S H Razafinime
11
, C Roca
80
, G Ron
109
, B Roskovec
110
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E Saul-Sala
17
, L Saldaña
12
, D W Schmitz
111
, K Scholberg
65
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B Shakya
112
, P L Slocum
12
, E L Snider
9
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H Th J Steiger
57,113,114
, A F Steklain
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, M R Stock
57
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F Sutanto
80
, V Takhistov
75
, R Tayloe
10
, Y-D Tsai
116
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Y-T Tsai
83
, D Venegas-Vargas
89
, M Wallbank
11
, E Wang
117
,
P Weatherly
104
, S Westerdale
54
, E Worcester
31
,WWu
9
,
G Yang
20
and B Zamorano
89
1
Universidad del Atlántico, Puerto Colombia, Atlántico, Colombia
2
Department of Physics & Laboratory for Particle Physics and Cosmology, Harvard
University, Cambridge, MA 02138, United States of America
3
School of Physics and Astronomy, University of Minnesota, Minneapolis, MN
55455, United States of America
4
William I. Fine Theoretical Physics Institute, School of Physics and Astronomy,
University of Minnesota, Minneapolis, MN 55455, United States of America
5
Perimeter Institute for Theoretical Physics, Waterloo, ON N2J 3W9, Canada
6
Columbia University, New York, NY, United States of America
7
CERN, Esplanade des Particules, 1211 Geneva 23, Switzerland
8
Illinois Institute of Technology, Chicago, IL, United States of America
9
Fermi National Accelerator Laboratory, Batavia, IL, United States of America
10
Indiana University, Bloomington, IN, United States of America
11
Department of Physics, University of Cincinnati, Cincinnati, OH 45221, United
States of America
12
Wright Laboratory, Department of Physics, Yale University, New Haven, CT,
United States of America
13
School of Physics, The University of New South Wales, Sydney NSW 2052,
Australia
14
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613,
Egypt
15
Institute for Particle Physics Phenomenology, Durham University, Durham DH1
3LE, United Kingdom
16
TRIUMF, Vancouver, British Columbia, Canada
17
Instituto de Física Corpuscular (IFIC)and Departamento de Física Teórica, Consejo
Superior de Investigaciones Científicas (CSIC)and Universidad de Valencia (UV),
E-46980, Valencia, Spain
18
Los Alamos National Laboratory, Los Alamos, NM, United States of America
19
Department of Physics, University of Wisconsin, Madison, WI 53706, United States
of America
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
2
20
Department of Physics, University of California, Berkeley, CA 94720, United States
of America
21
Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, United
States of America
22
Departament de Física Quàntica i AstrofÃsica and Institut de Ciéncies del Cosmos,
Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
23
Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
24
Department of Physics, School of Engineering Sciences, KTH Royal Institute of
Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden
25
University Autonoma Madrid, Department of Theoretical Physics, Madrid, Spain
26
The Oskar Klein Centre, AlbaNova University Center, SE-106 91 Stockholm,
Sweden
27
Université Paris-Saclay, Gif-sur-Yvette, France
28
University of Hawaii, 2505 Correa Rd, Honolulu, HI 96822, United States of
America
29
Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575,
United States of America
30
Massachusetts Institute of Technology, Cambridge, MA, United States of America
31
Physics Department, Brookhaven National Laboratory, Upton, NY, United States of
America
32
Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09.210-170,
Santo André, SP, Brazil
33
Universidad de Medellín, Carrera 87 N
o
30 - 65 Medellín, Colombia
34
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-00801,
Japan
35
J-PARC Center, Tokai, Japan
36
Laboratoire de Physique Nucleaire et de Hautes Energies, IN2P3/CNRS, Sorbonne
Universitè, Paris, France
37
Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via P. Giuria 1,
I–10125 Torino, Italy
38
Harish-Chandra Research Institute (A CI of the Homi Bhabha National Institute),
Chhatnag Road, Jhunsi, Allahabad 211019, India
39
School of Physics, University of Hyderabad, Hyderabad 500046, India
40
Tokyo University of Science, Department of Physics, Chiba, Japan
41
Imperial College London, London, United Kingdom
42
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia
43
Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm
108, Box 19059, Arlington, TX 76019, United States of America
44
University of Michigan, Ann Arbor, MI, 48109, United States of America
45
Kingʼs College London, WC2R 2LS, London, United Kingdom
46
Department of Physics, Sungkyunkwan University, Suwon 16419, Republic of
Korea
47
Department of Physics, Houston, Houston, Texas 77204, United States of America
48
INFN Sezione di Padova, I-35131 Padova, Italy
49
Department of Physics, Colorado School of Mines, Golden, CO, United States of
America
50
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049,
People’s Republic of China
51
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing
100049, People’s Republic of China
52
Center for Neutrino Physics, Department of Physics, Virginia Tech, Blacksburg,
VA 24061, United States of America
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3
53
Michigan State University, East Lansing, MI, United States of America
54
Princeton University, Princeton, NJ, United States of America
55
North Carolina Central University, 1801 Fayetteville Street, Durham, NC 27707,
United States of America
56
Max-Planck-Institut für Physik, München, Germany
57
Technische Universität München, Garching, Germany
58
Department of Physics, Pennsylvania State University, University Park, PA 16802,
United States of America
59
Colorado State University, Fort Collins, CO, United States of America
60
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin-Madison, Madison, WI 53706, United States of America
61
Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro,
C.P. 38097, 22451-900, Rio de Janeiro, Brazil
62
Department of Physics and Astronomy, University of California at Irvine, Irvine,
CA 92697, United States of America
63
Center for Underground Physics, Institute for Basic Science (IBS), Daejeon 34126,
Republic of Korea
64
TU Dortmund, Department of Physics, D-44221, Dortmund, Germany
65
Department of Physics, Duke University, Durham, NC 27708, United States of
America
66
University of Washington, Seattle, WA, United States of America
67
Pôle Théorie, Laboratoire de Physique des 2 Infinis Irène Joliot Curie (UMR 9012)
CNRS/IN2P3, F-91400 Orsay, France
68
Department of physics, The University of Utah, 201 Presidents’Cir, Salt Lake City,
UT 84112, United States of America
69
Institute of Physics, Sachivalaya Marg, Sainik School Post, Bhubaneswar 751005,
India
70
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States of
America
71
Jozef Stefan Institute, Jamova 39, Ljubljana, Slovenia
72
Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics
and Astronomy, Texas A&M University, College Station, TX 77845, United States of
America
73
Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku,
Tokyo 113-0033, Japan
74
Kyoto University, Department of Physics, Kyoto, Japan
75
Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS,
Japan
76
Department of Physics and Astronomy, Seoul National University, Seoul 08826,
Republic of Korea
77
HEPG, Pakistan Institute of Nuclear Science and Technology (PINSTECH),
Islamabad, Pakistan
78
Universidad del Magdalena, Carrera 32 N
o
22 - 08 Santa Marta, Colombia
79
Universidad de Pamplona, km 1, vía salida a Bucaramanga, Campus Universitario,
543050 Pamplona, Colombia
80
Lawrence Livermore National Laboratory, Livermore, CA, United States of
America
81
University of California Santa Barbara, Santa Barbara, CA 93106, United States of
America
82
Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan
83
SLAC National Accelerator Laboratory, United States of America
84
University of Mississippi, University, MS 38677, United States of America
85
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
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86
Argonne National Laboratory, Lemont, IL 60439, United States of America
87
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
88
University of Manchester, Manchester M13 9PL, United Kingdom
89
University of Granada & CAFPE, Granada, Spain
90
Department of Physics, Boston University, Boston, MA 02215, United States of
America
91
Instituto de Física, Universidade Federal de Goiás, Goiânia, GO 74690-900, Brazil
92
Department of Physics, Susquehanna University, Selinsgrove, PA, United States of
America
93
Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
94
Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, I-40126
Bologna, Italy
95
INFN, Sezione di Bologna, viale Berti Pichat 6/2, I-40127 Bologna, Italy
96
Department of Physics and Astronomy, University of Sheffield, Sheffield, United
Kingdom
97
University of Edinburgh, Edinburgh EH8 9YL, United Kingdom
98
Department of Physics and Astronomy, Purdue University, West Lafayette, IN
47907, United States of America
99
Joint Institute for Nuclear Research, Dubna, 141980, Russia
100
Temple University, Philadelphia, PA 19122, United States of America
101
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université
Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
102
Rutgers University, Piscataway, NJ, United States of America
103
National Institute of Standards and Technology, Gaithersburg, MD 20899, United
States of America
104
Department of Physics, Drexel University, Philadelphia, PA 19104, United States
of America
105
University of California San Diego, La Jolla, CA 92093, United States of America
106
Department of Physics, University of Florida, Gainesville, FL 32611, United States
of America
107
Department of Physics and Astronomy, Wayne State University, Detroit, Michigan
48201, United States of America
108
Department of Physics and Astronomy, University of South Carolina, Columbia,
SC 29205, United States of America
109
Hebrew University of Jerusalem, Israel
110
Faculty of Mathematics and Physics, Charles University, Prague, V Holešovičkách
2, 18000 Prague, Czech Republic
111
Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, United States of
America
112
Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22607 Hamburg,
Germany
113
Johannes Gutenberg Universität zu Mainz, Mainz, Germany
114
Cluster of Excellence PRISMA+, Mainz, Germany
115
Department of Mathematics, Universidade Tecnológica Federal do Paraná,
80.230-901, Curitiba, PR, Brazil
116
University of California, Irvine, CA 92697, United States of America
117
School of Physics and Microelectronics, Zhengzhou University, Zhengzhou,
Henan 450001, People’s Republic of China
118
Department of Physics, Case Western Reserve University, Cleveland, OH 44106,
United States of America
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
5
E-mail: alex.sousa@uc.edu
Received 12 December 2022
Accepted for publication 6 March 2024
Published 29 October 2024
Keywords: neutrino physics, light sterile neutrino, experimental neutrino
anomalies
Executive summary
Several decades of a rich and diverse program of experimental neutrino measurements have
provided an increasingly clearer picture of the elusive neutrino sector, and uncovered physics
not predicted by the Standard Model (SM), such as the existence of nonzero neutrino masses
implied by the surprising discovery of neutrino flavor mixing. This foundational discovery
represented a welcome resolution to decades-long experimental anomalies associated with
solar and atmospheric neutrino measurements.
Alongside this foundational discovery, experimental neutrino anomalies have been
observed that still remain unresolved, and have served as primary drivers in the development
of a vibrant short-baseline neutrino program, and in the launch of a multitude of com-
plementary probes within a large variety of other experiments. Two of these anomalies arise
from the apparent oscillatory appearance of electron (anti)neutrinos in relatively pure muon-
(anti)neutrino beams originating from charged-pion decay-at-rest, specifically the LSND
Anomaly, and from charged-pion decay-in-flight, the MiniBooNE Low-Energy Excess. Two
other anomalies are associated with an overall normalization discrepancy of electron (anti)
neutrinos expected both from conventional fission reactors, the Reactor Neutrino Anomaly,
and in the radioactive decay of Gallium-71, the Gallium Anomaly. In these two latter cases, no
oscillatory signature is observed, but the overall normalization deficit can be ascribed to rapid
oscillations that are averaged out and appear as an overall deficit.
Historically, these anomalies were first interpreted as oscillations due to the existence of
light sterile neutrinos that mix with the three SM neutrinos. This interpretation requires an
oscillation frequency Δm
2
1eV
2
, implying the addition of at least one neutrino to the three-
flavor mixing paradigm. This new neutrino would have to be a SM gauge singlet, thus it is
referred to as sterile, as LEP measurements of the invisible decay width of the Zboson show
only three neutrinos couple to the Zboson. However, this purely oscillatory interpretation is
disfavored by several other direct and indirect experimental tests. Consequently, recent years
have seen accelerating theoretical interest in more complex Beyond the Standard Model
(BSM)flavor transformation and hidden-sector particle production as explanations for the
anomalies. Experimental interest in testing a more diverse set of interpretations has also been
growing, as well as motivation to probe deeper into potential conventional explanations. The
119
Editor.
120
Contributor.
Original content from this work may be used under the terms of the Creative Commons
Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the
author(s)and the title of the work, journal citation and DOI.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
6
discovery of new physics associated with these anomalies would be groundbreaking, and
would have profound implications not only for particle physics but also for astrophysics and
cosmology.
This white paper provides a comprehensive review of our present understanding of the
experimental neutrino anomalies, charting the progress achieved over the last decade at the
experimental and phenomenological level, and sets the stage for future programmatic pro-
spects in addressing the anomalies. In a similar spirit to the ‘Light Sterile Neutrinos: A White
Paper’document from a decade ago [1], this new white paper is purposed to serve as a
guiding and motivational ‘encyclopedic’reference, with emphasis on needs and options for
future exploration that may lead to the ultimate resolution of the anomalies.
Developments over the past decade
Following the requirements identified in [1]has led to a broader understanding of viable
interpretations of the anomalies and strengthened experimental efforts—and experimental
capabilities—in that direction. Notably, the requirement to probe the anomalies with multiple
and orthogonal approaches (accelerator-based short/long-baseline, reactor-based short-base-
line, atmospheric neutrinos, and radioactive source)in the same spirit as employed for
neutrino oscillations has been realized through recent, ongoing, or impending experimental
programs:
1. The development of new radioactive sources and detectors for improved tests of the
Gallium Anomaly has been pursued and realized in the form of the BEST experiment.
2. The reactor antineutrino anomaly and subsequent reactor-based activities and new results
have placed a required emphasis on oscillation-testing short-baseline reactor experiments
and on improved understanding of reactor neutrino fluxes.
3. The community has just begun a comprehensive multi-channel/multi-baseline
accelerator-based short-baseline program to search for 3+Noscillations while directly
addressing the MiniBooNE anomaly both in regards to oscillatory and non-oscillatory
solutions.
4. Recent searches for smoking-gun signatures of light sterile neutrinos with high-energy
atmospheric neutrinos, such as the one performed by the IceCube Neutrino Observatory.
5. A direct test of the LSND anomaly using an improved decay-at-rest beam facility and
experimental arrangement has just begun in the form of the JSNS
2
experiment.
6. Beyond direct anomaly tests, many alternate techniques/facilities, including direct
neutrino mass measurements, long-baseline oscillation experiments, and atmospheric and
astrophysical neutrino experiments, have been applied to the sterile neutrino explanation
of the anomalies.
Primary focuses for the next decade
As the question of light sterile neutrino oscillations is further explored over the next several
years, the community’s efforts should be directed toward disentangling the plethora of pos-
sibilities that have been identified over the past ten years as viable interpretations of the
experimental anomalies in the neutrino sector. The goal of these collective efforts will be to
validate and solidify our understanding of the neutrino sector. Regardless of what the ongoing
and upcoming experiments observe—be it a deviation from the three-neutrino picture or
otherwise—the community should be prepared to address how to put these anomalies to test
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
7
or adequately distinguish between different interpretations. We see the main experimental,
analysis, and theory-driven thrusts that will be essential to achieving this goal being:
1. Cover all anomaly sectors: given the fundamentally unresolved nature of all four
canonical anomalies, it is imperative to support all pillars of a diverse experimental
portfolio—source, reactor, decay-at-rest, decay-in-flight, and other methods/sources—to
provide complementary probes of and increased precision for new physics explanations.
2. Pursue diverse signatures: given the diversity of possible experimental signatures
associated with allowed anomaly interpretations, it is imperative that experiments make
design and analysis choices that maximize sensitivity to as broad an array of these
potential signals as possible.
3. Deepen theoretical engagement: priority in the theory community should be placed on
the development of new physics models relevant to all four canonical short-baseline
anomalies and the development of tools for enabling efficient tests of these models with
existing and future experimental datasets.
4. Openly share data: fluid communication between the experimental and theory
communities will be required, which implies that both experimental data releases and
theoretical calculations should be publicly available. In particular, as it is most likely that
a combination of measurements will be needed to resolve the anomalies, global fits
should be made public, as well as phenomenological fits and constraints to specific
data sets.
5. Apply robust analysis techniques: appropriate statistical treatment is crucial to quantify
the compatibility of data sets within the context of any given model, and in order to test
the absolute viability of a given model. Accurate evaluation of allowed parameter space
is also an important input to the design of future experiments.
The white paper is organized as follows. Section 1provides an overall introduction and
motivation for seeking resolution of the experimental neutrino anomalies, and section 2intro-
duces each of the anomalies in detail, placing them within historical context. Section 3delves
into the theoretical interpretation of the anomalies, detailing phenomenological consequences of
various scenarios that have been or are being pursued. Section 4goes over the broader
experimental landscape, discussing the impact of null results, as well as potential conventional
explanations for the anomalies, while section 5covers results from astrophysical and cosmo-
logical indirect probes. Section 6reviews the very diverse landscape of future experimental
prospects that will be capable of addressing the anomalies. Finally, section 7reiterates our vision
for a path that will lead to the ultimate resolution of the anomalies, providing further discussion
and elaboration of the focal points for the next decade listed in this executive summary.
1. Introduction and motivation
The Nobel prize-winning discovery of neutrino oscillation [2–4]has led to a three-neutrino
mixing picture that is now established as a minimal extension to the Standard Model (SM),and
which is only empirically motivated. This picture prescribes an ‘Extended SM’(ESM),inwhich
the neutrino sector includes three distinct neutrino mass states that are each an independent
linear combination of the three neutrino weak eigenstates: ν
e
,ν
μ
,andν
τ
[5]. This discovery
stands as one of few indisputable pieces of evidence for new physics ‘beyond the SM’(BSM).
Generating neutrino masses is qualitatively different from the mass generation for any other
fermions in the SM. The Higgs mechanism for neutrinos would require the existence of a right-
handed neutrino, which would carry no SM gauge quantum number. This in turn would allow
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
8
for Majorana masses of these right-handed fields, opening up the possibility of a seesaw
mechanism [6–10]. Several other scenarios, involving different particle content, could also
explain the origin of neutrino masses, such as type-II and type-III seesaw models [11–16].In
general, the mechanism of neutrino masses would require the addition of particle content to the
SM that has never been observed. The lack of experimental indication of the scale of this new
physics makes the neutrino sector a promising portal to new physics. Many neutrino mass
models would predict observable deviations from the ESM and could lead to a rich phenom-
enology. In particular, the existence of new states or gauge interactions associated with neutrinos
could affect neutrino experiments in a variety of ways, for example as effects on oscillation
phenomenology or new particles produced in neutrino beams or in neutrino detectors.
In particular, interest in this direction has been fanned by a series of anomalous exper-
imental measurements, especially since the mid-1990ʼs, which suggested the existence of new
neutrino states. It is expected that these states should be ‘sterile’, i.e. non-weakly-interacting,
in order to avoid experimental constraints from invisible
¯
nnZ
decay measurements [17].
There is now a series of indications of neutrino phenomena deviating from the three-neutrino
(ESM)paradigm, many of which have the commonality of being observed primarily in
association with electron neutrino observations, from either electron neutrino or muon neu-
trino sources, with either Cherenkov or scintillator detectors, and at relatively ‘short base-
lines’from the neutrino sources
121
. These ‘short-baseline experimental anomalies’, and the
expansive and dedicated scientific program that has been launched over the past two decades
to address them, is the focus of this paper.
One of the most widely examined theoretical frameworks considered for the interpretation
of these anomalies is that of light (∼1eV)sterile neutrino oscillations [1]. This framework
generally extends the three-neutrino paradigm of the ESM to accommodate (3+N)light
neutrino masses and (3+N)neutrino flavor states, where Nrefers to additional neutrino mass
states with masses of order ∼1 eV. The latter are a linear combination of primarily Nsterile
neutrino eigenstates but contain a small admixture of weak neutrino eigenstates so that they
can participate in neutrino oscillations. This framework generally leads to observable neutrino
oscillations with appearance oscillation amplitudes of order 1% or less, and disappearance
oscillation amplitudes of up to tens of percent. The relatively small oscillation amplitudes are
constrained by unitarity considerations [18], and the known oscillation amplitudes from
‘medium-’and ‘long-baseline’neutrino oscillation measurements.
While the light sterile neutrino oscillation framework can, in theory accommodate all short-
baseline experimental anomalies to date, it fails to accommodate the lack of corresponding
oscillations in other short-baseline, long-baseline, and atmospheric neutrino measurements. One
particular experimental anomaly, contributed by the MiniBooNE experiment, exacerbates this
issue. The need to interpret compelling experimental results, on the other hand, has given rise to
an extensive experimental neutrino program, as well as a substantial body of related phenom-
enological work, including many viable interpretations, from modifications of three-flavor
neutrino mixing to potential couplings to hidden sectors, which we review here.
A consistent picture of short-baseline experimental anomalies has not yet formed, as will
be discussed in this paper. On the other hand, new experiments launched over the past decade
or about to be launched, with the goal of independently investigating either specific exper-
imental anomalies or specific theoretical interpretations, promise to deliver new and
121
We introduce and note that the term ‘short baseline’is used qualitatively, and more specifically it refers to
neutrino propagation distances of
(1km)for measurements performed with neutrino energy of
(1 GeV). More
broadly, it refers to a ratio of neutrino propagation distance relative to neutrino energy of ∼1 km GeV
−1
,
corresponding to a neutrino oscillation frequency Δm
2
of ∼1eV
2
.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
9
invaluable information that will either identify the underlying source(s)of these anomalies or
guide future scientific endeavors to better understand them. The paper further discusses
theoretical developments over the past decade, as well as future research programs with the
ability to further elucidate this picture, with attention to synergy and complementarity of both
planned and proposed programs.
Sterile neutrino states, if they exist, would reveal a new, unexpected form of a fundamental
particle and possibly new types of interactions in nature. This possibility, or other BSM
physics that may be the source(s)of the current experimental neutrino anomalies, has and will
continue to compel particle physicists toward further experimentation in this area in the
foreseeable future. The Discovery of new physics associated with these signals would be
groundbreaking and would have profound implications not only for particle physics but also
for astrophysics and cosmology. Additionally, in several scenarios, new physics associated
with these anomalies can have a significant impact on measurements of three-neutrino
oscillation parameters planned with ongoing and future long-baseline experiments, as well as
on absolute measurements of neutrino mass, further necessitating their resolution. Similarly,
new physics associated with these anomalies could connect to searches for neutrinoless
double βdecay, and direct or indirect probes for dark matter or other dark sector particle
searches. Alternatively, a clear null result, or an SM explanation for the current experimental
anomalies, would bring a welcome resolution to a longstanding puzzle and greatly clarify the
current picture in neutrino physics.
2. Experimental anomalies
There are four long-standing anomalies in the neutrino sector that have served as primary
drivers in the development of a vibrant short-baseline neutrino program over the last decade.
Two come from the apparent oscillatory appearance of electron (anti)neutrinos in relatively
pure muon-(anti)neutrino beams originating from charged-pion decay-at-rest, section 2.1, and
charged-pion decay-in-flight, section 2.2. Two more anomalies are associated with an overall
normalization discrepancy of electron (anti)neutrinos expected both from conventional fission
reactors, section 2.3, and in the radioactive decay of Gallium-71, section 2.4. In these two
cases, no oscillatory signature is observed, but the overall normalization deficit can be
ascribed to rapid oscillations at a high Δm
2
that are averaged out and appear as an overall
deficit. This section will describe all four of these anomalies in detail, presenting both their
experimental arrangements as well as the experimental (anomalous)results.
Historically, the results have been discussed primarily in the context of a 3 +1 scenario,
with a single sterile neutrino. As such, the results in this section are presented in this manner;
however, we emphasize that the current theoretical landscape strives to explore a much
broader set of possible interpretations of the anomalies, as we describe in detail in section 3.
Those include more exotic flavor conversions, section 3.1, dark sector particles produced in
neutrino scattering or in the neutrino source/beam itself, section 3.2, as well as more con-
ventional explanations due to background mismodeling or underestimation, section 3.3.
2.1. Pion decay-at-rest accelerator experiments
Pion decay-at-rest accelerator experiments provide a well-understood muon antineutrino flux
of a mean energy of ∼30 MeV, and negligible electron antineutrino flux contamination. As
such, detectors placed at relatively short baselines (∼30 m)with positron identification
capability offer sensitivity to nn
meoscillations. Past pion decay-at-rest experiments include
the Los Alamos Neutrino Detector (LSND)[19]and the KArlsruhe Rutherford Medium
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
10
Energy Neutrino (KARMEN)[20]experiments. Among the two, LSND observed evidence
for nn
meoscillations that could be parametrized by two-neutrino oscillations with a Δm
2
of
∼1eV
2
and an oscillation amplitude
q
m
sin 2
e
2of less than 1%. Although less sensitive,
KARMEN observed no evidence of such oscillations and therefore has been historically
referred to as a ‘null’experiment in terms of this framework [1]. The LSND anomalous result,
which motivated a number of follow-up experimental searches for short-baseline neutrino
oscillations over the past nearly three decades, is described below.
The LSND detector [21]at Los Alamos National Lab consisted of a cylindrical tank, 8.3 m
long with a 5.7 m in diameter, located 29.8 m from the neutrino source. LSND was designed
to search for oscillations nn
me. Neutrinos were produced from the decay chains of charged
pions to muons decaying at rest, with the charged pions produced using 798 MeV protons on
a target at the Los Alamos Neutron Science Center (LANSCE). Muon antineutrinos were
produced by the sequence of π
+
→μ
+
+ν
μ
and
m
nn++
m
++
e
e
. The related decay of
π
−
that would produce
n
e
is highly suppressed through pion capture on heavy nuclei in the
vicinity of the beam target. As a result, the intrinsic
n
e
contamination was expected to be
7.8 ×10
−4
smaller than the
n
m
flux.
The signal selection proceeded via the identification of a positron from inverse beta decay
(IBD),
n+ +
+
pe n
e, followed by detection of a 2.2 MeV photon from subsequent
neutron capture that is correlated with the positron both in position and time. The interactions
of ν
e
inherent in the beam via ν
e
+C
12
→N
12
+e
−
were not a major contributing back-
ground, as there was no correlated neutron capture accompanying these events, except for
accidental coincidences. The target consisted of 167 metric tons of mineral oil, which was
lightly doped with scintillator allowing for both the detection of Cherenkov light and isotropic
scintillation light. This light was detected with 1220 8”photomultiplier tubes (PMTs)spaced
uniformly around the inner surface of the tank. As the Cherenkov ring could be detected, this
allowed for the determination of both energy and angle of the outgoing positron.
Cosmic rays, although abundant, were not a major source of backgrounds for LSND, being
removed by timing cuts and usage of an active and optically isolated veto shield surrounding
the detector. True correlated 2.2 MeV photons were separated from coincident photons from
radioactivity using a likelihood ratio R
γ
variable cut; this was defined to be the likelihood that
the photon was correlated divided by the likelihood that the photon was accidental.
A series of LSND measurements were published, all in support of an excess of events
observed over that expected from beam-off and beam-on neutrino background. The final
results published in 2001 [19]concluded that an excess of events was observed, consistent
with two-neutrino oscillations, corresponding to a background-subtracted excess of 87.9 ±
22.4 (stat)±6.0 (sys)events. Distributions of the observed excess are reproduced in figure 1
s a function of both the observed positron energy and the reconstructed L/E
ν
, for the subset of
total selected events with R
γ
>10 (described as a clean sample of oscillation candidate
events); this selection corresponds to an excess of 49.1 ±9.4 events.
The 3 +1 sterile neutrino fit, which tests an effective two-flavor ν
μ
→ν
e
appearance
probability hypothesis under the short-baseline (SBL)approximation
D
»D ºmm0
21
231
2
,
was not performed simply in reconstructed neutrino energy, but as a likelihood in four
dimensional E
e
(electron energy),R
γ
(coincidence variable),z(electron distance along tank
axis)and
q
cos
(electron angle w.r.t neutrino beam)space. The best-fit point was found to be
at an oscillation amplitude of q=
m
sin 2 0.00
3
e
2with a mass splitting of Δm
2
=1.2 eV
2
. The
resulting allowed regions are shown in figure 2alongside then-contemporary experiments that
did not see a positive signal.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
11
Figure 1. The LSND anomalous events as a function of both L/E
ν
(left)and observable
electron energy (right), for the subset of total selected events with R
γ
>10 and
20 <E
e
<60 MeV. Note the blue shaded region is for a best fit two-neutrino
oscillation fitof
q=sin 2 0.003
2
and Δm
2
=1.2 eV
2
. Reprinted (figure)with
permission from [19], Copyright (2001)by the American Physical Society.
Figure 2. The results of a two-neutrino oscillation fit performed by the LSND
collaboration for all data with reconstructed electron energy 20 <E
e
<200 MeV,
showing the resulting 90 and 99% confidence level allowed regions for qm
sin 2 e
2and
Δm
2
. Shown also are the 90% CL limits from other contemporary experiments.
Reprinted (figure)with permission from [19], Copyright (2001)by the American
Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
12
2.2. Piondecay-in-flight accelerator experiments
The LSND evidence for two-neutrino oscillation beginning in the late 1990s prompted the
need for an independent follow-up experiment to test the result. Such test needed to rely on
different systematics and methodology, while preserving sensitivity to the same Δm
2
and
q
m
sin 2
e
2.Aπ
+
decay-in-flight accelerator beam can produce a muon-neutrino-dominated flux
with higher mean energy, providing an opportunity for an independent test at a longer
baseline, and through different detection methods. This independent test was realized with the
Booster Neutrino Beamline (BNB)at the U.S. Fermi National Accelerator Laboratory
(FNAL, or Fermilab)[22], providing a ∼99.5%-pure muon neutrino beam with a mean
neutrino energy of ∼600 MeV, sampled by the MiniBooNE Cherenkov detector [23].
Both MiniBooNE and BNB at Fermilab were designed in such a manner so as to have
comparable L/Eto that of LSND (L/E≈0.4−1.0 m MeV
−1
)but a longer baseline (540 m
relative to LSND’s30m)and higher energy (peak energy ∼700 MeV relative to LSND’s
∼50 MeV). Although initially envisaged as being a two-detector experimental setup, with a
near detector at L≈0 m and a far detector at L/E≈0.4−1.0 m MeV
−1
, the final MiniBooNE
experiment consisted of a single detector, which was a spherical tank, 12.2 m in diameter,
filled with 818 tons of mineral oil. The interior surface of the tank, including an outer veto
spherical shell region, was lined with 1520 8”PMTs, including the recycled usage of all 1220
PMTs from the LSND experiment. Cherenkov and scintillation photons emitted by particles
produced in neutrino interactions were used to differentiate electrons versus muons produced
in ν
e
versus ν
μ
interactions, respectively.
The primary reconstruction method in MiniBooNE uses the Cherenkov rings detected on
the inside surface of the detector to differentiate between electrons, muons and charged pions,
and neutral pions. Protons that fall below the Cherenkov threshold in mineral oil, ∼350 MeV
kinetic energy, cannot be observed by their Cherenkov rings. Prompt scintillation light,
however, can be used to estimate the energy of particles below the threshold. One crucial
point to understand MiniBooNE’s backgrounds is the fact that a single lone photon (which
subsequently pair-produces a collimated e
+
e
−
pair)is indistinguishable from a single electron
in terms of their Cherenkov ring reconstruction. The separation of neutral-current (NC)π
0
→
γγ events thus relies entirely on reconstructing two separate Cherenkov rings. As such, the
main backgrounds to searching for ν
e
from ν
μ
→ν
e
oscillations at MiniBooNE were:
1. Intrinsic ν
e
in the BNB. Although an extremely pure ν
μ
beam, the
()
0.5%
ν
e
and
n
e
in
the beam provide an irreducible background. These are constrained by the high-statistics
ν
μ
sample due to their common origin in meson decay chains.
2. NC π
0
events. In the scenario where one of the daughter photons from a NC π
0
decay is
missed the event is indistinguishable from a single electron. This can occur due to
overlapping Cherenkov cones, one photon exiting the detector before pair converting, or
extremely low energy secondary photons. The NC π
0
ʼs were constrained by a high-
statistics in situ measurement.
3. NC Δ→Nγ. Radiative decay of the Δbaryon is a predicted SM process that produces a
single photon, mimicking single-electron production in MiniBooNE.
4. ‘Dirt’events. The so-called ‘Dirt’events correspond to neutrino-induced events in which
the scattering takes place in the material surrounding the detector, but some particles
scatter inside the detector and are reconstructed. The majority of these are photons
scattering in from π
0
decays.
Although the primary observable corresponds to the reconstructed outgoing electron itself,
the results are often presented and interpreted in terms of quasi-elastic reconstructed neutrino
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
13
energy, defined as
⎛
⎝
⎜⎞
⎠
⎟
()(() )
() q
=---+-
--+ -
n
E
MEMBMM
MEEM
1
2
2
cos
,
QE nen ep
ne
eee
222
22
where M
n
,M
p
and M
e
are the masses of neutron, proton and electron respectively, E
e
is the
reconstructed energy of the electron, qcos eis the angle the reconstructed electron makes
relative to the neutrino beam, and
is the binding energy of the target nucleus.
The first results from MiniBooNE, published in 2007, used approximately a third of the
total data set collected by MiniBooNE, corresponding to a BNB proton beam delivery of
5.58 ×10
20
protons-on-target (POT). The result reported no evidence for oscillations within a
two-neutrino ν
μ
→ν
e
appearance paradigm [24], thus placing a 90% CL limit covering the
majority of the allowed LSND (
q
m
sin 2
e
2,Δm
2
)parameter space. Crucially, this oscillation
result was performed only for the region of reconstructed neutrino energy of
>
n
475 Me
QE
(assuming quasi-elastic scattering)
122
. While this first result contained no
significant excess in the
>
n
475 Me
QE
region, below this energy, an excess of events was
observed. This excess, further examined by the MiniBooNE collaboration in a subsequent
analysis with higher statistics, is often referred to as the MiniBooNE ‘Low-Energy Excess’
(or LEE), and consisted of 128.8 ±20.4 ±38.3 excess events above predicted backgrounds,
corresponding to 3.0σ, as reported in [25].
Unlike LSND, MiniBooNE was designed with the ability to switch from a neutrino- to an
antineutrino-dominated beam, by switching the charged-pion focusing magnetic field polar-
ity, preferentially focusing π
−
mesons produced in proton-Be interactions toward the detector,
resulting in a
n
m
-dominated neutrino flux. Although the intrinsic ν
e
and
n
e
contamination
remains very small in antineutrino mode (0.6%), the wrong sign contamination is not neg-
ligible (with 83.73%
n
m
and 15.71% ν
μ
components). As such, MiniBooNE repeated its
search for two-neutrino oscillations in antineutrino running mode in 2010, using data
corresponding to 5.66 ×10
20
POT. The antineutrino search was motivated by findings
supporting large observable CP violation in short-baseline oscillations involving two addi-
tional, mostly sterile, neutrino mass states with masses of order ∼1eV[26], as well as CPT-
or Lorenz-violating models suggested as alternative interpretations of LSND at the time
[27–29]. Given that LSND’s result was obtained with antineutrinos, an independent anti-
neutrino search—albeit less sensitive due to reduced statistics expected from a factor-of-two
suppression in flux—was motivated by the need to provide an independent test of LSND
regardless of CP or other symmetry violation assumption, and as a further probe of the LEE
anomaly. The results from MiniBooNE’sfirst nn
mesearch [30]followed in 2010, and
showed an excess extending both at low energy and in the oscillation signal region of
<<
n
E
4
75 300 MeV
QE
. The results were found to be consistent with two-neutrino
n
n
me
oscillations with a χ
2
probability of 8.7% compared to 0.5% for background only [30], with a
best fitatΔm
2
=0.064 eV
2
and
q=sin 2 0.96
2. When the fit was expanded to the whole
energy range,
>
n
200 Me
QE
, the best fit was found to be at Δm
2
=4.42 eV
2
and
q=sin 2 0.0066
2, which although the best fit itself lies outside LSND’s 99% allowed
contour, there was still significant overlap in the low Δm
2
allowed regions at the 90% CL.
122
This restriction was decided upon as part of the data unblinding process followed by the MiniBooNE
collaboration, supported by the findings that spectral information in this background-dominated region did not
contribute significantly to two-neutrino oscillation sensitivity, and furthermore a data to Monte Carlo prediction
discrepancy was observed with both the best-fit two-neutrino oscillation hypothesis and the SM prediction.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
14
Since those first results, MiniBooNE ran for approximately ten more years, collecting
BNB data corresponding to a total of 18.75 ×10
20
POT in neutrino running mode, and
11.27 ×10
20
POT in antineutrino running mode. Major updates were published in 2013 [31],
2018 [32]and 2020 [33], and for the remainder of this summary, we will concentrate on the
final 2020 results, unless noted otherwise. MiniBooNE’sfinal results are reproduced in
figure 4, showing an excess of data over background prediction in both neutrino and anti-
neutrino data sets, as a function of the reconstructed electron candidate energy and recon-
structed electron angle with respect to the beam. The excess is predominately evident below
600 MeV and has an overall significance of 4.8σ(combining neutrino and antineutrino
running mode data sets). This significance is almost entirely systematics-limited in nature, and
corresponds to 560.6 ±119.6 and 77.4 ±28.5 excess events in neutrino and antineutrino
running modes, respectively. The final best-fit parameters for the full neutrino and anti-
neutrino data sets, for a fit over the entire energy range <<
n
E
2
00 3000 Me
V
QE were found
to be at
q
D
==m0.043 eV , and sin 2 0.807,
222
with the best-fitχ
2
/ndof for the energy range <<
n
E
2
00 1250 Me
V
QE being 21.7/15.5
(probability of 12.3%)compared to the background-only χ
2
/ndof of 50.7/17.3 (probability
of 0.01%). While this best fit is close to maximal mixing and is ruled out by a number of
experiments (e.g. OPERA [34]), the 1σallowed regions stretches to much smaller mixing
angles as can be seen in figure 3overlapping substantially with the allowed LSND regions.
None of the upper portion of LSND’s allowed regions, the island at higher Δm
2
>10 eV
2
,is
within the combined MiniBooNE 95% CL.
Figure 3. The final MiniBooNE allowed regions for the full fit of all neutrino and
antineutrino running mode data. Reproduced from [33].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
15
While the overall number of excess events is consistent with that expected from two-
neutrino oscillations driven by LSND’s best-fit parameters, a key feature of these results,
highlighted in figure 4, is that the predicted signal from ν
μ
→ν
e
oscillations corresponding to
MiniBooNE’s two-neutrino oscillation best-fit parameters cannot accommodate the shape of
the excess. This is particularly the case in neutrino mode, especially in the most forward
region of the outgoing electron
q
cos
distribution (with θrepresenting the angle of the electron
relative to the incoming neutrino beam direction). A similar feature exists as a function of the
reconstructed neutrino energy (n
E
QE)distribution in MiniBooNE. While historically the
MiniBooNE excess was presented almost exclusively in terms of the reconstructed neutrino
energy (n
E
QE), this was primarily due to the most common contemporary interpretation being
that of a 3 +1 oscillatory effect. It is worth noting that if the origin of the excess is not
oscillatory in nature then additional information can be gained by studying the excess as a
function of other reconstructed variables. Reconstructed visible shower energy and shower
angle as shown in figure 4are two such examples, as is the reconstructed radial position of the
event in the detector and its timing relative to the beam, shown for neutrino mode running in
figure 5.
These observations have helped motivate and understand ‘conventional’interpretations
involving energy misreconstruction due to mismodeled nuclear effects [35], mis-estimated
Figure 4. The final MiniBooNE results corresponding to 18.75 ×10
20
POT in neutrino
mode (top figures)and 11.27 ×10
20
POT in antineutrino mode (bottom figures)for
both the reconstructed visible energy (left)and the reconstructed angle that the
Cherenkov cone makes with respect to the neutrino beam (right). Note that as the top
two figures corresponding to neutrino mode are from [33], and the bottom two for
antineutrino running more are from [32], the best-fit line does not correspond to the
exact same point in sterile parameter space. Reproduced from [32,33].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
16
backgrounds [36], as well as other beyond-SM physics [28,29,37–40]as the source of the
MiniBooNE anomaly. Many of these interpretations are discussed in section 3. On the
experimental front, the MicroBooNE experiment was proposed in 2008 to provide a direct
test of the MiniBooNE anomaly; MicroBooNE recent results are discussed in section 4.3.
2.3. Reactor experiments
Even in the simplest light sterile neutrino oscillation framework (see section 3.1.1), where one
additional, mostly-sterile neutrino mass state is assumed, non-zero ν
μ
→ν
e
oscillations with
1%-level amplitudes imply that both ν
μ
and ν
e
disappearance must occur at short baselines,
and at a level that should be observable with current and upcoming reactor experiments,
atmospheric neutrino measurements, or measurements carried out with near-only or near+far
detectors of long-baseline facilities at accelerators. In apparent consonance with this inter-
pretation, measurements of
¯
n
e
fluxes performed at short (of order 10–100 m)reactor-detector
distances were indeed found to be anomalously low. This energy-integrated flux deficit,
observed over a broad range of short baselines, is referred to as the ‘reactor antineutrino
anomaly’(RAA).
Reactors have played an important role in neutrino physics since their discovery because
they are prodigious generators of electron-flavor antineutrinos (
¯
n
e
). Reactor
¯
n
e
are produced
from beta decays of neutron-rich fission fragments generated by the heavy fissionable iso-
topes
235
U,
238
U,
239
Pu, and
241
Pu. After their production in the reactor core, these MeV-scale
¯
n
e
are emitted isotropically. (For a broader introduction to this neutrino source, see the
excellent reviews provided in [41–43]).
A typical reactor
¯
n
e
spectrum is composed of
¯
n
e
produced by hundreds of fission isotopes
whose yields and beta decay pathways are sometimes poorly understood. Modeling of this
complex neutrino source is thus extremely challenging. For this reason, before discussing
anomalies at reactor neutrino experiments, we should briefly overview reactor antineutrino
flux modeling methods. Modeling of reactor
¯
n
e
spectrum uses two state-of-the-art approaches:
the summation or ab initio method, and the beta conversion method. Both methods build
¯
n
e
predictions for individual fissioning isotopes and aggregate them for a given reactor fuel
composition.
Figure 5. The final MiniBooNE results in neutrino mode in terms of both the timing of
the events relative to the beam (right)and the reconstructed radial position of the
spherical detector. By studying the excess in terms of additional distributions like these,
a better understanding of the excess as well as the backgrounds has begun to emerge. In
this example, both the beam timing and radial distributions heavily disfavor an
underestimation of the ‘Dirt’component normalization being the source of the excess.
Reproduced from [33].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
17
The summation method uses β-decay information from nuclear databases to first estimate
¯
n
e
contributions of individual β-decay branches [44,45]. Individual beta branch contributions
are then summed together, with weights based on fission yields and branching fractions, to
obtain a total flux and spectrum for each fissioning isotope. Since nuclear databases are
incomplete and sometimes inaccurate [46], the inferred reactor antineutrino spectra have
potentially large and ill-defined uncertainties. Nonetheless, significant work is being done in
improving the inputs to [47–53]and accuracy of [46]these databases.
The beta conversion method instead sums together beta particle contributions from virtual
decay branches that empirically add up to a measured aggregate beta spectrum for each
individual fissioning isotope. After defining each virtual branch’s contribution in this manner,
the individual beta spectrum from each branch can be converted to an
¯
n
e
spectrum and
summed to generate a model of the aggregate
¯
n
e
spectrum specific to the fissioning isotope.
The modern converted
¯
n
e
spectra by Mueller et al [54]and Huber [55](HM model)are based
on the β-decay measurements of the isotopes
235
U,
239
Pu,
241
Pu performed at the Institut
Laue-Langevin (ILL)in the early 1980s [56–58]. An aggregate fission beta spectrum mea-
surement of
238
U was not performed at ILL
123
, since fission of
238
U required neutrons with
energies higher than those available at the thermal ILL facility. Reference [43]article pro-
vides an in-depth survey of both these methods.
With modern reactor
¯
n
e
experiments performing flux and spectrum measurements with
percent-level precision, sources of
¯
n
e
not accounted for in these two models play are also
important to consider. The
¯
n
e
arising from non-equilibrium effects [54,60]of the beta-
decaying isotopes represent one such source that is not included in the conversion method
since the β-decay measurements are done on shorter timescales where the off-equilibrium
effects do not have enough time to manifest. Reactor and site-specific
¯
n
e
are additional such
sources that have to be included for each individual experiment separately. These may include
¯
n
e
originating from the neutrons interacting with non-fuel reactor elements [61]and spent
nuclear fuel [62,63]placed in close proximity to the detectors.
Reactor neutrino experiments have typically used IBD,
¯
n
e
+p→e
+
+n, as the detection
mechanism of choice due to its relatively high cross-section and the substantial background
rejection capability made possible by the time-coincident signature it produces–prompt
positron energy deposition followed by the delayed spatially-correlated capture of the ther-
malized neutron. Since neutrons are significantly heavier than e
+
, the positron energies
measured by IBD detectors are used as a high-fidelity measure of the interacting neutrino
energy. The
¯
n
e
spectrum as a function of energy
¯
n
E
e
measured by a detector using the IBD
mechanism is:
() () ()
¯
¯
¯
¯
¯
å
ps=
n
n
n
n
n
N
EELNSE
E
d
d
1
4
d
d,1
pE
i
i
2
e
ee
e
e
where Lis the mean detector baseline from the reactor, òis the (typically energy-dependent)
efficiency, N
p
is the number of target protons, ¯
s
n
Eeis the IBD cross-section, and
()
¯
n
SEd
i
e
is the
antineutrino flux from isotope i. Whereas (
)
¯
n
SEdedecreases with energy, IBD cross section
increases with energy. Equation (1)has to be modified if the detector samples neutrinos from
multiple reactors, the presence of non-fissioning sources of neutrinos [64], or in the presence
of neutrino oscillations [65]. The uncertainties on
()
¯
n
SEd
i
e
and N
p
are typically the dominating
source of reactor-specific and detector-specific uncertainties.
123
Even though a
238
Uβ-decay measurement was performed in 2013 [59], the presented
¯
n
e
energy had a lower limit
of 2.875 MeV, and consequently ab initio has been the model of choice for this isotope.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
18
The event rate measured in reactor antineutrino experiments can be expressed in a con-
venient way as a ‘cross section per fission’σ
f,a
, often called ‘IBD yield’:
()
å
ss=f,2
fa
i
i
ai,
where ais the experiment label, σ
i
is the IBD yield for the fissionable isotope i(with i=235,
238, 239, and 241 for
235
U,
238
U,
239
Pu, and
241
Pu, respectively), and f
i
a
is the effective fission
fraction of the isotope ifor the experiment a. For each fissionable isotope i, the individual
IBD yield is given by
() () ()
ò
ss=F
nn n
n
n
EE Ed, 3
iE
E
iIBD
thr
max
where E
ν
is the neutrino energy, Φ
i
(E
ν
)is the neutrino flux generated by the fissionable
isotope i, and σ
IBD
(E
ν
)is the detection cross-section. The neutrino energy is integrated from
the threshold energy =
n
E
1.806 Me
V
thr . The numerical values of the σ
i
ʼs predicted by a
theoretical model depend on the way in which the integral in equation (3)is performed, taking
into account that the neutrino fluxes are given in tabulated bins.
The IBD yields σ
f,a
have been measured in a broad array of reactor antineutrino experi-
ments spanning three continents and nearly four decades. A full list of experimental mea-
surements is provided in table 1. Some measurements were performed at compact, highly
235
U-enriched research reactors, while others were performed at high-powered low-enriched
commercial core reactors. Experimental reactor-detector baselines in these experiments ran-
ged from less than 10 m to more than 1 km. Implemented IBD interaction detection tech-
nologies also varied widely between experiments. In some, IBD neutron detection was
enabled using
3
He counters, while in others, metal-doped liquid scintillators (
6
Li or Gd)were
used. Some efforts used large-volume scintillator regions to detect the prompt IBD positron
signal, while others possessed no capability to detect this signal. Despite the broad range of
employed technologies, baselines, and reactor types, experiments from the 1980s to the late
2000s were generally deemed to be consistent with state-of-the-art conversion and summation
predictions available at that time.
In 2011, new antineutrino flux calculations by Mueller et al [54]and Huber [55]using the
conversion method for
235
U,
239
Pu, and
241
Pu and the summation method for
238
U predicted
detection rates substantially different than previous estimates. In conjunction with the
reduction in the measured neutron lifetime, as well as the inclusion of the off-equilibrium
corrections, predicted IBD yields increased, leading to a 5%–6% discrepancy between this
need prediction and the average of existing measurements [54]. This discrepancy has come to
be known as the ‘reactor antineutrino anomaly’(RAA)[1,66]. Subsequent flux measure-
ments performed using blind analyses in reactor-based θ
13
experiments following the
inception of the RAA observed a similar flux deficit [67–69]. This development reduced the
likelihood of the RAA arising from historical neutrino measurements being biased toward an
agreement with contemporaneous flux predictions.
Figure 6shows the ratio of the measured to the predicted IBD yields as a function of the
distance between the reactors and the detectors. A model involving sterile neutrinos that mix
with active neutrinos has been invoked as a potential source for the discrepancy. Under the
sterile neutrino hypothesis, a portion of the
¯
n
e
from the nuclear reactor oscillate at frequencies
of
D
mne
w
2∼1eV
2
—much higher than the active neutrino oscillation frequencies–into sterile
states that go undetected, leading to a deficit in the measurements. Since the oscillation length
of eV-scale-mediated oscillations is much shorter than the baselines of most of the mea-
surements in question, the RAA would almost entirely be reflected in a common fixed IBD
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
19
Table 1. List of the experiments which measured the absolute reactor antineutrino flux [257]. For each experiment numbered with the index a:f
a
235
,
f
a
238
,f
a
239
,andf
a
241
are the effective fission fractions of the four isotopes
235
U,
238
U,
239
Pu, and
241
Pu, respectively;
s
fa,
exp is the experimental IBD yield
in units of 10
−43
cm
2
/fission;
R
a,HM
exp ,
R
a,EF
exp ,
R
a,HKSS
exp ,and
R
a,KI
exp , are the ratios of measured and predicted rates for the IBD yields of the models in
table 6;
d
a
exp is the total relative experimental statistical plus systematic uncertainty,
d
a
cor is the part of the relative experimental systematic uncertainty
which is correlated in each group of experiments indicated by the braces; L
a
is the source-detector distance. Reproduced from [257].CC BY 4.0.
aExperiment f
a
235
f
a
238
f
a
239
f
a
241
s
fa,
exp
R
a,HM
exp
R
a,E
F
exp
R
a,HKSS
exp
R
a,KI
exp
d
a
exp [%]
d
a
cor [%]L
a
[m]
1 Bugey-4 0.538 0.078 0.328 0.056 5.75 0.927 0.962 0.916 0.962 1.4 1.4 15
2 Rovno91 0.614 0.074 0.274 0.038 5.85 0.924 0.965 0.914 0.962 2.8 18
3 Rovno88-1I 0.607 0.074 0.277 0.042 5.70 0.902 0.941 0.892 0.939 6.4 3.1 2.2 18
4 Rovno88-2I 0.603 0.076 0.276 0.045 5.89 0.931 0.971 0.920 0.969 6.4 17.96
5 Rovno88-1S 0.606 0.074 0.277 0.043 6.04 0.956 0.997 0.945 0.995 7.3 18.15
6 Rovno88-2S 0.557 0.076 0.313 0.054 5.96 0.956 0.994 0.945 0.993 7.3 3.1 25.17
7 Rovno88-3S 0.606 0.074 0.274 0.046 5.83 0.922 0.962 0.911 0.960 6.8 18.18
8 Bugey-3-15 0.538 0.078 0.328 0.056 5.77 0.930 0.966 0.920 0.966 4.2 15
9 Bugey-3-40 0.538 0.078 0.328 0.056 5.81 0.936 0.972 0.926 0.972 4.3 4.0 40
10 Bugey-3-95 0.538 0.078 0.328 0.056 5.35 0.861 0.895 0.852 0.894 15.2 95
11 Gosgen-38 0.619 0.067 0.272 0.042 5.99 0.949 0.992 0.939 0.988 5.4 37.9
12 Gosgen-46 0.584 0.068 0.298 0.050 6.09 0.975 1.016 0.964 1.014 5.4 2.0 3.8 45.9
13 Gosgen-65 0.543 0.070 0.329 0.058 5.62 0.909 0.945 0.899 0.944 6.7 64.7
14 ILL 1.000 0.000 0.000 0.000 5.30 0.787 0.843 0.777 0.827 9.1 8.76
15 Krasnoyarsk87-33 10006.20 0.920 0.986 0.909 0.967 5.2 4.1 32.8
16 Krasnoyarsk87-92 10006.30 0.935 1.002 0.924 0.983 20.5 92.3
17 Krasnoyarsk94-57 10006.26 0.929 0.995 0.918 0.977 4.2 0 57
18 Krasnoyarsk99-34 10006.39 0.948 1.016 0.937 0.997 3.0 0 34
19 SRP-18 10006.29 0.934 1.000 0.923 0.982 2.8 0 18.2
20 SRP-24 10006.73 0.998 1.070 0.987 1.050 2.9 0 23.8
21 Nucifer 0.926 0.008 0.061 0.005 6.67 1.007 1.074 0.995 1.056 10.8 0 7.2
22 Chooz 0.496 0.087 0.351 0.066 6.12 0.990 1.025 0.979 1.027 3.2 0 ≈1000
23 Palo Verde 0.600 0.070 0.270 0.060 6.25 0.991 1.033 0.980 1.031 5.4 0 ≈800
24 Daya Bay 0.564 0.076 0.304 0.056 5.94 0.950 0.988 0.939 0.987 1.5 0 ≈550
25 RENO 0.571 0.073 0.300 0.056 5.85 0.936 0.974 0.925 0.973 2.1 0 ≈411
26 Double Chooz 0.520 0.087 0.333 0.060 5.71 0.918 0.952 0.907 0.953 1.1 0 ≈415
27 STEREO 10006.34 0.941 1.008 0.930 0.989 2.5 0 9−11
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
20
yield deficit in all relevant experiments [66]. The lack of an L/Echaracter in this anomaly
lends credence to a variety of alternate theories for its existence aside from sterile neutrino
oscillations, including flux modeling inaccuracies; an in-depth discussion of possible flux
model issues and recent modeling improvements is given in section 3.3.2. The most
straightforward way to conclusively affirm a BSM origin for the RAA is to observe its L/E
dependence; section 4.1.3 describes recent experimental efforts that probe this behavior via
searches for baseline-dependent
¯
n
e
energy spectrum distortions.
2.4. Radioactive source experiments
A complementary probe of electron neutrino disappearance to that of reactors is provided by
intense radioactive sources producing copious amounts of ν
e
, such as those employed by past
radiochemical experiments.
Radiochemical experiments were originally designed to detect neutrinos coming from the
Sun, making use of a reaction where neutrinos weakly interact with the detector chemical,
converting the initial element into a radioactive isotope through the reaction
() () ()
n
+-+
-
NA Z e NA Z,1 ,, 4
e
where Zand Aare the atomic and mass numbers, respectively. This very same neutrino
detection method was implemented by Ray Davis in the Homestake Gold Mine (Lead, SD),
using
37
Cl [70], which allowed him and his collaborators to successfully detect the neutrinos
predicted by the Standard Solar Model (SSM), an observation which led him to win the Nobel
Prize in Physics in 2002.
Later on, two other solar neutrino experiments were constructed, GALLEX [71]and
SAGE [72], this time using
71
Ga as the detector medium, as suggested initially in [73]. In this
case, the interaction of electron neutrinos with the gallium atoms leads to the emission of
electrons and the creation of
71
Ge atoms, which are then extracted and counted by means of
chemical techniques, giving information about the neutrino flux.
Figure 6. Ratio (R
a,HM
)of the measured to the predicted IBD yields as a function of
baseline. HM model is used for the predicted IBD yields. Each data point corresponds
to an experiment with the error bar representing the experimental uncertainty. The
green line and band show the average of R
a,HM
and average uncertainty respectively.
Reproduced from [257].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
21
The relevance of the physics being scrutinized (the flux of neutrinos coming from the Sun
as a test of the SSM), made it necessary to ensure the detection technique was correctly
understood. To do so, the GALLEX and SAGE Collaborations performed experiments under
controlled conditions, exposing the detectors to specific neutrino calibration sources. These
set of experiments are the so-called ‘Gallium radioactive source experiments’, which used
artificial
51
Cr and
37
Ar sources located inside the detectors, as schematically shown in
figure 7.
In these experiments, electron neutrinos are emitted during the electron capture decay of
the radioactive isotopes in the sources:
()
n
n
++
++
-
-
e
e
Cr V ,
Ar Cl , 5
e
e
51 51
37 37
with neutrino energies and branching ratios as shown in table 2, and the decay nuclear levels
shown in figure 8.
The electron neutrinos interact with the main component of the detectors through the process
described by equation (4), which for GALLEX and SAGE becomes:
()
n
++
-
eGa Ge , 6
e71 71
with the cross sections for each emitted neutrino energy as given in table 2.
Figure 7. Generic scheme of the radioactive source experiments. The radioactive source
(
37
Ar or
51
Cr)is located inside the tank containing liquid gallium.
Table 2. Energies, branching ratios and cross sections for the reaction in equation (6),
for neutrinos produced by each radioactive source (
51
Cr,
37
Ar)decay. Info from [78]
and [261]. In particular, the cross section values are extracted by interpolating the
calculations of J N Bahcall in [76]. Reprinted (table)with permission from [78],
Copyright (2008)by the American Physical Society.
51
Cr
37
Ar
E
ν
(keV)747.3 752.1. 427.2 432.0 811 813
B.R. 0.8163 0.0849 0.0895 0.0093 0.902 0.098
σ(10
−46
cm
2
)60.8 61.5 26.7 27.1 70.1 70.3
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
22
The experimental setup for both GALLEX and SAGE radioactive source experiments were
very similar, mainly consisting of a cylindrical tank containing the chemical component
acting as the detector (
71
Ga), and the radioactive source located inside this tank, as sche-
matically depicted in figure 7.
In order to determine the number of neutrinos produced by the radioactive source and
interacting with the detector, the
71
Ge atoms produced by reaction equation (6)are extracted
from the gallium by chemical mechanisms and specific cuts are applied to select the events of
interest (details of these procedures can be found in [71,72,74,75]), including the relevant
information about the ν
e
–
71
Ga cross section. Uncertainties on this cross section may sig-
nificantly impact the final result and its interpretation in terms of neutrino oscillations, as
discussed in section 3.3.3.
After the counting procedure, the activity of the source is computed and compared to the
previously directly measured activity. The ratio between the two numbers is reported in
table 3for the four performed experiments. It is important to note that the cross sections for
reactions (equation (6)) used to compute these numbers were the ones calculated by Bahcall
in [76]and that, as pointed out in [77], the corresponding uncertainties were not considered.
Further investigation of cross-section calculations, and their prospects for providing a ‘con-
ventional’explanation for the Gallium Anomaly, is provided in section 4.
As the main purpose of these experiments was to prove the experimental techniques used
for the detection of solar neutrinos, the obtained results allowed the two collaborations to
conclude that their setup and procedures were well understood and that the solar neutrino
measurements—a very large observed deficit on the neutrino flux when compared against the
SSM—were not due to any experimental artifact and were highly reliable.
More recently, however, the difference between measured capture rates (table 3)and
theoretical calculations was re-examined, especially in light of other indications of anomalous
flavor transition from the LSND and MiniBooNE experiments in the 1990s and 2000s. The
differences observed during this reiteration established what is known as the Gallium
Anomaly. Figure 9shows the experimental results mentioned above, together with the global
average, R
avg
=0.86 ±0.05, which is ∼3σless than unity.
Figure 8. Nuclear levels for the
51
Cr and
37
Ar radioactive sources decay, according to
equation (5). Reprinted (figure)with permission from [72,75], Copyright (1999, 2006)
by the American Physical Society.
Table 3. Ratio of predicted and observed
71
Ge event rates as measured by GALLEX
(using
51
Cr twice)and SAGE (
51
Cr and
37
Ar).
GALLEX SAGE
0.953 ±0.11 0.95 ±0.12
-
+
0.812
0.11
0.10
-
+
0.791
0.078
0.084
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
23
This discrepancy is usually interpreted as an anomalous disappearance of electron neu-
trinos trough short-baseline oscillations to sterile neutrinos in a framework of 3 +1 mixing
neutrinos. In the scheme in which one sterile neutrino at the eV mass scale is added to the
standard three-neutrino framework, the survival probability of electron (anti)neutrinos is
⎜⎟
⎛
⎝⎞
⎠
() ∣∣(∣∣) ()nn
=- - D
PUU
mL
E
14 1 sin 4,7
ee e e42422 41
2
where Lis the distance from the source to the detector, Eis the neutrino energy, Uis the 4 ×4
PNMS mixing matrix, and
D
=-mmm
41
24
21
2, is the squared-mass difference between the
heavy (mostly sterile)neutrino ν
4
and the (standard)light neutrino ν
1
(considering
that
D
»D »Dmmm
41
242
243
2
).
This model is implemented, for instance, in [78], where studies of the GALLEX and
SAGE results (with the cross sections listed on table 2)revealed a possible indication of
electron neutrino disappearance due to neutrino oscillations with
D
m0.1
41
2eV
2
, as the
contour plots in figure 10 show.
The relevance of these results has led the neutrino community to search for alternative
explanations, such as possible effects arising from cross section uncertainties, not considered
in the analysis leading to the contours in figure 10 (described in section 3.3.3), and to perform
new experiments (e.g. BEST, described in section 4.1.5)to test the deficit of electron neu-
trinos observed by the gallium radioactive experiments as described here.
The following section provides details on a diverse range of viable interpretations for these
anomalies, from modifications of three-flavor neutrino mixing to potential couplings to
hidden sectors.
3. Interpretations of the anomalies
In this section, we discuss the theoretical interpretations of the experimental anomalies dis-
cussed above. While seemingly compatible when presented within the empirical picture of
two-neutrino oscillations, the underlying source of the anomalies may or may not be con-
nected. In what follows, we describe three different categories of resolutions put forth in the
literature, including those that can explain some—but not necessarily all—of the anomalies.
Figure 9. Ratio of the observed and the predicted event rates as measured by the
different radioactive source experiments GALLEX and SAGE. The shadowed area
corresponds to the 1σregion around the weighted average, R
avg
=0.86 ±0.05.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
24
3.1. Flavor conversion
In this subsection, we discuss flavor-conversion-based explanations to the short-baseline
anomalies discussed in section 2.
We begin by discussing perhaps the simplest model that leads to flavor change in short
baselines: an extension of the ESM by the inclusion of a new light sterile neutrino, referred to
as the well-studied 3 +1 sterile neutrino model. In the most simple realization of the 3 +1
model, the sterile neutrino has no gauge interactions. It should be noted that, historically,
experimental collaborations such as LSND and MiniBooNE have analyzed their data sets
primarily under a two-neutrino oscillation hypothesis most closely represented by the 3 +1
model. Additionally, in this model, provided that the two-neutrino oscillation approximation
is valid, no observable CP violation effects are expected. Therefore, light sterile neutrino and
antineutrino oscillation searches are effectively sensitive to the same oscillation parameters.
Finally, we prepare the reader in advance, in that, the 3 +1 model has been shown to provide
an insufficient description to the globally available experimental data that have sensitivity to
its observable effects. Nevertheless, it has and will likely continue to be instructively used
within the community as a simple ‘measure’for developing, optimizing, and comparing
sensitivities of various experimental searches and comparing compatibility of different
experimental results, albeit with several caveats.
After discussing this simple model in some detail, we then consider extensions and var-
iations to this model, all of which can lead to flavor transitions at short baselines. The most
straightforward extension beyond 3 +1 is represented by the 3+Nmodel, where N=2, 3, K
light sterile neutrinos are introduced and associated with similarly light neutrino mass states.
Figure 10. Allowed regions in the Δm
2
–
qsin 2
2
parameter space obtained from the
combination of the GALLEX and SAGE radioactive source experiments. Reprinted
(figure)with permission from [78], Copyright (2008)by the American Physical
Society. Notice that
∣∣( ∣∣
)
q=-UUsin 2 4 1
ee
24242
.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
25
Other extensions often introduce non-standard interactions (NSIs)and neutrino propagation
effects.
3.1.1. 3 +1 light sterile neutrino oscillations
3.1.1.1. Sterile neutrinos. Sterile neutrinos provide one of the simplest extensions of the SM
that explain the non-zero mass of neutrinos. The right-handed, gauge-singlet fields (N)
R
,
sometimes denoted as
(
)nsR
, provide the missing chiral partners for the left-handed, interacting
SM neutrino fields
(
)n
aL
. Neutrinos would then acquire a mass just like any other SM fermion
via the Higgs mechanism,
na
mN
D
, with
=myv2
Dand vthe Higgs vaccum expectation
value. While this observation is sufficient to resolve the puzzle of neutrino masses, it raises
new questions. In particular, since N
R
would carry no charges under any SM gauge
symmetries, it could also have a Majorana mass, MN N
R
cR. In that case, the physical spectrum
could contain the light, mostly-active neutrinos, as well as potentially heavier, mostly-sterile
neutrinos that interact very weakly through mixing. Note that since Majorana masses violate
any one of the quantum numbers associated with N
R
, it would also indicate that lepton
number is violated by two units. Conversely, if lepton number is conserved, then Majorana
masses are not allowed, and neutrinos are purely Dirac particles, like any other SM fermion.
Most importantly, Majorana masses need not be related to the electroweak scale. In
principle, can take any value up to the Planck scale or the scale of gauge unification. If it takes
values larger than the electroweak scale or, more precisely, the scale of Dirac neutrino
masses, it would trigger the canonical Type-I seesaw mechanism [6,8–10,12,13,15,79,80].
The seesaw Lagrangian reads,
()É- - +
~
naa-
YLHN MNN
2h.c., 8
ij
ij
i
cjmass
where *
s=
~
H
iH
2is the conjugate of the Higgs doublet and Lis the lepton doublet. After
electroweak symmetry breaking,
()-
n-
MvYM Y
2,9
T
21
where M
ν
is the mass matrix for the light, mostly-active neutrinos. In its simplest realization,
the seesaw mechanism explains the smallness of the neutrino masses using a hierarchy of
scales between Dirac and Majorana masses. Mixing between the heavy neutrinos and the
active SM neutrinos, |U
αi
|, is typically of order ()
MM
D.
Other variations of the Type-I seesaw mechanism exist, including low-scale models
where the lightness of neutrino masses is explained instead by the approximate conservation
of lepton number. Seesaw models with pairs of heavy neutral leptons, Nand S, with opposite
lepton number, are often called extended seesaws. One of which, the inverse seesaw, has
these particles form pseudo-Dirac pairs with a small mass splitting given by μ, a lepton-
number-violating parameter. Light neutrino masses, in this case, are proportional to μ, which
in the limit μ→0, parametrically recovers lepton number conservation and massless
neutrinos.
In extended seesaws, it is also possible that some number of the sterile neutrinos remain
relatively light [81]. This may be due to cancellations, new symmetries, or because the
number of fields exceeds the number of large scales in the theory. In such cases, heavy
neutrinos can ‘seesaw’not only the light, mostly-active neutrinos but also some of the sterile
neutrinos, rendering them light as well. These models predict the existence of light sterile
neutrinos that mix with active neutrinos with large mixing angles. Finally, we note that while
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
26
the seesaw mechanism provides an elegant solution to the smallness of neutrino masses, we
cannot rule out the possibility that lepton number is indeed conserved and that neutrinos are
Dirac A fourth neutrino, in this case, would not necessarily be related to the origin of neutrino
masses but could exist based on a new pair of left and right-handed singlet fermions.
Sterile neutrinos can also solve other open problems in the SM. Heavy neutrinos above
the electroweak scale can generate the observed baryon asymmetry of the Universe via their
decays or oscillations. In this scenario, the lepton asymmetry generated by CP violation and
out-of-equilibrium processes involving heavy neutrinos is converted into a baryon asymmetry
via Sphalerons, non-perturbative SM processes. This scenario is referred to as Leptogenesis
[82]. In addition, light sterile neutrinos with masses of
(– )
1 100
keV can provide a warm
dark matter candidate [83–87], produced out-of-equilibrium by oscillations in the early
Universe. It is also possible that both of these issues are addressed by a whole new sector of
sterile neutrinos, such as in the proposed ν-minimal SM [88,89]
In this section, we discuss short-baseline oscillations generated by sterile neutrinos with
masses of order (– )
110 eV. These sterile neutrinos could very well play the role of the
seesaw partners, albeit triggering the mechanism at a relatively low scale [90,91].
Unfortunately, they would not provide direct evidence for Leptogenesis or sterile-neutrino
dark matter. Still, their discovery would be the first laboratory observation of a particle
beyond the SM and strongly motivate sterile-neutrino solutions to all open problems in
particle physics. Studying their properties and looking for potential lower and higher-scale
partners would be of great importance in this case.
3.1.1.2. 3 +1 oscillation probabilities. In the simplest 3 +1 model, the standard neutrino
sector is extended by an extra neutrino flavor ν
s
which is a gauge singlet and does not
experience weak interactions. The three neutrino flavors and the sterile neutrino are
admixtures of four neutrino mass eigenstates, where m
4
is assumed to be of order ∼1 eV,
motivated by the LSND observation. Parametrically, one can extend the 3 ×3 leptonic
mixing matrix to a 4 ×4 matrix U
αi
, with α=e,μ,τ,sand i=1, K, 4. Notice, however,
that the last row of this extended matrix is not related to experimental observables as it
pertains to the amount of sterile neutrino flavor in different beams. This matrix can be
parametrized by the usual three mixing angles and CP violation phase, plus three extra mixing
angles and two extra CP phases.
To avoid parametrization dependence, it is often helpful to work with the mixing matrix
elements U
e4
,U
μ4
, and U
τ4
directly. We assume that the fourth mass eigenstate is mostly
sterile and much heavier than the other ones, so that ∣∣
D
DDmmm,
41
231
221
2, allowing for the
approximation that
D
m31
2and
D
m21
2are degenerate and at zero. Furthermore, this new, large
mass splitting allows for short-baseline neutrino oscillations. In the limit where oscillations
due to
D
m31
2and
D
m21
2—the atmospheric and solar mass-squared splittings, respectively—
are negligible, short-baseline oscillations can be approximated by
⎜⎟ ⎜⎟
⎛
⎝⎞
⎠⎛
⎝⎞
⎠
() ∣∣(∣∣) ()
()
nn q- - Dº- D
nn
PUU
mL
E
mL
E
14 1 sin 41 sin 2 sin 4,
10
ee e e ee42422 41
2
22
41
2
⎜⎟ ⎜⎟
⎛
⎝⎞
⎠⎛
⎝⎞
⎠
() ∣∣(∣∣) ()
()
nn q- - Dº- D
mm m m
n
mm
n
PUU
mL
E
mL
E
14 1 sin 41 sin 2 sin 4,
11
42422 41
2
22
41
2
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
27
⎜⎟ ⎜⎟
⎛
⎝⎞
⎠⎛
⎝⎞
⎠
()∣∣∣∣ () ()nn qDºD
mm
n
m
n
PUU
mL
E
mL
E
4sin
4sin 2 sin 4.12
ee e42422 41
2
22
41
2
Note that the above makes no explicit assumption about U
τ4
(or, consequently, U
s4
);
however, by unitarity considerations, |U
e4
|
2
+|U
μ4
|
2
+|U
τ4
|
2
+|U
s4
|
2
=1. Note also that in
the above, we have focused explicitly on electron- and muon-neutrino flavors, given that
these are the transition channels that have been studied most extensively and where the short-
baseline anomalies occur.
The above three oscillation probabilities further define the effective mixing angles
()q
ab
sin 2
2
often used in the literature: ∣∣( ∣∣) q-=UU
4
1sin2
ee ee42422
,
∣∣( ∣∣) q-=
mm mm
UU
4
1sin2
42422
, and
∣∣∣∣ q=
mm
UU
4
sin 2
ee42422
. The two new CP violating
phases from the extended 4 ×4 mixing matrix do not lead to observable effects unless effects
from both
D
m41
2and either
D
m21
2or
D
m31
2are simultaneously relevant. In scenarios with more
than one light sterile neutrino (see section 3.1.3), CP-violating phases associated with the (3
+N)×(3+N)mixing matrix may be accessible. Returning to the 3 +1 scenario,
oscillations are relevant for L/E
ν
≈m/MeV or km/GeV if
D
»m1eV
41
22. Most notably, the
relationships among equations (10–12)imply that, if both |U
e4
|
2
and |U
μ4
|
2
are nonzero, then
electron-neutrino disappearance, muon-neutrino disappearance, and muon-to-electron-neu-
trino appearance must all occur at the same L/E
ν
. More explicitly, the oscillation amplitudes
for appearance and disappearance are related by
qqq
mmm
sin 2 1 4 sin 2 sin 2
eee
222
. This
relation allows for combinations of experiments to over-constrain the 3 +1 model, a feature
that global fits take advantage of when performing combined analyses to experimental data
sets on neutrino appearance and disappearance.
Finally, when an explicit parametrization of the 4 ×4 unitary mixing matrix Uis needed
for oscillations, six rotation angles and three CP phases are required. In addition to the three-
neutrino mixing parameters, three new angles, θ
14
,θ
24
, and θ
34
, and two new phases, δ
24
and
δ
14
, are defined, in accordance with [92]. The full mixing matrix is then given by
()
=
´
URSSRSR,13
4 4 34 24 14 23 13 12
where R
ij
is a real matrix of rotation by an angle θ
ij
, and S
ij
is a complex matrix of rotation by
θ
ij
with a CP phase of δ
ij
. The relationship between this parametrization to the effective
mixing angles as well as to the full matrix elements is shown in table 4.
3.1.1.3. Global analysis of 3 +1 oscillations. The present status of the 3 +1 model is best
examined through the lens of a global analysis. This allows each of the myriad of short-
baseline experiments to contribute to a single statistical model according to the strength of
their results. Global fits have been performed independently by several groups (see, e.g.
[93–106]). While all groups find a strong preference for a 3 +1 model compared to the SM,
driven mainly by LSND and MiniBooNE, a significant tension among data sets is also
consistently found. The tension lies in a simple fact: large enough mixings required to explain
the LSND and MiniBooNE anomalies simultaneously lead to a large disappearance
amplitude, particularly of muon neutrinos, and this is in tension with ν
μ
→ν
μ
data, which
provide strong limits on the value of qmm
sin 2
2.
Figure 11 shows the preferred region in the 3 +1 model parameter space of several
short-baseline appearance experiments, including the combination of all of them, at 99% CL
for two degrees of freedom (left panel), as well as, the regions preferred by all short-baseline
appearance experiments (right panel, red region)compared to the excluded region by all
disappearance experiments (blue line)at 99.73% CL for two degrees of freedom [102]. Note
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
28
Table 4. Relation between the different parametrizations of neutrino mixing parameters in a 3 +1 model. Modified from [103].
Effective angle Full 3 +1 model rotation angles Mixing elements
qsin 2
ee
2
q=sin 2
214
=4(1−|U
e4
|
2
)|U
e4
|
2
q
mm
sin 2
2
()qq qq=-4cos sin 1 cos sin
214 224 214 224
=4(1−|U
μ4
|
2
)|U
μ4
|
2
q
tt
sin 2
2
()qqq qqq=-4 cos cos sin 1 cos cos sin
214 224 234 214 224 234 =4(1−|U
τ4
|
2
)|U
τ4
|
2
q
m
sin 2
e
2
qq=sin 2 sin
214 224
=4|U
μ4
|
2
|U
e4
|
2
q
t
sin 2
e
2
qqq=sin 2 cos sin
214 224 234 =4|U
e4
|
2
|U
τ4
|
2
q
mt
sin 2
2
qqq=sin 2 cos sin
224 414 234
=4|U
μ4
|
2
|U
τ4
|
2
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
29
that the region to the right of the blue line is excluded, and that encompasses the entirety of
the appearance allowed region. While the left panel clearly indicates a strong preference for
the 3 +1 model over the usual three neutrino framework, the right panel clearly shows the
tension between appearance and disappearance data: the appearance and the disappearance
99.73% CL preferred regions are disjoint.
One can be more precise and quantify the amount of tension using the parameter
goodness-of-fit(PG)test [107], which compares the minimum chi-square values of the full
data set to the sum of minimum values of the individual data sets, that is
()cc ccº--.14
PG
2
global
2
app
2
dis
2
In [102], for example, this tension is found to yield a p-value of 3.7 ×10
−7
when assuming
that the cPG
2follows a chi-square distribution. Moreover, removing any individual null
experiment from the fit does not lead to significant improvements in the p-value, evidencing
that the tension is robust. Similar conclusions have been drawn by other global fits [103–106].
While this demonstrates the shortcomings of the 3 +1 scenario as an explanation of the
short-baseline anomalies, there are important caveats that should be highlighted. First, all
global fits to date have been performed assuming the validity of Wilks’theorem [108]. While
in many cases, Wilks’theorem is valid and, therefore, the test statistic follows a chi-square
distribution, this is not obvious in neutrino oscillation experiments. Reference [109]has
shown that these considerations are relevant for the interpretation of short-baseline reactor
experiments in terms of sterile neutrinos, and the assumption of Wilks’theorem can have a
significant quantitative impact on the statistical interpretation of the anomaly. Not only would
this change the CL of the allowed regions, but it would also affect the outcome of the
parameter goodness-of-fit test, and thus the ‘amount of tension’between appearance and
disappearance data. Therefore, the p-values quoted above should be taken with a grain of salt.
One example of the importance of the statistical treatment is shown in the left panel of
figure 12 in which a Bayesian analysis is compared to the outcome of a frequentist one [103].
For the Bayesian analysis, the translucent black, red and blue regions represent the 68%, 90%,
and 99% highest posterior density credible regions, respectively, while the brighter colors
Figure 11. Left: preferred regions by several ν
μ
→ν
e
appearance experiments in the 3
+1 scenario at 99% CL for 2 degrees of freedom. Right: preferred region of short-
baseline appearance experiments (red region), compared to the region excluded by
disappearance experiments (blue line)at 99.73% CL for 2 degrees of freedom.
Reproduced from [102].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
30
refer to the frequentist analysis. The allowed regions are quite different, which shows how the
statistical treatment can affect the identification of promising parameter space and the
statement of the tension between data sets. Another example can be found in the right panel of
figure 12, where the allowed regions for the appearance (below the red line)and
disappearance (above the red line)are shown [103].Ifa
D
>m1
41
2eV
2
cut is applied to
the appearance parameter space, the 99% confidence region moves to the hatched purple
region. The points within this region are still preferred with respect to the null hypothesis at
the 99% level and, additionally, overlap with the disappearance regions, despite being
disfavored when compared to the best-fit point in the 3 +1 scenario.
Besides all that, since reactor experiments drive the preference for nonzero U
e4
mixing,
there is an important caveat with respect to the reactor anomaly that should be discussed. The
reactor anomaly has originated in a discrepancy between data and theoretical expectations
based on the calculations of reactor antineutrino fluxes. Nevertheless, a large, unexpected
feature in the flux around 5 MeV has been identified, the so-called 5 MeV bump. This
outstanding feature lies outside the proposed theoretical uncertainties and puts in question the
anomaly itself. Flux ratios can be used to mitigate the impact of the 5 MeV bump [110]but at
the price of reducing the statistical power of the analysis. Therefore, more precise calculations
of the reactor antineutrino fluxes would help to further understand the reactor anomaly. A
detailed discussion of this issue can be found in 4.3.2.
3.1.2. 3 +1 light sterile neutrino oscillations and decoherence. When considering the 3 +1
model discussed above, one has assumed that neutrinos are always coherent. However, as
pointed out in [111], due to the lack of detailed calculations of the neutrino production and
detection mechanism, or from additional BSM effects, this is not guaranteed. In this section,
we follow the discussion given in [111]and point out that when interpreting experimental
data in the context of 3 +1 this possibility has been overlooked. This fact could partially or
completely resolve the existing tension between appearance and disappearance data sets.
Currently, when deriving constraints or preferred regions on the 3 +1 model, the
experiments assume that the neutrino state is a plane wave. It is well-known that the plane-
Figure 12. Left: 3 +1 global confidence regions (solid)are compared to Bayesian
highest posterior density credible regions (68%, 90% and 99% credible regions in
black, red and blue). Right: appearance-only (below red line)confidence regions
compared to disappearance-only (above red line), with D>m
1
41
2eV
2
appearance-only
regions shown in hatched purple. All confidence regions are shown in red, green, and
blue for 90%, 95%, and 99%. Reprinted from [103], Copyright (2020), with permission
from Elsevier.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
31
wave (PW)theory of neutrino oscillations [112–114]is a simplified framework that, upon
careful inspection, contains apparent paradoxes [115–117]. These can be resolved by
introducing the wave packet (WP)formalism [118–123]. The applicability of the PW
approximation has been studied in detail for the standard mass-squared differences [117,121,
124–126]and has been shown to be a good approximation for current and future neutrino
experiments. However, this has not been shown to be the case for mass-squared differences
relevant to the LSND observation.
In the WP formalism, the oscillation probability is given by
⎜⎟
⎜⎟
⎧
⎨
⎩⎛
⎝⎞
⎠⎛
⎝⎞
⎠⎫
⎬
⎭()
∣∣∣∣ **
åå
pp
s
=+ ---
ab a b a ab
b
=> 15
P U U UUUU iL
LL
L
L
2Re exp 2 2 ,
i
n
ii
ji
iji
jij
x
ij ij
1
22
osc
2
osc
2
coh
2
where U
αi
are the neutrino mixing matrix elements and Lthe experiment baseline. Here the
damping of the oscillations is parametrized by a length scale σ
x
that can be referred to as the
wave packet size [118,123–127]and depends on the neutrino production and detection
mechanisms. These lengths are defined as
()
ps
=D=D
LE
mLE
m
4and 42 ,16
ij
ji
ij x
ji
osc 2coh
2
2
the oscillation and coherence lengths, respectively. Here, Eis the energy of the neutrino and
D
mji
2the mass-squared difference between the ν
j
,ν
i
mass eigenstates. The two last terms in
the exponential of equation (15)smear the oscillation.
Most experiments fulfill
s
L
xij
osc and thus the first dampening term can be neglected.
This is not the case for the second one, which describes the decoherence arising from the
Figure 13. Overview of the solar potential, neutrino experiments, and relevant scales.
L
osc
(dotted gray and dashed pink)and L
coh
(dashed blue)are computed from
equation (16)using D=m1eV
41
2
2
and σ
x
=2.1 ×10
−4
nm for
L
ste
coh,nuc
[129], and
σ
x
=10
−11
m for p
L
ste
coh, flight [643]. Decoherence effects are expected at LL
coh
.
Reproduced from [111].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
32
separation of the mass eigenstates during their propagation at different velocities. Notice that
under a stationary situation, all the relevant information should be in the energy spectrum.
Therefore, this effect can be equivalently understood as an additional quantum uncertainty in
the measurement of the true neutrino energy by the experiment [128].
Figure 13 shows several oscillation experiments compared to the sterile oscillation scale
(
L
ste
osc)and the decoherence scale (
L
ste
coh
). For experiments with baselines smaller than
L
ste
coh
,
decoherence can be neglected, while experiments with larger baselines will experience
complete decoherence. Take into account that the effect of not resolving fast oscillations
experimentally is from an observational point of view identical to a decoherence effect.
Consequently, an experiment far above the
L
ste
osc line would also be effectively decoherent,
and no effect due to
L
ste
coh
would be manifest. This narrows the region of interest for the
decoherence of light sterile neutrinos to the low-energy region and in particular to the reactor
and radioactive sources experiments.
To show the impact of the wave packet separation [111]chooses the smallest value
allowed by oscillation experiments for the wave packet size, σ
x
=2.1 ×10
−4
nm [129,130],
and performs analyses searching for sterile neutrinos with and without the PW approximation.
Notice that this value is far from some first-order estimations of the wave packet in various
contexts [118,120,122,123]; however, [111]decided to be agnostic and use an experimental
result that should be robust even in more exotic scenarios. The global analysis performed in
[111]considers the null results from Daya Bay [131,132], NEOS [133], and PROSPECT
[134,135]and the anomalous results observed from radioactive sources by BEST [136].
The main result of [111]is presented in figure 14, which shows the two-sigma exclusion
contours for these experiments and the positive hint regions at two sigma by BEST, in both
Figure 14. Impact of the smearing. On the left, the y-axis represents the ratio between
the 3 +1 and the 3 expected events in the NEOS experiment, for the reactor
antineutrino anomaly (RAA)best-fit parameters [133]:D=m2.32 eV
41
2
2
and
q=sin 2 0.14
214 . On the right, the solid pink and solid blue contours bound the
exclusion region from Daya Bay, NEOS and PROSPECT; at two sigma for the PW
approximation and WP formalism, respectively. The preferred region at two sigma for
the BEST experiment is shaded for the PW approximation (pink)and the WP
formalism (blue). Both figures are obtained for σ
x
=2.1 ×10
−4
nm. Reproduced from
[111].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
33
formalisms. The WP results become compatible not only at large values of
D
m41
2but also at
the region around
D
=m2eV
41
22.
Reference [111]finds that the damping of the oscillations due to the wave packet size
may have important consequences for low-energy light sterile neutrino searches,
accommodating apparently contradictory results. The result strongly motivates further
studies to improve our understanding of the physics involved in the production and detection
of the nuclear reactor and radioactive source neutrino experiments.
3.1.3. 3+N light sterile neutrinos. The generic model with three active and Nsterile neutrino
states can be considered a viable explanation of the anomaly seen experimentally. But it also
provides a sterile-sector model-independent framework for non-unitarity [137,138]tests.
We define the unitary mixing matrix Uin the whole (3+N)×(3+N)space, and denote
its 3 ×3 active space sub-matrix as N. Then, the probability of active neutrino oscillation
P(ν
β
→ν
α
)in matter can be written in the simple form as [138]
( ) [( )( )( ) ( )]
() [( )( )( ) ( )] ( )
()
***
**
åå
å
nn= + -
´---
baab a
baba b
aba b
=¹
¹
P NN NXNXNX NX
hhx NX NX NX NX h h x
2Re
sin 2Im sin ,
17
j
jj
jk
jjkk
kj
jk
jjkkkj
1
32
2
where α,β=e,μ,τdenote the active neutrino flavor indices, i,j,k=1, 2, 3 are the indices
for the light mass eigenstates, and all oscillations involving heavier mass eigenstates with
m0.1 eV
J
22, which are dominantly sterile, are averaged out.
In equation (17),P(ν
β
→ν
α
)is the leading term in a expansion by the active-sterile
transition sub-matrix Win U[138]. The zeroth order Hamiltonian contains the 3 ×3 active
space sub-matrix with the kinetic term plus matter potential given by diag(a−b,−b,−b),
where a(b)denotes the Wolfenstein matter potential due to CC (NC)interactions, with a
decoupled N×Nsterile block. Here, h
i
(i=1, 2, 3)denote the energy eigenvalues of zeroth-
order active states and Xis the unitary matrix which diagonalizes the zeroth-order active part
Hamiltonian. ab
in equation (17)is a probability leaking term which takes the same form in
vacuum and in matter [137,138]as
∣∣∣∣ ()
å
º
ab a b
=
+
WW.18
J
N
JJ
4
3
22
The probability leaking and W
2
correction terms—in contrast to high-scale unitarity
violation, observation of ab
in equation (18)would testify for low-scale unitarity violation.
Unfortunately, a detailed study of the sensitivity to high-scale unitarity, namely the
constraints on ab
, has only been performed for JUNO [137]; see figure 15.
Another unique prediction of the 3+Nmodel with low-mass sterile neutrinos is the
presence of higher-order W
2
corrections. These can be in principle measured and provide a
way to differentiate this scenario from high-scale unitarity violation, where the mostly-sterile
mass states are assumed to be kinematically forbidden and do not participate in neutrino
oscillations. The term is explicitly evaluated and plotted in figure 16 [138]. Notice the
peculiar energy- and zenith-angle dependence of the term shown in figure 16. The relevant
energy region of ρE=50–1000 (gcm
−3
)GeV may be explored by beam or atmospheric
neutrino experiments; for example, Super-K, Hyper-K/HKK, DUNE, IceCube, or KM3NeT-
ORCA, can probe this parameter space using low- to high-energy observables.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
34
Finally, another marked difference between low- and high-scale unitarity violation is that
there is no deviation in the production and detection cross sections of neutrino. This is
because in the low-scale scenario both CC and NC vertices are not modified since all mass
eigenstates, including the mostly-sterile states, are kinematically allowed in the processes.
3.1.4. Light sterile neutrino oscillations and NSIs. While many attempted solutions to the
hints of anomalous ν
μ
→ν
e
appearance at LSND and MiniBooNE have focused on those
experiments, it is also conceivable to see if the strong constraints from MINOS/MINOS+
[139]and IceCube [140]could be alleviated. As these constraints are at larger energies and
over longer baselines, they would be subject to modification by non-standard neutrino
interactions [141]in either the active or sterile sector. Thus a scenario with the usual sterile
neutrinos explaining the short-baseline accelerator hints along with a new matter effect to
modify the imprint of that sterile neutrino in the long-baseline accelerator and atmospheric
constraints could be consistent with all the data. This was investigated in [142–145], which
found that, while it could be possible to simultaneously explain some of the data sets in this
fashion, explaining all seems to be impossible, even with both a sterile neutrino and a new
interaction. In particular, [145]found that a model with a new interaction between sterile
neutrinos and baryons provides an excellent fit to LSND, MiniBooNE, and IceCube data; but
cannot simultaneously fit MINOS+data due to a disagreement in the preferred values of θ
34
.
Other approaches, such as [146], used beam neutrinos forward scattering off of a locally
overdense relic neutrino background to give rise to a matter effect with an energy-specific
resonance that can reproduce the MiniBooNE observed excess.
More recently, [147]reiterated that these tensions with long-baseline experiments occur
because new matter effects generically distort the active (anti-)neutrino mixing and mass
spectrum. A dark sector model with both neutrino and vector portals was then proposed in
[147]that avoids these large active spectrum distortions and is fully compatible with long-
baseline experiments, including T2K, NOvA, MINOS/MINOS+, IceCube/DeepCore, and
KamLAND. In this model, quasi-sterile neutrinos from a dark sector are charged under a light
vector mediator with feeble couplings to SM fermions. This leads to new matter effects that
generate resonant active-to-quasi-sterile neutrino oscillations within a narrow window of
energy, ∼250–350 MeV, to explain the MiniBooNE low energy excess. The MiniBooNE
excess at mid-to-high energies, E
ν
400 MeV, as well as the LSND and Gallium anomalies,
Figure 15. Constraint in
∣∣
å-
=
U
iei ee
1
32
space at 1σ,2σand 3σCL expected to be
obtained by JUNO like setting assuming the flux uncertainty of 3% (left panel)and 6%
(right panel). Reproduced from [137].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
35
are explained by an additional ‘vanilla’sterile neutrino which does not participate in the
resonant oscillations. Besides being fully testable by the SBN program, the new matter effects
in this model have interesting implications for solar neutrinos.
3.1.5. Decaying light sterile neutrinos. As discussed above, global fits to the neutrino data
show that the 3 +1 sterile neutrino model suffers from internal inconsistency amongst the
datasets [103,107]. This ‘tension’in the global fits motivates considering more complicated
physics scenarios. More complicated physics scenarios could involve neutrino decay.
Neutrinos are not protected from decay in the SM, i.e. radiative neutrino decay of the two
Figure 16. The order W
2
correction terms, () ()
()
d
nn nnº+
ma ma ma
PP
2, are
shown as a function of the distance traveled by neutrinos in the Earth assuming a
common
=m0.1 eV
J
22
. The top, middle and bottom panels are for α=e,τ, and μ,
respectively. In each panel the three cases are shown: N=1 with maximal ma
(solid
line), the universal scaling model with N=3(see [138], dotted line), and the order W
2
correction terms only (dashed line). The blue (red)lines are for E=10 (100)GeV, and
the leaking term is taken as ()()=´
mtmmm -
, , 20, 95, 9.6 10
e
5
for N=1.
Reproduced from [138].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
36
heavier of the three known neutrino mass states (ν
1
,ν
2
, and ν
3
)can occur, albeit, extremely
slowly [148,149]. Scenarios that include decay of the eV-scale neutrino mass state, ν
4
, are
referred to as “3+1+decay.”
The class of 3 +1+decay models can be divided into two scenarios: visible decay and
invisible decay. In the visible decay scenario, one of the decay daughters is an active neutrino,
which could be detected, while the other is undetectable, Beyond the Standard Model (BSM).
In the invisible decay scenarios, all decay daughters are BSM and invisible, i.e. undetectable.
In either scenario, an additional degree of freedom (DOF)is introduced to those from a 3 +1
model: strength of the coupling that mediates the decay, which determines the ν
4
lifetime.
Decay of the ν
4
state causes a dampening of oscillations, resulting in different neutrino
transition probabilities than in the 3 +1 model.
Invisible decay—the 3 +1+decay model involving visible and invisible neutrino decay
was explored in the case of the IceCube Neutrino Observatory [150]. IceCube can search for
anomalous muon-neutrino disappearance due to the existence of eV-scale sterile neutrinos
[151,152]. It was shown that this model can change the interpretation of the IceCube one-
year null result, which had set a strong constraint on the 3 +1 model [153].
The 3 +1+decay model with invisible decay was fit to short-baseline data in [103], and
subsequently, fits to the IceCube one-year dataset were combined with the short-baseline fits
[154]. This model improves over the 3 +1 model with a Δχ
2
of 9.0, with one additional
DOF. The aforementioned tension in the global fits can be quantified with a parameter
goodness-of-fit[107]. The 3 +1+decay model reduces the tension from a χ
2
/DOF of 28/2to
19/3.
A search for the invisible 3 +1+decay model using eight years of IceCube has found a
preference for this model over either the three-neutrino or 3 +1 models [155]. Under the
assumption of Wilks’theorem, the three-neutrino model is disfavored with a p-value 3% and
the 3 +1 model is disfavored with a p-value of 5%. Incorporation of this result into global fits
is expected to further reduce the tension from what was found in [154]. The Short-Baseline
Neutrino Program at Fermi National Accelerator Laboratory offers another opportunity to
search for this model of sterile neutrinos [156].
Visible decay—visible decays were discussed in [157]as an explanation of the LSND
results. There, the authors proposed that a mostly-sterile neutrino ν
4
, of either Dirac of
Majorana nature, could be produced in μ
+
decays and decay into ν
e
and
n
e
in between the
source and the detector, thereby leading to an effective flavor transition. The decay was fast
due to the interactions of ν
4
with a massless scalar particle, f. Subsequently, references
[158–160]expanded on this scenario and argued that it could explain the MiniBooNE excess
as well.
In [160],aSU(2)-invariant model is proposed where a Dirac sterile neutrino ν
s
interacts
with a massive scalar particle f. In the mass basis, the mostly-sterile state ν
4
mixes with the
electron- and muon-neutrinos, and therefore can be produced in both π
+
and μ
+
decays. The
relevant interaction Lagrangian is given by
()
*
å
fn n nÉ- - +
a
aa
gU U gUWℓ
2h.c., 19
ssi si44 44
where U
si
is the mixing between the sterile state ν
s
and the massive eigenstate ν
i
,g
s
the parity-
conserving, sterile neutrino coupling to the scalar f, and gis the weak coupling constant.
The authors in [160]performed a fit to the MiniBooNE and LSND data. The results are
shown in figure 17. While most of the signal at MiniBooNE comes from π
+
→μν
4
production, at LSND, both π
+
→μ
+
,
m
nnm
++
e4as well as
m
nn
++
ee4contribute to the
rate of inverse-beta-decays. This is because of the subsequent
f
nndecays, which
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
37
generate an apparent
nn
transition. This effective transition is strongly constrained by
solar antineutrino searches [161].
The presence of the scalar DOF in the theory also helps reconcile the model with
cosmology [160,162–172]. The secret, self-interactions in the sterile sector provide a new
matter potential for sterile neutrinos in the early universe that suppresses their production.
Another possibility is that the steriles interact with an ultra-light dark matter background,
which also suppresses production in the early Universe [169,170]. For more details, see
section 5.1.3.
3.1.6. Lepton number violating muon decays. In this section, we focus on the possibility of
using Lepton Number Violation (LNV)muon decays in addition to neutrino oscillations as an
explanation for the LSND experiment. While not necessarily providing a full solution to the
short-baseline puzzle, this scenario is worth considering because it is allowed by all data, it
can be realized in explicit models, and is testable. Additionally, when considered in tandem
with the 3 +1 model, it opens up some parameter space in the 3 +1 neutrino oscillations
scenario by accounting for some of the LSND observation.
Lepton-flavor violating NSIs are very strongly constrained by theoretical consistency
requirements and charged lepton flavor experiments. It has been pointed out in [173]that ΔL
≠0 interactions can evade these constraints. In [174]it was shown that, while most ΔL≠0
effective operators are strongly constrained by high-precision measurements of the Michel
parameters in muon decays, two such operators retain the SM prediction of ρ=δ=3/4 and
are thus allowed. In addition, theoretical models that led to these two self-consistent effective
operators were also developed. These effective operators are:
[( ¯)( ) (¯)( )]⟨∣ ∣⟩ ( )mn n mn n-
Ce ℓ C H ,20
ReL aL
TLReL aL
TeL10
()()⟨∣∣⟩ ()
*
nmn
eC C H .21
L
TeL R
TR202
This type of NSI would lead to
¯¯
m
nn++
m
++
e
e, which would directly contribute to
the muon decay-at-rest (DAR)signal in LSND. Accommodating the entire DAR signal
Figure 17. The preferred mixing of the light sterile neutrino with the muon and electron
flavors, |U
e4
|
2
and |U
μ4
|
2
, to explain the MiniBooNE and LSND anomalies in the
decaying-sterile-neutrino model of equation (19). Reproduced from [102].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
38
through such NSI would conflict with the KARMEN experiment, which also used a muon
DAR beam. However, it is possible to achieve good agreement between the two experiments
when one combines the LNV NSI and oscillations through a sterile neutrino, due to the
differences in baselines. The LNV NSI would clearly not affect the pion decay beams in the
other short-baseline accelerator experiments. The oscillation parameters obtained in [174]in
the presence of the LNV NSI for LSND+KARMEN are compatible with those of global fits
that include the MiniBoone and other data which rely on neutrinos from semileptonic pion
decays.
It is thus interesting to consider how the presence of such LNV NSI can change the
allowed sterile neutrino oscillation parameter space through the additional contribution to the
LSND signal. This scenario would be testable by the different effects it produces in muon
decay versus hadronic decay beams. In specific model realizations, it might also be possible to
observe the effects of the new particles associated with the generation of the LNV operators in
future collider experiments.
3.1.7. Large extra dimensions and altered dispersion relations (ADRs). Scenarios with sterile
neutrino ADRs adopt additional terms in the standard dispersion relation ∣∣
=+
E
pm
222
.
These terms make the oscillation amplitude energy-dependent, thus offering more freedom to
accommodate various constraints and anomalies arising in short-baseline neutrino
experiments. There exist various realizations of this scenario, including Lorentz violation
and sterile neutrino shortcuts in warped extra dimensions [37,175,176]. The effect implied
resembles standard matter effects but features a different energy dependence and typically
applies for neutrinos and antineutrinos in the same way.
The basic idea is that active-sterile neutrino mixing is unaltered at low energies; however,
a resonance conversion is present when the effect of the ADR minimizes the effective mass
squared difference between active and sterile neutrinos. This effect is suppressed significantly
for energies above the resonance energy. This allows to decouple sterile neutrinos at high
energy and to evade stringent constraints from atmospheric and long-baseline accelerator
neutrino experiments while offering the possibility to make small active-sterile neutrino
mixing, observed or constrained in solar and reactor neutrino experiments, compatible with
anomalies in short-baseline experiments such as LSND and MiniBooNE.
A challenge of such approaches is to find data sets compatible with all constraints in a
complete framework with three active neutrinos. As has been pointed out in [177], the
requirement to obtain the same flavor structure of active neutrinos below and above the
resonance requires three sterile neutrinos whose mass squared differences reflect the active
neutrino mass spectrum and feature democratic active-sterile flavor mixing. Moreover,
different ADRs and, consequently, resonance energies are necessary for the three sterile
flavors to avoid the cancellation of oscillation effects. In figure 18, the evolution of the
various effective Δm
2
ʼs is shown symbolically [177].
The consequent parameter space has five parameters beyond that of the SM with three
massive, active neutrinos; namely a universal active-sterile Δm
2
and mixing
qsin2
plus three
ADR parameters or resonance energies for the sterile flavors, respectively. As has been
stressed in [178], where the phenomenology of two exemplary data points has been studied, it
is not an easy task to find a combination of parameters that is compatible with all constraints,
especially with both MiniBooNE and T2K that probe similar energy regions. Obviously, a
conclusive verdict on the potential of ADR models would require a thorough scan of the
complete parameter space. In [177], various promising Benchmark Mark Points (BMPs)have
been analyzed. In particular BMP4 (see figure 19 for the energy dependence of Δm
2
ʼs for this
concrete data set)looks promising in this respect, as it leads to a muon-neutrino disappearance
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
39
and electron-neutrino appearance probability that is sharply peaked around the resonance
energy =
E
223.6 MeV
Res (see figure 20). Moreover, BMP4 features a rather small active-
sterile mixing angle q=-
sin 10
24
that seems not to be excluded by MicroBooNE, according
to the analysis in [179]. In fact, the large Δm
2
or order 30 eV
2
leads to fast oscillations that
allow exploiting the difference in baselines between MiniBooNE and MicroBooNE (541 m
versus 470 m)that amounts to roughly 8% of the oscillation length (corresponding to an
oscillation probability reduced by 25% at resonance for MicroBooNE with respect to
MiniBooNE)and that may be increased by finetuning the parameters.
Figure 18. Evolution of various Δm
2
ʼs in ADR scenarios: symbolically. Reproduced
from [177].CC BY 4.0.
Figure 19. Evolution of various Δm
2
ʼs for the specific example of BMP4. The vertical
colored regions correspond from left to right to the energy ranges probed by reactor and
Gallium experiments, LSND, MiniBooNE, and long-baseline accelerator experiments,
respectively. Reproduced from [177].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
40
In summary, ADRs represent a well-motivated and interesting tool to alter standard
neutrino oscillations that may prove useful to explain the intricate framework of anomalies
and constraints characterizing short-baseline neutrino oscillations.
3.1.8. Lorentz violation. The standard-model extension (SME)is an effective field theory
framework to look for Lorentz symmetry violation (LV)[28]. The main interest of LV as an
explanation to short-baseline anomalies is the flexibility of the SME-based Hamiltonian. One
could design a suitable Hamiltonian using the SME to reproduce all neutrino and antineutrino
oscillation data without the standard neutrino mass term. For example, the bicycle model
[180]has the seesaw-mechanism-like texture to reproduce L/Eoscillation behavior at high
energy, even though Hamiltonian only has CPT-odd SME coefficient aand CPT-even SME
coefficient cthat make ∼Lor ∼L·Eoscillation behaviors. The effective Hamiltonian of the
bicycle model in 3 ×3flavor basis matrix has following the texture,
⎛
⎝
⎜⎞
⎠
⎟()~h
aE c c
c
c
00
00
.22
eff
This model demonstrates the possibility that LV can imitate the standard three massive
neutrino oscillations. The tandem model [29]follows this, which can reproduce existing
neutrino data at that time, including LSND.
The SME Lagrangian can be extended to include higher-order terms [181]. Since LV is
related to a new space-time structure motivated by quantum gravity, it is natural to expect LV
to show up in the non-renormalizable operators of the effective field theory. This further
increases the number of model-building possibilities. The puma model [182,183], for
instance, is based on higher-order SME terms. The relevant Hamiltonian for this model is
given by
⎛
⎝
⎜⎞
⎠
⎟⎛
⎝
⎜⎞
⎠
⎟⎛
⎝
⎜⎞
⎠
⎟()~+ +hm
EaE cE
2
111
111
111
111
100
100
100
000
000
,23
eff
225
where m
2
,a, and care tunable parameters. Suitable choices of these three parameters in this
texture can reproduce all neutrino data at that time, including LSND and MiniBooNE.
However, at present time this model is in tension with measurements by MINOS. The
solution of this Hamiltonian provides energy-dependent oscillation lengths shown in
figure 21. One line is used to reproduce solar and reactor neutrino data at low energy, and
another line is used to reproduce atmospheric and long-baseline muon-neutrino disappearance
Figure 20. P(ν
μ
→ν
e
)and P(ν
μ
→ν
μ
)oscillation probabilities for MiniBooNE and the
specific example of BMP4. Reproduced from [177].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
41
data. Around 30 to 300 MeV, these two lines drastically change shapes, and this region is
used to reproduce LSND and MiniBooNE data. The model also uses a CPT-odd term which
can make a difference between neutrino and antineutrino results. However, this model does
not produce short-baseline reactor neutrino disappearance data (Daya Bay, Double Chooz,
Reno)and long-baseline electron neutrino appearance data (T2K, NOvA). Thus, at present,
this model is rejected as an explanation of the short-baseline puzzle.
Future of neutrino oscillation models based on Lorentz violation—it may be possible to
construct an LV-based neutrino oscillation model beyond the puma model to reproduce all
existing data including LSND, MiniBooNE, and other short-baseline results. However, such a
model would have more fine-tuned parameters with an unusual texture or artificial cutoffs.
The difficulty to construct such a model is because LV-motivated terms have zero (∝E
0
)
to a higher power with energy (∝E
1
,E
2
,K), and they dominate neutrino oscillations at high
energy. So parameters introduced to explain short-baseline anomalies in general conflict with
other oscillation data due to the lack of L/Eoscillation behavior, which requires E
−1
term in
the Hamiltonian. One possibility is to introduce an unusual texture discussed above because
they can reproduce L/Ebehavior with fine-tuned parameters. Another possibility is to
introduce fine-tuned cutoffs in LV terms so that LV terms are limited to only certain regions
to explain short-baseline anomalies. Therefore, LV-based models to explain short baseline
anomalies would be unnatural, even if they exist. This is true for any other similar approach
based on effective field theory, regardless of whether they are Lorentz violating or not.
Finally, the LV-based neutrino oscillation models can also be tested by studying the time
dependence of the anomalies. This is the smoking-gun signature that differentiates this
proposal from others. Interestingly, the MiniBooNE antineutrino data set shows a preference
for a non-zero time-dependent LV component; however, this is in tension with the constraint
on LV from MINOS.
3.2. Dark sectors in scattering and in the beam
The difficulty of resolving the various short-baseline anomalies by invoking solely neutrino
flavor transformations, as detailed throughout section 3.1, has led to more exotic proposals,
where light dark sectors can be produced alongside neutrinos in the beam or inside neutrino
detectors, and mimic the experimental signatures. These model scenarios typically explain,
for instance, the MiniBooNE and LSND results without violating the null results from other
experiments.
Figure 21. Solutions of the puma model [182,183]for neutrinos (left)and antineutrinos
(right)are shown by solid and dashed curves. Dotted lines are solutions from the solar
and atmospheric Δm
2
. The horizontal axis is the energy and the vertical axis is the
propagation length. Experimental regions are mapped by boxes or segments. Reprinted
(figure)with permission from [182,183], Copyright (2011)by the American Physical
Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
42
In this subsection, we highlight a few related classes of models that fit this description—
section 3.2.1 discusses a model in which neutrinos are endowed with large transition magnetic
moments, where upscattering from a light SM neutrino into a heavier neutral lepton Ncan be
mediated through photon exchange with the nucleus. Section 3.2.2 details a model in which N
interacts with a light-dark photon, where light-neutrino upscattering into this new state is
mediated by the new force carrier, and Nsubsequently decays into e
+
e
−
pairs.
Models with long-lived particles produced at the neutrino source are also discussed.
Section 3.2.3 discusses a model with long-lived HNLs that propagate to the detector and
decay into e
+
e
−
and single-γfinal states. In section 3.2.3, a dark matter model with light
mediators is presented. The particles are produced in charged meson decays and upscatter
inside the detector to produce electromagnetic showers.
3.2.1. Transition magnetic moment. Several extensions of the SM consider the existence of
sterile neutrinos with Dirac or Majorana masses at or above the MeV scale. By convention,
the mass eigenstates that are mostly in the direction of these sterile neutrino models are
usually referred to as heavy neutral leptons (HNL), denoted here by N. Additional interactions
notwithstanding, HNLs and light sterile neutrinos refer to the same class of particles which
differ only in their mass value. Depending on the model, they can behave either as Majorana
or (pseudo-)Dirac particles.
Similar to the sterile neutrino models discussed above, Ncan mix with SM neutrinos and
interact with the Zand Wbosons through mixing. However, it is also possible that this mixing
is too small to be observed, and that these HNLs can be produced and decay via additional
interactions. One interesting example is that of a transition magnetic moment between light
SM neutrinos and N, described by the effective Lagrangian
¯()
*
ns ng=- - +
aa mn mn aamm
dNF
gUNZhc
2.., 24
NL N
where d
α
is the transition magnetic moment between Nand SM neutrino weak eigenstate ν
α
,
F
μν
is the electromagnetic field strength tensor,
()
s
gg gg=-
mn mn nm
i
2
, and U
α
Nis the
mixing between ν
α
and N. Note that in an effective theory language the operator that gives
rise to the first term is found at dimension six, namely,
˜s
amn mn
L
a
LH NB
c
2, and thus d
α
∝
c
α
v/Λ
2
, with v=174 GeV being the Higgs vacuum expectation value. The second term
above induces an effective vertex between an SM neutrino, a heavy neutrino, and the Z,
which arrives due to mixing between ν
α
and N.
The effective vertex introduced in equation (24)gives rise to new interactions relevant
for existing and future neutrino experiments. First, the dipole model opens up new decay
modes for mesons through off-shell virtual mediators, which can provide a source of heavy
neutrinos at beam-dump experiments. For example, one introduces the weak mediated decay
π
+
→ℓ
+
ν
*
→ℓ
+
Nγand the Dalitz-like decay π
0
→γγ
*
→γNν. Additionally, heavy
neutrinos can be produced by the Primakoff up-scattering of SM neutrinos off a nuclear target
Avia the interaction νA→NX. Finally, the typical observable signal in the dipole model is
the decay of a heavy neutrino to an SM neutrino and a photon via the process N→νγ. The
relevant Feynman diagrams for these processes are shown in figure 22.
It is also possible that HNLs have non-negligible mixing with SM neutrinos, in which
case the upscattering of SM neutrinos to HNLs can be mediated by both the photon, referred
to as electromagnetic (EM)production, or the SM Zboson referred to as weak production. In
this case, the mixing of Nwith muon neutrinos is the most relevant since most neutrinos in
accelerator experiments are ν
μ
and
n
m
.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
43
LSND —the dipole model can explain the observed LSND excess via upscattering on
carbon [40]
()
n
ng
m
C NnX nX,25
12
where the ν
μ
comes from π
+
→μ
+
ν
μ
decay-in-flight in the LANSCE beam-stop. The
Compton scattering and pair production of the photon from Ndecay mimic the signal of the
prompt e
+
, which is detected in coincidence with the capture of the recoil neutron in
equation (25). A heavy neutrino mass of m
N
∼50 MeV can reasonably explain the LSND
anomaly while avoiding constraints from the KARMEN experiment [40]. While [40]
considered weak production, subsequent studies showed that EM upscattering dominates in
this region of parameter space. Nevertheless, the original solution can still be accommodated
in non-minimal scenarios involving more than one heavy neutrino [184].
MiniBooNE—regarding MiniBooNE, since the detection of e
±
relies on reconstructing
Cherenkov rings, this signature is indistinguishable from photons in the detector. Thus, the
dipole model can provide an explanation of the MiniBooNE through the decay channel N→
νγ. In this case, the dominant source of heavy neutrinos in MiniBooNE comes from the
Primakoff up-scattering of SM neutrinos produced in the BNB. Depending on the lifetime of
the N, this can happen off of nuclei either in the dirt between the BNB and MiniBooNE or in
the target material of the detector itself. We note that the decays of the heavy neutrino must be
sufficiently prompt to be consistent with the timing distribution of the MiniBooNE
excess [33].
The upscattering to Ncould proceed via EM or weak interactions with the protons of
hydrogen or both with carbon nuclei in an incoherent or coherent fashion. The hadronic
tensor in this case is the same as in elastic and quasi-elastic interactions of electrons and
neutrinos on the corresponding targets (see chapter 4 of [185]for details). As shown in figure
16 of [186], the EM cross section on nuclei is dominated by the coherent mechanism; the
incoherent one is suppressed by Pauli blocking at low four-momentum transfers, where the
amplitude is enhanced by the photon propagator. On the contrary, the incoherent reaction is
dominant in the weak part.
Electromagnetic upscattering only—the EM upscattering scenario with negligible N
mixing with SM neutrinos has been explored in a number of studies [184,187–190], which
Figure 22. Left: dipole model interactions channels relevant for neutrino experiments which
are introduced by the effective vertex in equation(24)(figure from [189]); right: preferred
regions in dipole model parameter space to explain short-baseline anomalies, along with
constraints from existing experiments. Reproduced from [189,191].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
44
suggest that the energy distributions of the MiniBooNE excess can be accommodated by a
dipole-coupled heavy neutrino with
()=m100 Me
V
N
and (–)=
m-- -
d
10 10 GeV
76 1
.
The MiniBooNE angular distribution, however, can only be explained with EM upscattering
when m
N
300 MeV. In that case, the produced HNL is less boosted and decays more
isotropically.
One can also consider extending the model to include an ()
1e
V
sterile neutrino in
addition to the dipole-coupled HNL. Such a model can explain MiniBooNE through a
combination of upscattering into Nand eV-sterile-neutrino oscillations. If
()>m100
N
MeV, other low-energy experiments like LSND would not be sensitive to it, but they would
still be sensitive to oscillations. This combination of effects has been found to decrease the
tension in the sterile neutrino global picture [191].
Transition magnetic moment with weak production—we now consider weak production
of HNLs in MiniBooNE. With the parameters proposed in [184], the forward-peaked
dominant coherent EM contribution leads to a very narrow angular distribution not observed
in the experiment (see figure 2 of [190]). The agreement can be improved by including
production via the SM Z boson, which is less forward. The parameters can be constrained to
the allowed range established in [40], but there are more stringent bounds for U
μN
,in
particular from radiative muon capture: μ
−
p→nνγ, experimentally investigated at
TRIUMF. Setting m
N
to the allowed minimum of 40 MeV to have the largest possible upper
bound in the mixing: |U
μN
|
2
=8.4 ×10
−3
[192], the best fitfinds t=´
-
+-
9.1 10
N1.5
1.1 10
seconds, BR =´
m-
+-
1.7 10
1.4
2.4
5
with a χ
2
/DoF =104/54. The different contributions to
the excess are singled out in figure 23. A reasonable description of the angular distribution
requires a suppression of the EM strength, as reflected by the small BR
μ
compared to the
original proposal of BR
μ
=10
−2
, while increasing U
μN
as much as possible: its upper limit
prevents from obtaining a more satisfactory description of the data.
Figure 23. Photon events from radiative decay of N,
N
at the MiniBooNE detector in ν-
mode (top)and ¯
n
-mode (bottom)compared to the MiniBooNE excess. For details, see
[190]and [186]. Reproduced from [186]. © IOP Publishing Ltd. CC BY 3.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
45
These results show that the heavy neutrino radiative decay hypothesis is not particularly
successful in the simultaneous description of both the energy and the angular distribution of
the excess, even with a degree of parameter fine-tuning. Nevertheless, based on MiniBooNE
data alone, it cannot be fully excluded, at least as a partial source of the excess. Using the
same number of POT as for figure 37 and the best-fit parameters, the photon events predicted
at MicroBooNE are displayed in figure 24. With a total number of events of more than twice
the SM ones and clearly more forward peaked, testing this possible explanation of the
anomaly is within reach of the MicroBooNE experiment. It also warrants further studies for
the new generation of experiments, SBND and ICARUS.
Other constraints—we now briefly discuss existing and projected constraints on the
heavy neutrino transition magnetic moments. For m
N
1 GeV, neutrino–electron scattering
cross section measurements from Borexino, CHARM-II, DONUT, and LSND can be
Figure 25. Dark neutrino production and decay inside the MiniBooNE detector.
Figure 24. Photon events from Nradiative decay at MicroBooNE for 6.6 ×10
20
POT
in ν-mode. For details, see [190]and [186]. Reproduced with permission from [190].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
46
translated into bounds on the transition magnetic moment [189,193–197](see the discussion
in section 4.2.2). A single-photon search from the NOMAD experiment can be used to set a
limit ν
μ
A→(N→ν
μ
γ)A[198,199]. Future single-photon searches at Fermilab’s short
baseline program may be able to probe parameter space relevant for the MiniBooNE
anomaly [189].
Figure 26. Left: the spectrum of dark neutrino events in neutrino and antineutrino
energy spectrum, as well as in the angular distribution at MiniBooNE. Right: fit to the
neutrino-energy distribution at MiniBooNE in a dark neutrino model with a light dark
photon (
<
¢
mm
Z4
). Reproduced from [203].CC BY 4.0.
Figure 27. Left: Fit to the neutrino-energy distribution (left)and angular distribution
(right)at MiniBooNE in a dark neutrino model with a heavy dark photon (
<
¢
mm
Z4
).
Reproduced from [204].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
47
At higher heavy neutrino masses, collider experiments can provide bounds on transition
magnetic moments by looking for single-photon events with missing energy [189]. One can
also constrain heavy neutrino transition magnetic moments using measurements of the relic
4
He abundance from Big Bang Nucleosynthesis and inferred Supernova 1987A cooling rates
[189]. The proposed SHiP detector at CERN may also be able to set leading limits on heavy
neutrino transition magnetic moments, especially for the d
e,τ
couplings [189,200].
Additionally, experiments such as Super-Kamiokande, IceCube, DUNE, and Hyper-
Kamiokande may be able to place limits on the dipole model by taking advantage of the
unique double-bang topology of ν−Nup-scattering and subsequent Ndecay [193,201,202].
A subset of these limits, as well as the preferred regions to explain the short baseline
anomalies, are shown in figure 22. We look forward to future experiments to shed light on
heavy neutrino dipole portal explanations of short baseline anomalies.
3.2.2. Dark neutrinos. Many extensions of the SM to accommodate neutrino masses involve
HNLs that mix with the SM neutrinos. If these HNLs interact via additional mediators, e.g. a
dark photon from a secluded U(1)
X
, and their masses are in the ∼MeV–GeV, then the
upscattering of SM neutrinos into these so-called ‘dark neutrinos’, followed by dark neutrino
decay, can explain the LEE observed by MiniBooNE [203,204]. Similar to the dipole model
(section 3.2.1), since MiniBooNE cannot distinguish an electron from a photon, it also cannot
distinguish either of these from a pair of overlapping e
+
and e
−
. If the e
+
e
−
pair are
sufficiently collinear, or the energy of one of the particles falls below the detector energy
threshold, the EM shower of the pair mimics that of a single electron or photon.
HNLs can be produced via rare meson decays (e.g. from kaons), and then decay inside
the detector [205,206], however, the signals predicted in this scenario can be delayed with
respect to the neutrino beam, and tend to lead to forward-peaked angular distributions.
However, if the new particles are produced in neutrino upscattering inside the detector,
provided their decays are sufficiently short-lived (()t<
c
10
LAB ns at MiniBooNE), they
can be registered in coincidence with the SM neutrinos. Scenarios where e
+
e
−
pairs are
produced in this fashion (not restricted to the dark neutrino model)have been studied in detail
in [203,204,207–215].Wefirst discuss the original proposals based on a dark photon and
then move on to newer proposals involving scalar particles.
Dark photon models—in addition, these models face none of the problems of the popular
3+1 oscillation explanation of the MiniBooNE excess, as the phenomena observed at the
different SBL experiments decouple in this framework. Finally, there is the possibility of
connecting these models to other prominent questions of particle physics. The discovery of
neutrinos with hidden interactions would be a very strong indication of the existence of dark
sectors that could contain the theorized dark matter. With the SBN program currently
underway, there is the opportunity to probe large regions of the LEE model parameter space,
but also more generic models of dark sector HNLs.
In [203,204,207,208,214,216], the mediator of upscattering is a dark photon. A
simplified model can be used to understand the experimental signatures. In it, an electrically-
neutral fermion ν
D
is charged under dark
()
¢
U
1
symmetry and is assumed to mix with SM
neutrinos,
()
n
na mt=å=
aa
=
UeD,,,,
iii
1
4
where Uis a 4 ×4 unitary matrix. The
mediator of this new gauge group then kinetically mixes with the SM photon via
(
)ˆ
e¢
mn
mn
XF2
, which leads the electrically-charged SM fermions to acquire a small coupling
to the dark photon,
¢
Z
. The low-energy simplified Lagrangian reads
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
48
()
*ng eÉ- ¢-¢
mmm
m
gU U NZ eZ J ,26
DDDi iint 4
EM
where g
D
is the
()
¢
U
1
gauge coupling,
m
J
EM
the SM electromagnetic current, and εis the
kinetic mixing parameter. We define N≡ν
4
. In a full model, Nmay be of Dirac or Majorana
nature.
Since the dark photon interacts with the SM electric charge in an analogous way to the
photon, the upscattering cross section can be calculated in an analogous way to the transition
magnetic moment case, replacing the leptonic vertex and the propagator by a massive one.
When the dark photon is light, coherent scattering with the nucleus is dominant and the rate is
enhanced by the number of protons in the nucleus, Z, with respect to scattering on individual
protons. For
¢
m1Ge
V
Z
, the incoherent contributions start to dominate and the upscattering
can kick a proton out of the Carbon nucleus in MiniBooNE, for example. In models where the
HNL only mixes with muon neutrinos, the upscattering cross section can be shown to scale as
∣∣
s
µ
nm
mUU
ANA D44
2
by virtue of the unitarity of U. Therefore,
s
n
mANA
can be readily
constrained by existing limits on the active-heavy mixing |U
μ4
|
2
for every choice of |U
D4
|
2
,
which usually takes values close to unity.
The decay of the HNL is prompt when
<
¢
mm
Z4
, where the dark photon is produced on
shell and decays to e
+
e
−
. Decays to light neutrinos are suppressed by the mixing angle
combination |U
Di
U
Dj
|
2
, which is small for i<4. This regime produces very forward-going
HNLs, which subsequently decay to boosted e
+
e
−
pairs. While this produces more e
+
e
−
events that mimic single photon or single electron showers, it also leads to very forward-
peaked angular distributions, in contrast with MiniBooNE’s observation [33]. The angular
spectrum is less forward for m
N
300 MeV, however, at those masses constraints from high-
energy experiments are severe [217].
For heavy dark photons,
>
¢
mm
Z4
, the decay is a three-body one and, therefore, the
HNL is much longer-lived. Reference [204]proposed a model where |U
τ4
|
2
?|U
μ4
|
2
, so that
the decay process is effectively N→ν
τ
e
+
e
−
. A similar proposal was made in [208,209]
where a model with two HNLs was used. In that case, the heaviest HNL decays to the
intermediary state with a lifetime that is not suppressed by active-heavy mixing. Due to the
heavy mediator, the upscattering happens with a larger Q
2
, and the angular distribution can be
less forward. The best agreement with the angular distribution is found when the dark photon
interferes with the SM Z.
Dark scalars—HNLs can also interact with additional scalars that play the role of the
dark photon discussed above. In this case, the upscattering cross section lacks the t-channel
singularity and does not asymptote to a constant, but rather falls as n
E12at large energies.
Therefore, if the dark sector particles have masses of
(
)
100
MeV, the upscattering process is
largest at the energies of LSND and MiniBooNE and may avoid constraints from high-energy
experiments altogether. Models of this type have been discussed in [210–213].
Dark scalars and neutrino polarizability—as pointed out in [210], the scalar mediator
can also lead to the production of photons pairs via the decay chain N→ν(S→γγ).At
MiniBooNE, if Sis lighter than the pion, it will be more boosted and its decays to overlapping
photons would mimic the excess signal. It is also possible that the branching ratios for S→
e
+
e
−
and S→γγ are both sizeable, in which case the excess would display a non-trivial
shape in energy and angle.
A scalar mediator coupling to both neutrinos and photons induces a parametrically
enhanced neutrino polarizability, i.e. in low energy processes the scalar can be integrated out,
resulting in dimension 7 Rayleigh operators of the form
(
¯)nn
mn mn
PFF
iL j (or
(
¯)˜
nn
mn mn
PFF
iL j if
the mediator is a pseudoscalar)[218]. For light mediators, with masses below ∼MeV, there
are stringent constraints on such neutrino polarizability models from cosmology and stellar
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
49
cooling. For mediators in the MeV to few GeV regime, relevant for the MiniBooNE anomaly,
these models can be probed at a multitude of neutrino facilities, from measurements of solar
neutrino scattering (Borexino and Xenon-nT)to observations in high energy neutrino beams
(DUNE ND), as well as using beam dump facilities and at precision e
+
e
−
collider
experiments such as Belle II [218].
Explaining LSND—some of the models proposed in the literature above can, in principle,
also explain the LSND anomaly. This sets a more stringent requirement on the theory since it
requires the upscattering process to produce a neutron in the detector. The new signal should
mimic the inverse-beta-decay signature with at LSND, with a prompt electromagnetic signal
followed by delayed neutron capture. This already eliminates the dark photon as a potential
solution, since the couplings with neutrons are much more suppressed than those with
protons. In addition, depending on the mass of the heavy neutrino, the upscattering process
may have too large of a threshold to be initiated by πor μdecays at rest. Instead, for masses
of
(
)
100
MeV, one may take advantage of the number of pions that decay in flight. This
requires a large cross section, since the at these energies is much smaller than the decay-at-rest
one. Models of this type were proposed in [212,213], where the heavy neutrinos are produced
via the exchange of a new scalar boson with large couplings to neutrons.
Broad requirements to explain MiniBooNE and LSND—such proposals must conform to
strong demands from (a)cross section requirements in order to yield a sufficient number of
total events in both LSND and MB, (b)the measured energy and angular distributions in both
experiments, and finally, (c)compatibility of the new physics model and its particle content
with bounds from an extensive swathe of particle physics experiments [189,192,193,
213,217,219–232].
We compare how scalar and vector mediators perform in helping to achieve a
simultaneous understanding of both anomalies. Our treatment is necessarily brief, and for
details and a full set of references on all that follows the reader is referred to [233].
We start by breaking up the interaction into two parts. We first consider the tree-level
process leading to the up-scattering of an incoming muon neutrino, ν
μ
, to a heavy neutral
lepton (N
2
)in the neutrino detector as shown in figure 28(a), with the underlying assumption
that it subsequently decays promptly in the detector into either of the final states shown in
figures 28(b)and (c). The mediator for the up-scattering process could be either a light neutral
vector boson
¢
Zor a light CP-even scalar H. The relevant interaction Lagrangian for the up-
scattering process in each case is given by
(¯)¯()ng g=¢++¢
nmmmm
¢¢ ¢
CNZhcCUUZ.. , 27
ZZ
iL Lj n
Znn
int
Figure 28. Feynman diagrams for the production and the subsequent decay of the N
2
in
LSND and MB.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
50
(¯)¯()n=++
n
C N H hc C UUH.. , 28
HH
iL Rj n
Hnn
int
where U
n
is the nucleon field and i,j=1, 2, 3. For simplicity, we assume that for both
mediators (
¢
Zand H), the coupling to a proton is the same as its coupling to a neutron. The
up-scattering cross section depends on the overall product of the coupling constants n
¢¢
C
C
Z
n
Z
(
n
C
C
Hn
H
)for the vector (scalar)mediator.
Based on the Lagrangian above and the benchmark parameter values in figure 5,we
compute the coherent and incoherent cross sections (shown in figure 29)for both mediators,
required for generating the central value of the number of excess events in MB, which is 560
[33]. From figure 29, we note that the scalar and vector-mediated cross sections behave
distinctly, and our representative calculations bring out the following qualitative points:
(a)For all cases the cross section initially rises as the energy is increased from its lowest
values, however, it subsequently drops for a scalar mediator whereas it remains
approximately flat with increasing energy for a vector mediator. This is true for both the
coherent and incoherent parts. As the neutrino energy rises, it is this relatively rapid drop
in the cross section for Hthat allows solutions with a scalar mediator to comfortably skirt
constraints [217]coming from CHARM II [234]and MINERνA[235], compared to the
¢
Zmediated process.
(b)It can also be seen from figure 29 that the coherent contribution dominates over the
incoherent part for lighter mediator masses, whereas the reverse is true for the higher
mass choice for mediators.
(c)For LSND, contributions to events come from the incoherent part of the cross section
only, due to the presence of a neutron in the final state. In the region in the left panel of
Figure 29. The incoherent (coherent)cross section per CH
2
molecule (C atom)as a
function of incoming neutrino energy. The overall constants for different kinds of
mediator masses are taken from table 5.
Table 5. The overall coupling values for the vector and scalar mediators for different
values of mediator masses (
¢
m
ZH
)to produce 560 N
2
in the MB final state. The mass of
N
2
is 100 MeV.
¢
m
ZH n
¢¢
C
C
Z
n
Z
n
C
C
Hn
H
50 MeV 1.04 ×10
−8
9.3 ×10
−8
1 GeV 8.5 ×10
−7
2.14 ×10
−6
300 MeV —5.35 ×10
−7
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
51
figure 29, we note that the energy drops from MB (∼800 MeV)to LSND DAR flux
values (∼150–200 MeV). Note that for =
¢
m1Ge
V
ZH (solid curves), while the
incoherent cross section drops for both mediators, the vector cross section has lower
values to begin with compared to the scalar. It also drops more rapidly. For example, it
can be seen that the cross section for the
¢
Zdrops an order of magnitude over this energy
range for
=
¢
m1Ge
V
Z
. For =
¢
m50 Me
V
ZH
(dashed curves), over this energy range,
the incoherent scalar cross section is significantly higher than that for the vector. In fact,
it increases as the energy is lowered, unlike its vector counterpart. This reduction in the
incoherent vector cross section at energies (<800 MeV)makes it more difficult for
models with a vector to give a sufficient number of electron-like excess events at LSND,
even though by using a high enough ¢
mZone may successfully evade the CHARM II and
MINERνA bounds. However, on the other hand, too low m
H
gives many more events
than those observed in LSND, both in the 20–60 MeV visible energy range which
recorded data, and beyond 60 MeV, where only a limited number of events were seen.
(d)Finally, for scalar mediators, especially those with low masses m
H
;100 MeV, the cross
section tends to rise at low values of E
ν
. However, in such models, if the primary decay
modes of N
2
are to invisible daughters, as in [211], the incoherent interaction would
mimic the neutral current interaction νN→νN. This has been measured at MB [236]at
these energies and found to be in agreement with the SM, providing an important
restriction on such models.
Overall, the cross section and mediator mass considerations for a common solution thus
appear to favor scalar mediators over vectors. Secondly, our representative calculations also
point to a preference for lighter (but not ultra-light)mediators if both excesses are to have a
simultaneous solution.
An examination of the angular distribution of MB is also helpful from the point of view
of imposing requirements on proposed solutions. The excess in MB is distributed over all
directions but is moderately forward. The cross section responsible for the production of N
2
as
a function of the cosine of the angle between the momentum direction of N
2
and the beam
direction has been studied in a bin-wise manner in [233]for both the coherent and incoherent
contributions. It was found that when =
¢
m50 Me
V
ZH
, almost all the produced N
2
are in the
most forward bin for both mediators. However, as the mediator mass is increased to 1 GeV,
there was a shift in the distribution, and the other bins were also populated for both types of
mediators, even though there were qualitative differences between the two. From this, at first
it appears that using a single scalar mediator and adjusting its mass to an intermediate value,
as well as the mass of N
2
will allow us to find a common solution to the two anomalies as well
as match the angular distribution in MB. However, further examination based on
considerations related to the energy distributions in LSND and MB (for details, see [233])
reveals that this is not the case if good fits to both anomalies are desired.
Overall, as detailed in [233], energy distributions in LSND and MB, the angular
distribution in MB, when combined with the stringent constraints on light singlet scalars, all
suggest the use of a scalar doublet, with one light and one moderately heavy partner. We find
this leads to a degree of angular isotropy while allowing a large number of events in the
forward direction, consistent with observations. A combination of a moderately heavy and a
light mediator complement each other well when a common solution to the two anomalies is
sought. An example solution to both anomalies that incorporates all the features that have
been obtained in our study has been provided in [213].
Our insistence on a solution that addresses both anomalies simultaneously is, of course, a
choice. It restricts proposed solutions in ways that attempt to explain the anomalies
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
52
individually do not. However, it is noteworthy that once we demand this, and adhere to the
dictates of the cross section, the observed energy and angular distributions in both
experiments as well as the many constraints from various experiments [233], then we are led
to a simple extension of the SM that (i)resolves both anomalies, (ii)provides a portal to the
dark sector, (iii)accounts for the experimentally observed value of the muon g−2 and ((iv)
addresses the issue of neutrino mass via a Type I seesaw, in conformity with the global data
on the observed values of neutrino mass-squared differences in oscillation experiments, as
shown in [213].
3.2.3. Long-lived heavy neutrinos.Heavy neutrino decays to single photons—in [205], the
authors propose a solution to the MiniBooNE excess with a heavy neutrino that interacts with
muon-neutrinos through mixing as well as through a transition-magnetic moment. The model
is the same as the one presented in figure 24, but contrary to the solution in section 3.2.1, the
mixing angle |U
μN
|and transition magnetic moment d
μ
are small, such that the heavy neutrino
decays only in macroscopical distances. In particular, if the lifetime is larger than the distance
between the target and the MiniBooNE detector, ()t
c
500
0m, then the heavy neutrino
can be produced in pion and kaon decays via mixing, K→μN, travel to the detector, and
decay inside the active volume due to the transition magnetic moment, N→νγ.
While the model was shown to successfully reproduce the energy spectrum of the
MiniBooNE excess, the decay process tends to produce very forward signatures. A better
agreement with the angular spectrum is achieved for larger masses of the N. However, if the
heavy neutrino is too massive, its arrival in the MiniBooNE detector is delayed with respect to
the SM neutrinos. This delay is proportional to the
(
)mE
NN
2, and should not exceed values
much larger than several nanoseconds, as the excess events have been observed to be in the
same time window as the beam neutrinos [33]. This sets a strong constraint on the mass of the
heavy neutrino. For masses below 150 MeV, where agreement with the timing requirements
can be achieved, production in pion decays should also be considered.
Heavy neutrino decays to axion-like particles—in order to account for the MiniBooNE
excess, [206]proposes an extension of the SM with Dirac HNL that couples to a leptophilic
axion-like particle (ℓALP). The HNL, denoted by N
D
to emphasize its Dirac nature, mixes
with the three SM neutrino flavors, ν
β
. The flavor and mass eigenstates, ν
jL
and N
D
, can be
transformed into each other by means of a unitary matrix U[203]:
()
å
n
n=+
bbb
=
UUN.29
j
jjL D
1
3
4
The relevant Lagrangian includes the interaction of ℓALPs with sterile neutrinos and electrons
[237]:
() ()nggn gg=-
+
mmm
a
fccee
2,30
aℓ
a
ND D e
55
where f
a
is the ℓALP decay constant, c
N
and c
e
are the dimensionless parameters for the ℓALP-
sterile neutrino and ℓALP-electron couplings, respectively.
Our ℓALP scenario is sketched in figure 30. In this framework, the sterile neutrino with a
mass m
N
of
(
)
100
MeV, the ℓALP with a mass m
a
of (
)
10 MeV and an inverse decay
constant ()--
c
f10 GeV
ea21
are considered. The Dirac-type sterile neutrino N
D
,
produced from charged kaon decays through its mixing with the muon neutrino, travels a
distance of 500 m and decays into a ℓALP and a muon neutrino inside the MiniBooNE
detector. The electron-positron pairs produced from the ℓALP decays can be interpreted as
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
53
electron-like events provided that their opening angle is sufficiently small. We verify that with
appropriate choices of the parameters, the sterile neutrino and ℓALP have the proper mean
decay lengths consistent with the setup of the MiniBooNE experiment. We also make sure
that the values of the parameters adopted in our model are allowed by the astrophysical and
experimental constraints.
Following the approach applied in [205], the angular and visible energy spectra in the
neutrino mode are computed and compared with the results of the MiniBooNE experiment, as
shown at the top of figure 31. At the bottom panel, the predicted total event numbers are
obtained after summing over the spectra and shown as the contours consistent with the
MiniBooNE excess at the 1σto 3σlevels on the
(
∣∣)
m
mU,
N42
and
(
∣∣)
m
cf U,
ea42
planes, with
the constraints obtained from other experiments. We find that the scenario with the sterile
neutrino mass in the range 150 MeV m
N
380 MeV and the neutrino mixing parameter
between ∣∣
m
--
U10 10
10 428
can explain the MiniBooNE excess.
3.2.4. Dark matter particles. Since the neutrinos at MiniBooNE are produced primarily from
charged meson decays and the decays of daughter muons of those charged mesons, neutrino-
based solutions can accommodate the absence of any excess in the dump mode, in which the
charged mesons are no longer focused by magnetic horns, unlike the neutrino and
Figure 30. ℓALP scenario for the explanation of the MiniBooNE excess. Lis the travel
distance of the sterile neutrino, Dis the diameter of the MiniNooBE detector, and θ
a
is
the scattering angle of the ℓALP. Reproduced from [206].CC BY 4.0.
Figure 31. The comparison of the numerical results of the angular and visible energy
spectra in the ℓALP scenario and the data of the MiniBooNE experiment in the neutrino
mode. Reproduced from [206].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
54
antineutrino modes. Essentially, the neutrino-based explanations work well because a key
feature of the excess seems to be correlated to the focusing or suppression of charged mesons.
This poses a challenge to dark sector interpretations of the excess (e.g. using π
0
or dark
bremsstrahlung production channels [223,224]), which have been more constrained and less
holistic in their explanation of the excess with respect to their counterparts in neutrino BSM
physics thus far. One solution proposed in [215]opens up the possibility for dark sector
explanations by means of connecting the dark sector to the physics of charged meson decays,
something that had previously been overlooked. The authors in [215]considered various DM
scenarios involving couplings to muons, namely those in equations (31),(32), and (33):
¯¯ ()fmm g lfÉ+
¢+¢+
maamn mn
ggZuuFF
4h.c., 31
Sn
¯¯ ˜()mg m g l
É+
¢+¢+
maamn
mn
ig a g Z u u aF F
4h.c., 32
Pn
5
()()( )()É+ ++ +
¢+¢¢
mm
mmm
mmm
m

eV VJ gV gVJ gV gVJ.33
VDD
11, 22, EM 11, 22, 11, 22,
Here, three massive bosons have been introduced; a long-lived scalar fand pseudoscalar
a, and a short-lived vector ¢
a
A
decaying to DM fermions χ,
c
¢
with
¢º¶ ¢-¶ ¢
mn mnnm
FAA
. The
muonic couplings allow for the 3-body decays of the form M→μνX(M=π
±
,K
±
)became
possible, as shown in figure 33. The 3-body nature of this decay mechanism is not phase-
space suppressed in the contraction of ν
†
μ
↑
, as opposed to the ordinary 2-body decay which
selects out only the combination ν
↓
μ
↑
. The branching ratios for scalar, pseudoscalar, and
vector DM production are shown in figure 34. In the
V
scenario, the detector signature
would then take place through DM upscattering, (cccc¢¢
+-
NN ee
), while scenarios
Sand
P
consider long-lived f/ascattering in the detector through a Primakoff-like process
fN→γNvia a heavy mediator
¢
Z
. The parameter space which fits the MiniBooNE excess for
S,
P
, and
V
is shown in figure 35.
However, the muonic portal is not the only possibility, and DM production in the 3-body
π
±
and K
±
decays from DM-quark couplings can also be treated. In this sense, the scope of
Figure 32. Best-fit regions to the MiniBooNE excess in the HNL and ℓALP parameter
space. Limits and best-fit regions are shown on the (∣∣)
m
mU,
N42(left)and
(∣∣)
m
cf U,
ea42
(right)planes. Reproduced from [206].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
55
Figure 33. 3-body charged meson decay into a scalar, pseudoscalar, or vector.
Analogous processes exist for π
−
and K
−
decay. Reproduced from [215].CC BY 4.0.
Figure 34. Branching ratios for the 3-body production of scalars, pseudoscalars, and vectors
via a charged meson with mass =p
++
M
mm,K. Reproduced from [215].CC BY 4.0.
Figure 35. The credible regions for fits to the MiniBooNE cosine spectrum with
V
(left)and
SP,(right)are shown at 68% (dark-shaded)and 95% (light-shaded).
Reproduced from [215].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
56
the 3-body decay solution can cover several coupling schemes, and should be testable at other
experiments with similar meson production capabilities.
This has broad implications for accelerator facilities, such as LBNF (DUNE), that also
have magnetic focusing horns that should be sensitive to forward-produced DM from the
meson decays. Constraints on the parameter space from accelerator-based searches at
CHARM, MINERνA, and T2K can also be considered, but their smaller POT and exposures
do not give them sensitivity to the MiniBooNE excess. Other neutrino experiments such as
CCM, JSNS, and COHERENT that produce stopped mesons and lack magnetic focusing
horns can also probe the parameter space relevant for the excess, since while the DM signal
from meson decays will be isotropic, their detectors are situated much closer to the beam
targets to be sensitive to the DM flux.
3.3. Conventional explanations
While the majority of the explanations explored above rely on some new or BSM physics to
give rise to the various anomalies, the possibility that the origin lies in more conventional
explanations, such as an underestimated background, mis-modelling in simulation, or over-
constrained cross-section uncertainties, must still be considered. While these explanations are
generally difficult to test directly without access to (often)collaboration-internal experimental
tools and data sets, there have been several attempts in recent years to test individual
anomalies in this direction. In one such example [36], it was shown that allowing a combi-
nation of theoretical uncertainties in different background channels to fluctuate in unison is
not sufficient to resolve the MiniBooNE anomaly; however, it can reduce the significance of
the MiniBooNE excess. In this section, we discuss several such possible ‘conventional’
interpretations for the anomalies.
3.3.1. Single-photon production. The solution to the MiniBooNE puzzle may have
important implications for our understanding of neutrinos and their interactions. In addition
to the interpretation in terms of new physics, the MiniBooNE anomaly could be a
manifestation of new forces of nature, while unaccounted or poorly modeled SM backgrounds
cannot be entirely discarded. Once Cherenkov detectors like MiniBooNE misidentify single
photon tracks as electrons, the excess of events could be due to their products through both
SM and BSM mechanisms.
In the SM, single photons can be emitted in NC interactions, NC1γ, on nucleons,
(¯)(
¯)
n
nnngNN
, or on heavy nuclei, via incoherent or coherent (where the nucleus
remains in its ground state)scattering. Theoretical models for the elementary NC1γ
[238–240]take into account s- and u-channel amplitudes with nucleons and Δ(1232), but also
heavier baryon resonances, in the intermediate state, figure 36. The structure of nucleon pole
terms at threshold is determined by symmetries. The extension towards higher energy and
momentum transfers, required to predict cross sections at MiniBooNE, is performed by the
introduction of phenomenologically parametrized weak and electromagnetic form factors.
The same strategy has been adopted for resonance terms The Δ(1232)excitation followed by
radiative decay is the dominant mechanism, as correctly assumed by MiniBooNE, but the
contribution of non-resonant terms is also sizable. The uncertainty in the elementary
NC1γcross section is dominated by the leading N−Δaxial transition coupling, (
)
=
C
q0
A
52
,
which is related to the ΔNπcoupling (known from πNscattering)by a Goldberger-Treiman
relation, but has also been found to be ()=
C
0 1.18 0.07
A
5[241]from data on πproduction
induced by neutrino scattering on hydrogen and deuterium. It is worth stressing that the ΔNγ
couplings responsible for the resonance radiative decay are directly related to helicity
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
57
amplitudes A
1/2,3/2
known with few-percent accuracy from photo-nucleon interactions [5].
Furthermore, owing to isospin symmetry, these quantities also constrain the vector part of the
weak Δproduction. This implies that large uncertainties in the Δradiative decay couplings
are at odds with hadron phenomenology but would also have an observable impact in weak
pion production. Among the non-resonant contributions, t-channel ω-meson exchange, was
proposed as a solution for the MiniBooNE anomaly [38]because of the rather large (although
uncertain)couplings and the ωisoscalar nature, which enhances its impact on the coherent
NC1γreaction. However, actual calculations found this contribution small compared to Δ
(1232)excitation [238,242]. Nuclear effects, in particular the broadening of the Δresonance
in the nucleus, are important for single photon emission [240,243].On
12
C they cause a
reduction of about 30% in the cross section (see figure 9 of [240]).
With the ingredients outlined above, the SM single-γcontribution to the number events
in the MiniBooNE detector and their distributions have been calculated [244,245]using the
available information about the detector mass and composition (CH
2
), neutrino flux and, quite
significantly, photon detection efficiency. Results are to a large extent consistent with the
(data based but relying on an improvable reaction model)MiniBooNE estimate (figures 4, 6
and 8 of [245])and, therefore, insufficient to explain the excess. The impact of two-nucleon
meson-exchange reaction mechanisms has been recently investigated [246]and found to be
small (a factor of around 9 at E
ν
=500 MeV compared to single-nucleon mechanisms).In
[247]it was estimated that the NC1γbackground should be enhanced by a factor between
1.52 and 1.62 over the MiniBooNE estimate, depending on the energy range and mode. Such
an enhancement, shrinks the excess and significantly reduces the appearance-disappearance
tension in global fits but is at odds with the earlier described theoretical calculations. An
upper limit for the NC1γcross section on liquid argon has been recently obtained by the
MicroBooNE experiment [248], as discussed in the following section. It disfavors that the
excess could be solely attributed to this reaction channel but new results with higher statistics
are required for a firm conclusion. Assuming 6.6 ×10
20
POT from the experiment’s run plan,
the distributions of the NC 1γevents calculated with the model of [240]are given in figure 37
(adapted from [249]). Comparison to future data shall offer valuable information about this
process.
3.3.2. Reactor flux modeling. One conventional explanation for the Reactor Antineutrino
Anomaly (RAA)has been gaining momentum thanks to the significant experimental and
theoretical progress made in the past decade. Reactor neutrino experiments that can measure
oscillations without any reliance on reactor neutrino models (discussed further in
Figure 36. Feynman diagrams for NC single photon emission considered in the
literature. The first two diagrams stand for direct and crossed baryon pole terms with
nucleons and baryon resonances in the intermediate state. The third diagram represents
t-channel meson exchange contributions. Reproduced from [186]. © IOP Publishing
Ltd. CC BY 3.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
58
section 4.1.3)have been chipping away at RAA-suggested sterile neutrino oscillation
parameter space. Additionally, neutrino, nuclear physics, and nuclear theory evidence have
recently emerged suggesting that RAA may, at least in part, be caused by problems with
reactor flux models. While experimental developments are discussed in section 4.3.2, recent
theoretical advancements in the flux prediction landscape that lend support to non-BSM
origin to the RAA are discussed here.
The statistical significance of the RAA depends not only on the magnitude of offset
between reactor
¯
n
e
data and the Huber-Mueller prediction but also on the size of the error
bands applied to those predictions. In the years following the inception of the RAA in 2011, a
variety of reactor modeling studies have argued that the 2%–3% error budget assigned to this
prediction is likely underestimated. In particular, the role of forbidden beta transitions in
altering the
¯
n
e
flux and spectrum reported by conversion predictions is not considered in the
formulation of Huber-Mueller model error bands [55]. When naive treatments of forbidden
decay contributions are included in the prediction, variations in the flux of 4% or more are
observed [250]and are reflected in the community-driven report in [251]. On the other hand,
a more recent conversion calculation (termed the HKSS model)that attempts to account for
forbidden transition contribution using nuclear shell model-based calculations shows strong
deviations from the Huber-Mueller model in spectral shape. However, it finds no major
discrepancy in reported IBD yields [252].
The past ten years have also brought about substantial development of state-of-the-art
summation calculations, thanks to improved nuclear data evaluations and new nuclear
structure measurements for a range of high-Q, high-yield fission daughters [47–53]. The
improved summations can be compared to conversion calculations to provide an assessment
of the latter’s robustness. As early as 2012, improved summation calculations were shown to
generate reduced flux predictions with respect to earlier iterations [253], indicating modest
over-prediction of
238
Ufluxes in the Huber–Mueller prediction. When comparing to
conversion predictions, modern summation calculations were shown to predict different fuel-
dependent
¯
n
e
flux variations [254]. Most recently in 2019, Estienne, Fallot et al [44]used
comprehensive improvements and updates in nuclear databases to generate a summation
model (referred to as the EF Model)with a total predicted flux of a few percent lower than the
measured global IBD yield average, but with a
235
U prediction ∼6% smaller than that
predicted by the HM conversion model. These comparisons are suggestive of a possible issue
with conversion-predicted fluxes for individual isotopes.
Figure 37. SM prediction for NC1γevents at MicroBooNE for 6.6 ×10
20
POT in ν-
mode. Reproduced from [186]. © IOP Publishing Ltd. CC BY 3.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
59
The IBD yields predicted by these various models can be compared to the global IBD
yields listed in table 9and to specialized Daya Bay [255]and RENO [256]dataset reporting
yields as a function of varying contents of the reactor cores; the latter datasets are described
further in section 4.3.2. In particular, if comparisons are made under the hypothesis that the
RAA is generated by sterile neutrino oscillations, the different reactor flux models generate
substantially differing interpretations. To illustrate, figure 38 shows the contours of the 2σ
allowed regions in the (JDmsin 2 ,
ee
241
2)plane of 3 +1 active-sterile neutrino mixing
parameters [257]. One can see that an indication in favor of neutrino oscillations only for the
HM and HKSS conversion models, which exhibit a significant reactor rate anomaly above 2σ
(see table 7). Considering the EF model, for which the reactor rate anomaly is less than a few
percent, the 2σexclusion curves in figure 38 allow only small values of Jsin 2 ee
2, including
J=sin 2 0
ee
2
, which corresponds to a lack of any statistically significant indication of sterile
neutrino oscillations. It should be noted here that error estimates for summation calculations
are ill-defined, but are generally expected to be similar in magnitude to those provided by
conversion predictions; efforts to provide more robust error envelopes are underway [258].
For all the reactor flux models, it is also worth noting that upper bounds exist for the
value of the mixing parameter Jsin 2 ee
2, with exact limits dependent on the value of
D
m41
2. For
D
m2eV
41
22the upper bounds for Jsin 2 ee
2are between 0.14 and 0.25. Figure 38 shows that
these bounds and the solar bound [259]are in agreement, but in tension with the large mixing
[136]required to explain the anomaly of the GALLEX [260], SAGE [75], and BEST [136]
gallium experiments with short baseline neutrino oscillations. This is a puzzling recent
development in the phenomenology of short-baseline neutrino oscillations that may require an
explanation extending beyond both conventional explanations and the simplest possible
model of 3 +1 active-sterile neutrino mixing.
3.3.3. The gallium anomaly and interaction cross-section uncertainties. The first analysis
establishing the existence of the Gallium Anomaly [78]did not consider the uncertainties on
the cross section of the detection process in equation (6)and, as mentioned in previous
sections, this has been a source of subsequent investigation as a possible avenue for resolving
this anomaly.
It is now clear that this quantity is of paramount relevance for the possible interpretation
of the Gallium Anomaly. Different calculations of the cross section have been published after
the seminal work by Bahcall [76], and the values are summarized in table 8.
Also, it has been pointed [77]that the rather large uncertainties come from the fact that
only the cross section of the transition from the ground state of
71
Ga to the ground state of
71
Ge is known with precision from the measured rate of electron capture decay of
71
Ge to
71
Ga. In fact, recent improvements on measurements of this transition [261–263]indicate that
the Gallium Anomaly persists. However, electron neutrinos produced by processes in
Table 6. Theoretical IBD yields of the four fissionable isotopes in units of 10
−43
cm
2
/fission predicted by different models [257]. Reproduced from [257].CC BY 4.0.
Model σ
235
σ
238
σ
239
σ
241
HM 6.74 ±0.17 10.19 ±0.83 4.40 ±0.13 6.10 ±0.16
EF 6.29 ±0.31 10.16 ±1.02 4.42 ±0.22 6.23 ±0.31
HKSS 6.82 ±0.18 10.28 ±0.84 4.45 ±0.13 6.17 ±0.16
KI 6.41 ±0.14 9.53 ±0.48 4.40 ±0.13 6.10 ±0.16
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
60
equation (5), can also be absorbed through transitions from the ground state of
71
Ga to two
excited states of
71
Ge at 175 keV and 500 keV.
When the aforementioned uncertainties are taken into account, different results for
the total cross section for the radioactive sources are obtained, resulting in changes to the
measured and expected
71
Ge event rates. On the other hand, complete calculations of the
Figure 38. Contours of the 2σallowed regions in the (JDmsin 2 ,
ee
241
2)plane obtained
from the combined neutrino oscillation fit of the reactor rates in table 7and the Daya
Bay [255]and RENO [256]evolution data. The blue, red, green, and magenta curves
correspond, respectively, to the HM, EF, HKSS, and KI models in table 6. Also shown
are the contour of the 2σallowed regions of the Gallium anomaly obtained in [136]
from the combined analysis of the GALLEX, SAGE and BEST data (orange curve),
and the 2σbound obtained from the analysis of solar neutrino data in [259](dark red
vertical line). Reproduced from [257].CC BY 4.0.
Table 7. Average ratio
R
mod obtained in [257]from the least-squares analysis of the
reactor rates in table 1and of the Daya Bay [255]and RENO [256]evolution data for
the IBD yields of the models in table 6. The RAA columns give the corresponding
statistical significance of the reactor antineutrino anomaly. The descriptions of all the
models are given in text. Reproduced from [257].CC BY 4.0.
Model Rates Evolution Rates +Evolution
R
mod RAA
R
mod RAA
R
mod RAA
HM
-
+
0.936
0.023
0.024
2.5σ-
+
0.933
0.024
0.025 2.6σ
-
+
0.930
0.023
0.024
2.8σ
EF -
+
0.960
0.031
0.033 1.2σ
-
+
0.975
0.030
0.032
0.8σ
-
+
0.975
0.030
0.032
0.8σ
HKSS -
+
0.925 0.023
0.02
5
2.9 σ-
+
0.925 0.024
0.02
6
2.8σ
-
+
0.922
0.023
0.024
3.0σ
KI
-
+
0.975
0.021
0.022
1.1σ-
+
0.973 0.02
2
0.023 1.2 σ0.970 ±0.021 1.4σ
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
61
cross sections of the interaction process, equation (6), for neutrinos produced by
51
Cr and
37
Ar
sources are given in [264]as
⎜⎟
⎛
⎝⎞
⎠()ss x x=+ +1BGT
BGT
BGT
BGT .34
gs 175
175
gs
500
500
gs
Here, σ
gs
is the cross section of the transitions from the ground state of
71
Ga to the ground
state of
71
Ge, BGT
gs
is the corresponding Gamow–Teller strength, and BGT
175
and BGT
500
are the Gamow–Teller strengths of the transitions from the ground state of
71
Ga to the two
excited states of
71
Ge at about 175 and 500 keV as shown in figure 39. The coefficients of
BGT
175
/BGT
gs
and BGT
500
/BGT
gs
are determined by phase space: ξ
175
(
51
Cr)=0.669,
ξ
500
(
51
Cr)=0.220, ξ
175
(
37
Ar)=0.695, ξ
500
(
37
Ar)=0.263 [76].
Table 9shows the different values of the rate when four different approaches (other than
the one by Baxton, R
B
)are used to compute the cross sections [264]:R
HK
uses information
about the Gamow–Teller strengths from Haxton [265]and Krofcheck et al [266]; for R
FF
, the
corresponding numbers are taken from Frekers et al [261];R
HF
uses BGT
175
from Haxton and
BGT
500
from Frekers et al; and R
JUN45
uses calculations using nuclear shell-model wave
functions obtained by exploiting recently developed two- nucleon interactions [267](see also
[268]for additional details).
The last column of table 9shows the corresponding weighted average for each case
showing the Gallium Anomaly with a statistical significance of 3σ, 2.9σ, 3.1σ, and 2.3σ,
respectively for the last four cases. This confirms the Gallium Anomaly and retains the
indication in favor of a short-baseline disappearance of electron neutrinos, possibly due to
neutrino oscillations. Figure 40 shows the 90% contours in the |U
e4
|
2
–
D
m41
2plane obtained
from the analysis of the measured and expected
71
Ge event rates, considering the neutrino
survival probability equation (7), where one can see that the squared-mass difference
D
m41
2
Table 8. Summary of the cross section values recently published.
σ(10
−46
cm
2
)References
-
+
5
8.1 0.16
0.21 [76]
59.3 ±0.14 [263]
59.10 ±0.114 [548]
56.7 ±0.06 [268]
59.38 ±0.116 [674]
Figure 39. Nuclear levels for the
71
Ga transitions to
71
Ge. Reprinted (figure)with
permission from [264], Copyright (2012)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
62
allowed values are ∼1eV
2
or larger, for the different approaches to compute the ν
e
−
71
Ga
cross section.
A revision of the statistical significance of the Gallium Anomaly considering different
calculations of the neutrino detection cross section, has been performed to compare the 3 +1
neutrino oscillation hypothesis with the Reactor Antineutrino Anomaly and with the inclusion
of data from tritium experiments and from experiments measuring solar neutrinos (Giunti et al
2022b). Remarkably, it was found that the Gallium Anomaly is in strong tension with bounds
obtained from the other data sets. In addition, when all data are combined, the corresponding
parameter goodness of fit is below 0.042%, implying a tension of ∼5σ, leading to the
conclusion that it should be necessary to seek for alternative solutions to the shortbaseline
oscillations for this anomaly.
Table 9. Ratios of measured and expected
71
Ge event rates in the GALLEX and SAGE
experiments. The last column corresponds to the weighted average [264]. Information
in the last row is from [268]. Reprinted (table)with permission from [264], Copyright
(2012)by the American Physical Society. Reproduced from [268].CC BY 4.0.
GALLEX
1
GALLEX
1
SAGE
Cr
SAGE
Ar
Avg.
R
B
0.95 ±0.11 -
+
0.81 0.11
0.10 0.95 ±0.12 0.79 ±0.08 0.86 ±0.05
R
HK
0.85 ±0.12 0.71 ±0.11 -
+
0.84
0.12
0.13 0.71 ±0.09 0.77 ±0.08
R
FF
0.93 ±0.11 -
+
0.79 0.11
0.10 -
+
0.93
0.12
0.11
-
+
0.77
0.07
0.09
0.84 ±0.05
R
HF
-
+
0.83 0.11
0.13 0.71 ±0.11 -
+
0.83
0.12
0.13 -
+
0.69 0.09
0.10
-
+
0.75
0.07
0.09
R
JUN45
0.97 ±0.11 0.83 ±0.11 0.97 ±0.12 0.81 ±0.08 0.88 ±0.05
Figure 40. The 90% allowed regions in the |U
e4
|
2
–Dm41
2plane obtained from the analysis
of the measured and expected
71
Ge event rates. Reproduced from [268].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
63
3.4. Summary of interpretations
A summary of the interpretations detailed in this section is provided in table 10. The columns,
from left to right, are the following: broad classes of models; specific models that fall in each
class; the experimental signature of each model; which anomalies each model can address
(LSND, MiniBooNE, Reactor and Gallium anomalies, respectively), and the corresponding
references. For convenience, in the first column, we also indicate the sections of this docu-
ment that are related to each class of models.
Finally, in table 11 we summarize which experimental efforts can probe which signatures
of new physics that can address the anomalies. For concreteness, we focus on experiments
that are either recent, are expected to be upgraded, or are still under proposal. The leftmost
column shows broad classes of experiments grouped arbitrarily by their source and type of
experiment. The other columns present which specific experiments, in each of these classes,
can probe a given experimental signature resulting from different interpretations of the
anomalies. For clarity, the ‘decays in flight’column title refers to particles produced by the
decay of mesons, muons, or taus in flight.
4. Broader experimental landscape
In this section, we review the broader landscape of existing experimental results with relevant
sensitivity to interpretations of the LSND, MiniBooNE, Reactor, and Gallium anomalies.
4.1. Flavor conversion
Other short-baseline, as well as long-baseline, neutrino experiments can look for anomalous
flavor conversions. In the following sections, we discuss direct tests of MiniBooNE and
LSND in ν
μ
→ν
e
and nn
mesearches, as well as in ν
μ
and ν
e
disappearance. We also
discuss the ν
e
and
n
e
disappearance in the context of the Gallium and reactor anomalies, where
both null results and hints are observed.
4.1.1. Pion decay-at-rest accelerator experiments. The KARMEN (KArlsruhe Rutherford
Medium Energy Neutrino)experiment was located at the highly pulsed spallation neutron
source ISIS of the Rutherford Laboratory (UK). ISIS protons had an energy of 800 MeV and
were delivered to the water-cooled Ta-D
2
O target with a repetition rate of 50 Hz. The time
structure of the ISIS protons (double pulses with a width of 100 ns separated by 325 ns)
allowed a clear separation of ν
μ
events due to π
+
decay from
¯
n
m
and ν
e
events due to μ
+
decay.
The KARMEN detector [269]was a segmented liquid scintillator calorimeter, located
17.7m from the ISIS target at an angle 100 degrees relative to the proton beam. The active
target consisted of 65 m
3
of liquid scintillator segmented into 608 modules with gadolinium-
coated paper placed between modules for efficient detection of thermal neutrons. KARMEN
performed a search for
¯¯
n
n
me
oscillations, analogous to the LSND search, using (¯)n
+
pen,
e
and found measured rates agreed with background expectations [20]. The sterile neutrino
90% confidence interval (C.I.)obtained by the KARMEN measurement is shown in figure 41
in relation to the LSND allowed regions. Although KARMEN did not see the LSND-like
signal, it did not exclude the entirety of the LSND 99% allowed regions although it did
strongly disfavour the larger Δm
2
>10 eV
2
solutions.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
64
Table 10. New physics explanations of the short-baseline anomalies categorized by their signature. Notation: ✓—the model can naturally explain
the anomaly, ✓—the model can partially explain the anomaly, ✗—the model cannot explain the anomaly.
Category Model Signature Anomalies References
LSND MiniBooNE Reactors Sources
Flavor transitions
sections 3.1.1–
3.1.3,3.1.5
(3+1)oscillations oscillations ✓✓ ✓✓Reviews and global fits [102,103,105,106]
(3+1)w/invisible
sterile decay
oscillations w/ν
4
invisible decay
✓✓ ✓✓ [150,154]
(3+1)w/sterile
decay
ν
4
→fν
e
✓✓ ✓✓ [158,161–675]
Matter effects
sections 3.1.4,
3.1.7
(3+1)w/anom-
alous matter
effects
ν
μ
→ν
e
via matter
effects
✓✓ ✗✗ [142,146,676–678]
(3+1)w/quasi-
sterile neutrinos
ν
μ
→ν
e
w/reso-
nant ν
s
matter
effects
✓✓ ✓✓ [147]
Flavor violation
section 3.1.6
Lepton-flavor-vio-
lating μdecays
m
nna
++
ee✓✗ ✗✗ [173,174,679]
neutrino-flavor-
changing
bremsstrahlung
ν
μ
A→efA✓✓ ✗✗ [680]
Decaysin flight
section 3.2.3
Transition magn-
etic mom., heavy ν
decay
N→νγ ✗✓ ✗✗ [205]
Dark sector heavy
neutrino decay
N→ν(X→e
+
e
−
)
or N→ν(X→γγ)
✗✓ ✗✗ [206]
Neutrino scattering
sections 3.2.1,
3.2.2
neutrino-induced
upscattering
νA→NA,N→
νe
+
e
−
or N→νγγ
✓✓ ✗✗ [203,204,207–214]
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
65
Table 10. (Continued.)
Category Model Signature Anomalies References
LSND MiniBooNE Reactors Sources
Transition magn-
etic mom. or
polarizability
photons
νA→NA,N→νγ
or νA→νγA
✓✓ ✗✗[40,184,186,187,189,191,218,232,681]
Dark matter Scat-
tering
section 3.2.4
dark particle-
induced
upscattering
γor e
+
e
−
✗✓ ✗✗ [215]
dark particle-
induced inverse
Primakoff
γ✓✓ ✗✗ [215]
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
66
Table 11. Summary of future experimental prospects to probe new physics explanations of the anomalies. We emphasize that all experiments can
constrain the new physics models discussed in this paper in one way or another, but we list those that can provide a direct test of the respective
model.
Source 3 +1 oscillations
Anomalous
matter effects Lepton flavor violation
Decays in
flight
Neutrino-
induced
upscattering
Dark-particle-induced
upscattering
Reactor DANSS upgrade, JUNO-
TAO, NEOS II, Neutrino-4
upgrade, PROSPECT-II
Radioactive
source
BEST-2, IsoDAR, THEIA,
Jinping
Atmospheric IceCube upgrade, KM3NET, ORCA and ARCA,
DUNE, Hyper-K, THEIA
IceCube upgrade, KM3NET, ORCA and
ARCA, DUNE, Hyper-K, THEIA
Pion/kaon decay-
at-rest
JSNS
2
, COHERENT, CAP-
TAIN-Mills, IsoDAR,
KPIPE
JSNS
2
, COHERENT,
CAPTAIN-Mills, Iso-
DAR, KPIPE, PIP2-BD
COHERENT, CAP-
TAIN-Mills,
KPIPE, PIP2-BD
Beam Short
Baseline
SBN SBN
Beam long
baseline
DUNE, Hyper-K, ESSnuSB DUNE, Hyper-K, ESSnuSB, FASERν, FLArE
Muon decay-in-
flight
νSTORM νSTORM
Beta decay and
electron
capture
KATRIN/TRISTAN, Project-
8, HUNTER, BeEST,
DUNE-
39
Ar, PTOL-
EMY, 2νββ
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
67
4.1.2. Pion decay-in-flight accelerator experiments
4.1.2.1. Short-baseline experiments.MiniBooNE. While MiniBooNE’sν
e
and
¯
n
e
appearance searches in the Fermilab BNB have resulted in the observation of anomalous
excesses, MiniBooNE BNB ν
μ
and
¯
n
m
CC measurements have been relatively well
understood, including a disagreement between data and the Monte Carlo prediction that has
been attributed to cross-section effects and uncertainties [270]. As a result, MiniBooNE has
been able to perform searches for ν
μ
and
¯
n
m
disappearance, both exclusively, and inclusively,
resulting in limits (using approximately the first half of data collected by MiniBooNE)as
shown in figure 42 [271]. The results complement those from prior short-baseline ν
μ
and
¯
n
m
disappearance searches, from the CCFR [272]and CDHS [273]experiments.
It should be noted that, in these searches, due to the lack of a near detector (ND), large
flux and cross-section uncertainties limited MiniBooNE’s sensitivity particularly in the high
Δm
2
range, where (fast)oscillations are expected to lead to an overall normalization deficit,
and are thus masked by systematic uncertainties on the overall ν
μ
and
¯
n
m
CC rate
normalization. More powerful searches were performed by MiniBooNE in combination with
measurements by the SciBooNE experiment, as described next.
MiniBooNE/SciBooNE. The SciBooNE experiment was located 100 m downstream
from the BNB target and ran simultaneously with MiniBooNE from 2007 to 2008. A
simultaneous ν
μ
disappearance search under a (3+1)scenario was performed in the
SciBooNE and MiniBooNE detectors with the BNB operating in forward horn current mode
[274]. A separate
¯
n
m
disappearance search was performed in the SciBooNE and MiniBooNE
detectors with the BNB operating in reverse horn current mode [275]. Exclusion (at 90% CL)
Figure 41. The KARMEN sterile neutrino 90% C.I. compared to other then
contemporary experiments. Reprinted (figure)with permission from [20], Copyright
(2002)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
68
regions for these two searches are shown in figure 43, and are consistent with exclusion limits
from other accelerator-based neutrino experiments, including the short-baseline CCFR and
CDHS experiments, and the long-baseline MINOS experiment [276], as well as a
MiniBooNE-only search limit.
MiniBooNE-NuMI. In addition to neutrinos from the BNB, MiniBooNE has also been
able to study neutrinos from the Fermilab-based NuMI beam, viewed by MiniBooNE at an
off-axis angle of 6.3°[277]. MiniBooNE measured both ν
e
and ν
μ
CCQE events from the
NuMI off-axis beam (with no wrong-sign discrimination), as shown in figure 44 (top). While
an appearance or disappearance search with these data sets was not performed by
MiniBooNE
124
, the data was found to agree with expectation. The NuMI off-axis beam at
the MiniBooNE location is much higher in ν
e
content than the BNB, as well as in neutrinos
contributed from kaon decays in the beamline. Because of a higher intrinsic ν
e
background,
this data set was particularly limited in sensitivity to light sterile neutrino oscillations.
Figure 42. MiniBooNE’s 90% CL sensitivity (dashed line)and limit (solid line)for ν
μ
(top)and
¯
n
m
(bottom)disappearance under a 3 +1 scenario. Previous limits by CCFR
(dark grey)and CDHS (light grey)are also shown. Reprinted (figure)with permission
from [271], Copyright (2009)by the American Physical Society.
124
The MiniBooNE-NuMI ν
e
data set has been analyzed under a 3 +1 appearance scenario in [94], where it was
shown that, despite the small observed data excess, the data showed no significant preference for oscillations over the
null hypothesis.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
69
MicroBooNE. Recently MicroBooNE has published its first results on direct oscillation
searches due to light sterile neutrinos [278]. The analysis uses high-statistics CC ν
μ
and CC ν
e
selections, developed as part of the inclusive ν
e
search [279], with data collected over a three
year period with a total exposure of 6.369 ×10
20
protons-on-target, representing
approximately half of the total MicroBooNE data-set. A full 3 +1 neutrino model was
studied, capitalizing on the seven channels of ν
e
and ν
μ
selections. Although a small deficit of
ν
e
was observed, the data was found to agree with the 3ν(no-sterile)hypothesis within the 1σ
level. Since the data was found to be consistent with the no-sterile hypothesis, exclusion
contours were calculated and can be found in figure 45, where regions of the LSND anomaly
at both high Δm
2
and low Δm
2
were excluded. As the analysis makes use of a a very pure ν
e
selection, exclusions are shown both for ν
e
appearance (
)qmesin 2
2
and ν
e
disappearance
(
)qeesin 2
2
profiling over the other parameters of the full 3 +1fit.
This work highlighted an important aspect of studying full 3 +1 neutrino oscillations in
the BNB. As the BNB is a ν
μ
dominated beam with a non-negligible intrinsic ν
e
component,
cancellation can occur in any ν
μ
→ν
e
appearance signal due to ν
e
→ν
e
disappearance
occurring in parallel. This cancellation can lead to a diminished oscillation effect in
comparison to when one studies the (un-physical)2νapproximation. The use of the NuMI
beam, which has a different ratio of intrinsic ν
e
to ν
μ
could help break this cancelletion effect
and includion of the NuMI beam data in the 3 +1 result is an ongoing effort for the
MicroBooNE collaboration.
Prior to this collaboration result, the publicly available MicroBooNE ν
e
CC data sets
[279–282]have also been studied by the phenomenology community [179,283]and in
combination with the MiniBooNE data by the MiniBooNE collaboration [284]. Although
these studies involve several assumptions and approximations that are not inherent in the
official results, the qualitative conclusions are largely the same, with the exception of the
analysis [283]which founds a preference for ν
e
disappearance at the ∼2σlevel but notably
did not use the full systematic uncertainty accounting of the collaboration’s data release.
However, a more recent analysis [179], as well as the official collaboration release,
incorporated systematic uncertainties from the collaboration’s data release and accounting for
Figure 43. MiniBooNE-SciBooNE 90% CL limits from a joint ν
μ
disappearance search
(left)[274]and a joint
¯
n
m
disappearance search (right)[275]. Reprinted (figure)with
permission from [274,275], Copyright (2012)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
70
Figure 44. Top: reconstructed energy distributions of ν
μ
(left)and ν
e
(right)events in
MiniBooNE from the NuMI off-axis beam. The figure is from [277]. Bottom: limit
extracted from a fit to the ν
e
distribution under a 3 +1 hypothesis. Reprinted (figure)
with permission from [94,277], Copyright (2009)by the American Physical Society.
Figure 45. The MicroBooNE 3 +1 CLs exclusion contours at the 95% CL in the plane
of Dm41
2versus (left)qm
sin 2 e
2and (right)q
sin 2
ee
2. A full 3 +1 treatment was
implemented, with parameters not shown profiled over for the sensitivity and resulting
data exclusions. Shown also is the (unphysical)ν
e
appearance-only and ν
e
disappearance-only sensitivities for comparison. Reproduced from [278].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
71
neutrino energy reconstruction smearing found this preference for ν
e
disappearance to be
statistically insignificant.
Reference [179]has also provided the first analysis of the effect of MicroBooNE’sν
e
results in the context of a light sterile neutrino explanation of MiniBooNE. This includes both
an analysis in the ‘simplified two-flavor’model, in which only ν
μ
→ν
e
oscillations are taken
into account, without significant ν
μ
→ν
μ
or ν
e
→ν
e
effects, consistent with MiniBooNE
analyses prior to 2022 as well as the complete 3 +1 model. It is found that, while
MicroBooNE prefers the null hypothesis, i.e. no new sterile neutrino, the allowed regions
from MiniBooNE at ∼3σare still allowed at the same confidence level by the MicroBooNE
results, see left panel of figure 46. Given its large dataset, the results of MicroBooNE’s
inclusive analysis [279]are found to be the most statistically powerful, while the CCQE
sample provides a considerably weaker constraint. Besides that, the MiniBooNE collabora-
tion has performed a fit of both MiniBooNE and MicroBooNE CCQE data [281]to a 3 +1
sterile neutrino model [284], properly accounting for oscillations in the backgrounds. As
expected, the impact of adding MicroBooNE’s CCQE sample to the fit has a marginal effect
on the preferred regions for the 3 +1 model, see right panel of figure 46. While the two
experiments’results are combined into a joint likelihood, the systematic uncertainties that the
two experiments have in common, particularly those associated with their common neutrino
flux from the booster neutrino beam and the neutrino-nucleus cross section model, have not
been combined.
NOMAD. The NOMAD experiment [285], which ran at CERN using protons from the
450 GeV SPS accelerator, employed a conventional neutrino beamline to create a wideband
2.5–40 GeV neutrino energy source. These neutrinos were created with a carbon-based, low-
mass, tracking detector located 600m downstream of the target. This detector had fine spatial
resolution and could search for muon-to-electron and muon-to-tau oscillations. No signal was
observed in either mode, and this experiment set a limit to ν
μ
→ν
e
appearance that excluded
Figure 46. Left: preferred regions in the simplified two-flavor model for MiniBooNE
(gray), MicroBooNE inclusive analysis (blue), MicroBooNE CCQE analysis (red),
KARMEN (green), and OPERA (brown)as indicated. For reference, the predicted
sensitivity of SBN is also shown. Reproduced from [179].CC BY 4.0. Right: preferred
regions in the 3 +1 model parameter space for a MiniBooNE-only fit and a joint fit
including the MicroBooNE ν
e
CCQE result. Reproduced from [284].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
72
the majority of the 99% CL-allowed LSND region above 10 eV
2
at 90% CL, but had a
significantly worse limit than KARMEN below 10 eV
2
.
CCFR. The CCFR experiment was carried out at Fermilab in 1984 [286].Theexperiment
made use of a narrow band beamline, with meson energies set to 100, 140, 165, 200, and 250
GeV, yielding ν
μ
and
¯
n
m
beams that ranged from 40 to 230 GeV in energy. A two-detector
experimental setup carried out a disappearance search, with the ND at 715 m and the far detector
(FD)at 1116 m from the center of the 352 m long decay pipe. The calorimetric detectors were
constructed of segmented iron with a scintillator and spark chambers, and each had a
downstream toroid to measure the muon momentum. The data showed no evidence for a
distance-dependent modification of the neutrino flux and ruled out oscillations of ν
μ
into any
other single type of neutrino for 30 <Δm
2
<1000 eV
2
and
()q>-sin 2 0.02 0.20
2.
CDHS. The CDHS experiment [287]at CERN searched for ν
μ
disappearance with a two-
detector design of segmented calorimeters with iron and scintillator. The experiment used
19.2 GeV protons on a beryllium target to produce mesons that were subsequently focused
into a 52 m decay channel. The detectors were located 130 m and 885 m downstream of the
target. The experiment set a limit at 95% CL and set constraints that are comparable to the
MiniBooNE ν
μ
disappearance limit described above, but extending to slightly lower Δm
2
.
4.1.2.2. Long-baseline experiments. The phenomenology of sterile neutrino-driven
oscillations at long baselines consists of interference phenomena arising from at least two
distinct oscillation frequencies and several scale-determining mixing angles and phases. In the
context of a 3 +1 model with the addition of one new flavor state ν
s
and a new mass state ν
4
extending the three-flavor PMNS matrix to a 4 ×4 unitary matrix, and assuming the
parametrization U=R
34
R
24
R
14
R
23
R
13
R
12
, the extended matrix is written as:
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
()
()
()
()
=-+
-+-
---
dd
mm ddd d
tt ddd
ddd
--
--+ -
--
--
U
UU sc s
UU sss csc cs
U U csss cc c ss c s ccs
U U cs s c ccs sscc ccc
ee
ee
ee
ee
,
35
ee
ss
12 i13 14 14
12 i13 14 24 13 23 24 i14 24
12 i13 23 24 34 13 23 34 i13 14 24 34 14 24 34
12 i13 23 24 34 13 23 34 i13 14 24 34 14 24 34
13 14
13 14 24 24
24 13 14
24 13 14
which introduces three new mixing angles, θ
14
,θ
24
, and θ
34
, two new CP violating phases, δ
14
and δ
24
, and one new linearly independent mass-splitting that is chosen to be
D
m41
2in this
case. Neglecting Δ
21
and using unitarity to rewrite any terms containing U
α1
or U
α2
, the
probability of ν
μ
survival in a 3 +1 model can be written as
() ∣∣(∣∣∣∣)
∣∣∣∣ ∣∣( ∣∣ ∣∣) ()
nn»- - - D
-D---D
mm m m m
mm m m m
PUUU
UU U U U
14 1 sin
4sin41 sin.36
3232422
31
32422
43 4 232422
41
Of particular interest are NC neutrino interactions, since as the three active flavors
participate in the NC interaction at the same rate, the NC sample is insensitive to three-flavor
oscillations between ND and FD. However, if a sterile neutrino exists, sterile-neutrino
appearance would cause a depletion in the NC channel. The NC survival probability is thus
defined as 1 −P(ν
μ
→ν
s
). Similar to equation (36), this can be written as
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
73
() ∣∣∣∣
∣∣∣∣
()( )
()( ) ( )
nn-»- D
-D
- D-D+D
- D+D-D
mm
m
PUU
UU
Z
Z
114sin
4sin
4 Re sin sin sin
2 Im sin 2 sin 2 sin 2 , 37
ss
s
32322
31
42422
41
231 243 241
31 43 41
where
**
=
mm
ZUUUU
ss4433
. The phenomenology of ν
μ
-CC and NC disappearance driven by
sterile neutrino oscillations is complicated at long baselines due to the interference of three-
flavor oscillations and sterile oscillations, which do not occur at short baselines. To perform
two-detector analyses typical of long-baseline accelerator neutrino experiments, effects at
both short and long baselines must thus be understood.
For instance, in the case of the short-baseline oscillation, only probed by the ND, the
oscillation probability for NC disappearance is approximately given by
() ()nn q q q-»- D
m
P
1
1 cos cos sin 2 sin , 38
s414 234 224 241
where
D
=
D
ji
mL
E4
ji
2
. For the typical beam neutrino energies and ND baselines, when
D
<m0.05
41
2, oscillations are not visible in the ND. Starting at
D
m41
2∼0.5 eV
2
, oscillations
begin to be visible at low energies in the ND, and as
D
m41
2increases, the first oscillation
maximum moves to higher energies. At sufficiently high
D
m41
2values, the entire ND sees
rapid oscillations that can no longer be resolved and are seen as a constant normalization shift
described by
() ()nn q q q-»-
m
P
1
11
2cos cos sin 2 . 39
s414 234 224
For ν
μ
-CC at the ND, the oscillation probability can be approximated as
() ()nn q»- D
mm
P1 sin 2 sin , 40
224 241
which behaves similarly to NC disappearance except it depends only on θ
24
, and in the rapid
oscillation case the normalization shift is given by
(
)q12sin2
224.
However, when considering long baselines, terms oscillating at the atmospheric
frequency cannot be neglected. Approximating the NC disappearance probability to first
order in small mixing angles gives
()
()
nn q q q
qq
dq q
-»- D
-D
+D
m
P1 1 cos cos sin 2 sin
sin sin 2 sin
1
2sin sin sin 2 sin . 41
s414 234 224 241
234 223 231
24 24 23 31
In this expression, the first term is identical to the short-baseline approximation. The second
and third terms both oscillate at the atmospheric frequency. If θ
34
>0, the second term is non-
zero, and if dsin 24 and θ
24
are non-zero, the third term will not be zero. In either case, this
creates an oscillation dip visible at the FD regardless of the value of
D
m41
2. It is notable that
this will happen even though NC disappearance cannot occur in the standard three-flavor
paradigm. It should also be noted that the third term is CP-odd, since NC disappearance is
effectively sterile neutrino appearance, so
¯
n
data will also add to the sensitivity of long-
baseline experiments to sterile neutrinos.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
74
For ν
μ
-CC disappearance, expanding to second order in small mixing angles one finds
()
()
nn q q
q
»- D
-D
mm
P1 sin 2 cos 2 sin
sin 2 sin , 42
223 24 231
224 241
which can be rewritten as
()
()
nn q
qq
q
»- D
+D
-D
mm
P1 sin 2 sin
2 sin 2 sin sin
sin 2 sin . 43
223 231
223 224 231
224 241
The first term is the standard approximation for three-flavor ν
μ
-CC disappearance. The second
term also oscillates as a function of
D
m31
2, the atmospheric frequency, but it is driven by
sterile mixing. Even at large
D
m41
2values, this term does not enter into rapid oscillations.
Thus, even for large mass splittings where the ND is well inside the rapid oscillation regime,
the FD will still show shape variations in addition to normalization changes due to the terms
oscillating at the atmospheric frequency with a magnitude that scales with
qsin
224.
Furthermore, when considering ν
μ
disappearance alone, one could define an effective
atmospheric mixing angle to account for both sterile and standard oscillations by combining
the first two terms in equation (43):
()qqq=
s
in 2 sin 2 cos 2 . 44
223
eff 223 24
While it may seem this would imply that the depth of the atmospheric dip would be
insensitive to the large
D
m41
2regime, it actually provides a constraint due to
q
23
eff having been
measured to be close to maximal. Due to the
qcos 2 24
factor, a non-zero θ
24
can only drive
q
23
eff
away from maximal.
In addition, experiments that can make precise measurements of ν
e
CC interactions can
look for ()
n
-
e-CC disappearance at the far detector following
()
()
() ()
nn q
q
»- D
-D
--
P1 sin 2 sin
sin 2 sin , 45
ee 213 231
214 241
valid only if one assumes sterile-driven muon neutrino disappearance and electron neutrino
appearance do not occur.
Finally, it is worth noting the near detectors of long-baseline experiments can be used to
conduct short-baseline searches following the same methodologies described in
section 4.1.2.1
MINOS/MINOS+. The main injector neutrino oscillation search (MINOS)experiment
was a long-baseline neutrino oscillation experiment using the neutrinos at the main injector
(NuMI)neutrino beam and two detectors placed within a 735 km baseline. The NuMI beam is
produced by collisions with a graphite target of protons accelerated to 120 GeV at Fermilab’s
Main Injector. The secondary products of these collisions, pions, and kaons, are focused by
two parabolic magnetic horns and eventually decay into muons and neutrinos inside a 675
m-long decay pipe filled with helium. The muons are absorbed in the rock and neutrinos
continue towards the 1 kton ND, 1 km downstream of the target, and beyond, towards the
5.4 kton FD. The relative positions of target and horns can be changed to tune the beam
spectrum to lower or higher neutrino energies. The MINOS run concluded in 2012, with a
total exposure of over 15 ×10
20
protons-on-target (POT)in neutrino and antineutrino mode
since the start of data taking in 2005. The MINOS+experiment operated the MINOS
detectors using the NuMI beam upgraded from 320 to 700 kW of beam power, part of the
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
75
NOvA experimental setup. Instead of the low-energy configuration used for the MINOS run,
MINOS+used the NOvA medium-energy configuration, which for MINOS+corresponds to
a neutrino energy spectrum peaked around 7 GeV, as shown in figure 47. Exposure of the
MINOS+detectors to a beam peaked above the three-flavor oscillation maximum provided
excellent sensitivity to new physics through precise measurements of muon neutrino
disappearance between the ND and FD. MINOS+operated from 2014 through 2016 and
accumulated only neutrino mode data. A combined analysis of the 10.6 ×10
20
POT of
MINOS neutrino data and 5.8 ×10
20
POT of MINOS+neutrino data using a two-detector
fitting technique placed stringent limits on sterile driven muon neutrino disappearance within
a3+1 model, as shown in figure 48 [139]. The null results from MINOS/MINOS+are one
of the primary drivers, along with IceCube results, of the large tension between appearance
and disappearance data when attempting to explain observations purely through sterile
neutrino mixing. This is further evidenced in combinations with reactor data looking for
electron (anti)neutrino disappearance, as described in section 4.1.3.4
NOvA. The NuMI off-axis ν
e
appearance (NOvA)experiment is a long-baseline
accelerator neutrino experiment based at Fermilab and the Far Detector Laboratory at Ash
River, Minnesota. NOvA has as its primary goal to measure three-neutrino mixing
parameters, including the determination of the neutrino mass ordering, by looking for the
appearance of electron neutrinos or antineutrinos, and the disappearance of muon neutrinos or
antineutrinos, using the NuMI neutrino beam produced at Fermilab. This is accomplished by
using two detectors separated by 810 km, placed 14 mrad off the NuMI beam axis. Due to the
off-axis placement, the detectors sample a narrow range of neutrino energies between 1 and
4 GeV, peaking at 2 GeV as shown in figure 49. This configuration is chosen to drastically
reduce the feed-down of NC interactions of higher-energy neutrinos, which typically
represent the dominant background to the measurement of ν
e
CC interactions in on-axis
experiments. The 0.33 kton ND is located underground next to the MINOS ND hall at
Fermilab, while the 14 kton FD is positioned at the surface in Ash River, Minnesota. Both
detectors are composed of extruded 32-cell PVC modules filled with liquid scintillators. The
Figure 47. The NuMI neutrino energy spectrum for the MINOS+medium-energy tune,
shown as the red solid line. The NOνA spectrum shown in blue is obtained with the same
tune at a 14 mrad offset from the beam axis (MINOS+is on-axis). For comparison, the
spectrum corresponding to the NuMI low-energy tune used by MINOS is shown as
the gold histogram. Reprinted from [644], with the permission of AIP Publishing.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
76
cells are read out by 32-pixel avalanche photodiodes (APDs). NOvA began collecting data in
2014 and has so far accumulated large samples in both neutrino-dominated and antineutrino-
dominated modes.
NOvA placed constraints on sterile neutrinos via searches for differences in the rate of
NC neutrino interactions between the Near and Far detectors. The analysis was based on
6.05 ×10
20
protons-on-target taken in neutrino-dominated mode, and 95 NC candidates were
selected at the Far Detector compared with 83.5 ±9.7(stat.)±9.4(syst.)events predicted
assuming mixing only occurs between active neutrino species. Therefore, NOvA found no
evidence of active-sterile neutrino mixing. Interpreting these results within a 3 +1 model
results in constraints on the sterile mixing angles of θ
24
<20.8°and θ
34
<31.2°at the 90% C.
L. for 0.05 eV Dm0.5
241
2eV
2
, the range of mass splittings for which no significant
oscillations over the ND baseline are expected [288]. The energy spectrum of the NC selected
candidates at the Far detector is shown along with a comparison of the allowed regions for the
sterile matrix elements obtained by NOvA with similar constraints by SuperK and IceCube-
DeepCore in figure 50.
NOvA has also reported results on the first search for sterile antineutrino mixing in an
antineutrino beam, using an exposure of 12.51 ×10
20
protons-on-target from the NuMI beam
at Fermilab running in antineutrino-dominated mode. NOvA observed 121 NC antineutrino
candidates at the FD, compared to a prediction of 122 ±11(stat.)±15(syst.)assuming
mixing between only three active flavors. Therefore, no evidence for
¯¯
n
n
m
s
oscillations is
observed. In this case the 3 +1 model constraints on the mixing angles are found to be θ
24
<25°and θ
34
<32°at the 90% C.L. for Dm
0
.05 eV 0.5 eV
241
22[289]. The
Figure 48. The MINOS and MINOS+90% Feldman–Cousins exclusion limit
compared to the previous MINOS result [645]and results from other experiments.
The Gariazzo et al region is the result of a global fit to neutrino oscillation data [646].
Reproduced from [139].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
77
antineutrino energy spectrum at the FD and obtained allowed regions are shown in figure 51.
Finally, NOvA has recently presented results from a two-detector fit at Neutrino 2022, using
similar techniques to the MINOS/MINOS+experiment, extending limits on the θ
24
and θ
34
angles over a large range of
D
m41
2values. These results are presented in figure 52.
T2K. The Tokai-to-Kamioka experiment [290]is a neutrino oscillation experiment based
in Japan. T2K’s primary goal is to measure three flavor neutrino oscillation parameters. An
intense source of (anti)neutrinos is produced at J-PARC and is directed toward a series of
detectors placed 280 m from the target, and a massive detector 295 km away (Super-
Kamiokande, SK [291]). The neutrino beam composition is predominantly muon neutrino
flavor, with a small (0.5%)fraction of electron neutrinos [292]; the beamline elements can be
configured to produce a predominantly antineutrino beam as well. The ‘near detectors’
include the INGRID detector [293], WAGASCI detectors [294,295], and ND280 detector
suite. These detectors observe interactions from slightly different neutrino energy spectrums,
with INGRID’s peak neutrino energy approximately at 1 GeV (on-axis), ND280 at 0.6 GeV
(2.5 degrees off-axis), and WAGASCI at 0.8 GeV (1.5 degrees off-axis). T2K has operated
since 2009 and has produced a series of results on light sterile neutrinos using the ND280
detectors and SK with subsets of the data taken. T2K plans to install improvements to the
ND280 detector [296], and, with improvements to the beamline, T2K will have further
opportunities for updated or expanded analyses between detectors.
CC electron neutrino interactions were selected in ND280 to test for 3 +1ν
e
disappearance, motivated by radiochemical experiments [71,72,297]and discrepancies in
reactor experiments energy spectra [66]. Isolating CC ν
e
candidates was challenging, with
significant backgrounds to the ν
e
selection from photons (from, for example, the inactive
material surrounding the active scintillator target). These backgrounds were controlled by
dedicated photon selections and with additional systematic uncertainty estimation on the
production of π
0
from neutrino interactions on non-scintillator materials. The analysis also
Figure 49. The plot on the left displays the predicted neutrino energy spectra of the
NuMI beam during the NOνA run, including the on-axis spectrum sampled by MINOS
+as the dotted line, as well as the spectrum at different off-axis positions. The 14 mrad
off-axis position of the NOvA detectors is identified by the red line. The plot on the
right shows neutrino energy as a function of the parent pion energy and the angle
between the neutrino and the decaying pion. Reproduced with permission from [647].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
78
assumes no ν
μ
disappearance, and systematic uncertainty from the flux and cross section
models were reduced using dedicated ν
μ
selections as is done for T2K three flavor oscillation
analyses. T2K excludes regions of interest at 95% CL with 5.9×10
20
POT between
approximately q>sin 2 0.3
ee
2and
D
>m7eV
eff
22
[298]. An updated analysis of large mixing
regions would be useful in light of recent MicroBooNE results [280].
A search for light sterile neutrinos using SK has been performed in 2019 [299], using
14.7×10
20
(7.6×10
20
)POT in neutrino (antineutrino)mode. It is focusing on a 3 +1 model
where a single sterile neutrino is added and assumed to be mixing with ν
2
and ν
3
mass
eigenstates through new parameters θ
24
and θ
34
(T2K has limited sensitivity to other
parameters, that are thus neglected θ
14
=δ
14
=δ
24
=0°).
The analysis consists of a simultaneous fit of the CC muon, electron and NC neutrino
samples. While CC channels are mainly sensitive to the new mass splitting
D
m41
2and to θ
24
,the
NC channel measures the active neutrino survival probability and is also sensitive to θ
34
.The
five CC analysis samples are the same as the one used in standard oscillation analyses [300],but
it has been the first time NCπ
0
(single π
0
production where the pion decays and produces two
Cherenkov rings)and NC γ-deexcitation samples are used in oscillation measurements.
Figure 50. Left: calorimetric energy spectrum for NC neutrino candidates in the NOvA
FD data compared with three-flavor prediction; right: the NOvA 68% (dashed)and 90%
(solid)Feldman–Cousins non-excluded regions (shaded)in terms of |U
μ4
|
2
and |U
τ4
|
2
,
where it is assumed that
q=cos
1
214
in both cases, compared to SuperK and IceCube-
DeepCore constraints. Reprinted (figure)with permission from [288], Copyright (2017)
by the American Physical Society.
Figure 51. Left: calorimetric energy spectrum for NC antineutrino candidates in the
NOvA FD data compared with three-flavor prediction; Right: the NOvA 68% (dashed)
and 90% (solid)Feldman–Cousins non-excluded regions (shaded)in terms of |U
μ4
|
2
and |U
τ4
|
2
, where it is assumed that
q=cos
1
214
in both cases, compared to SuperK
and IceCube-DeepCore constraints. Reproduced from [289].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
79
Most of the systematic parameters are constrained in the same way as in the 3 flavor
analysis (using e.g. ND constraints), but additional 30% normalization uncertainties are added
for the new NC samples. The joint maximum-likelihood fits allows to draw exclusion limits in
the
(
)qDmsin ,
224 41
2plane: the most stringent limits on θ
24
are obtained for
D
<´ -
m310eV
41
232
. Similarly, limits in the
()
qqqsin , cos sin
224 224 234 plane have been
obtained although more statistics in the NC samples and additional systematic studies are
needed to further improve the measurement. A comparison of the exclusion regions obtained
with other existing constraints is shown in figure 53.
One limitation of work to date on T2K is the completeness of the assessment of
interaction model uncertainties as applied to short-baseline analyses. T2K analyses so far
assume no ν
μ
disappearance, however the interaction model systematic uncertainties are
assessed based on external and ND280 measurements. Those measurements are placed close
to production and therefore could be sensitive to a ν
μ
disappearance signal, potentially biasing
a dedicated ν
μ
disappearance search. T2K studied the possible impact of a subset of
interaction model uncertainties on a ND280 ν
μ
disappearance result [301]and found it to be
robust, but this does not consider a full re-assessment of where external data is used to inform
the model. Current efforts in T2K cross-section measurements and the implementation of
ab initio computations in the context of three-flavor analysis would greatly benefit such
studies as well. Certain event selections, like coherent neutrino interactions or low ν
selections [302]may have better theoretical understanding for a single detector analysis, but
can be challenging to use due to statistics or acceptance for T2K.
In the future, joint analyses, including ν
μ
disappearance, ν
e
appearance/disappearance
may also be performed either between several near detectors (with different technologies and/
Figure 52. Left: NOvA 90% Feldman–Cousins excluded region in
qsin
224 versus Dm41
2,
obtained from a two-detector fitting method, compared to allowed and exclude regions
from other experiments. Right: NOvA 90% Feldman–Cousins excluded region in
qsin
234
versus Dm41
2, compared to limits reported by other experiments. Reproduced
from [648].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
80
or neutrino energy spectra)or benefiting from the complementary coverage of near versus far
facilities. The upgraded near detector, for example, will have improved detection thresholds
and sensitivity to neutrons, possibly enabling the selection of NC events at the near site.
OPERA and ICARUS. The Oscillation Project with Emulsion-tRacking Apparatus
(OPERA)was a long-baseline accelerator neutrino experiment that sampled the CERN
Neutrinos to Gran Sasso (CNGS)beam with a detector placed at the Gran Sasso laboratory
(LNGS)730 km from the neutrino production source, having as primary physics goal to
observe ν
μ
→ν
τ
appearance. This goal required the use of emulsion detection technology,
such that the detector was a hybrid apparatus made of a nuclear emulsion/lead target
complemented by electronic detectors. The detector ‘target’region had a total mass of about
1.25 kt and was composed of two identical sections, each with 31 walls of emulsion cloud
chamber bricks, interleaved by planes of horizontal and vertical scintillator strips used to
select bricks in which a neutrino interaction had occurred. The exquisite spatial resolution
afforded by the emulsion layers enabled the identification of the characteristic ‘kink’due to
the decay of the final-state τparticle from a ν
τ
interaction. The target region was
complemented by a magnetized muon spectrometer.
Reconstruction of neutrinos interacting within the emulsion layers was conducted by
automated scanning robots. Due to the high-energy tau production threshold (nt
E
3.5
GeV), the CNGS neutrino flux was distributed at higher energies than other LBL experiments,
as shown in figure 54 [303]. OPERA collected CNGS beam data from 2008 to 2012, with an
integrated exposure of 17.97 ×10
19
protons-on-target. A total of 19 505 neutrino interaction
events in the detector target were recorded by the electronic detectors, of which 5603 were
fully reconstructed in the emulsion layers.
Figure 53. The T2K 90% CL. exclusion limits on
qsin
224 as a function of Dm41
2
compared to other experiments. Areas on the right are excluded. Reproduced from
[299].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
81
OPERA used its full data sample to conduct a search for sterile neutrino mixing within
the context of a 4-flavor (3 active +1 sterile)model based on both the ν
τ
and ν
e
appearance
channels, with the ν
μ
CC disappearance channel not being considered given the low
sensitivity to sterile mixing for that channel due to ambiguities with potential NC
disappearance [34].Defining ∣∣∣∣q=
mt t m
UUsin 2 4
24242,∣∣∣∣q=
mm
UUsin 2 4
ee
24242, exclusion
regions of
D
m41
2versus
q
m
t
sin 2
2
and
q
m
sin 2
e
2were computed and are shown in figure 55. The
result is restricted to positive
D
m41
2values since negative values are disfavored by results on
the sum of neutrino masses from cosmological surveys [304]. The results are consistent with
no active-sterile neutrino mixing. For
D
>m0.1eV
41
22, the upper limits on
q
m
t
sin 2
2
and
q
m
sin 2
e
2are set to 0.10 and 0.019 both for the case of Normal Ordering and Inverted
Ordering. The values of the oscillation parameters
(
)qD= =
m
m0.041eV , sin 2 0.92
e
41
222
corresponding to the MiniBooNE combined neutrino and antineutrino best-fit[32]are
excluded with a p-value of 8.9 ×10
−4
, corresponding to a significance of 3.3σ.
The ICARUS (imaging cosmic and rare underground signals)experiment operated the
T600 liquid argon time projection chamber detector, with a fiducial mass of 447 tons, exposed
to the same CNGS beam as OPERA, and located at the same 730 km from the neutrino
production target in the LNGS. The baseline and CNGS beam typical energy determine that
ICARUS is primarily sensitive to sterile mixing in the region where L/E∼36.5 km GeV
−1
.
ICARUS conducted a search for sterile neutrino mixing by looking for excess ν
e
appearance
in the data sample collected in 2010 and 2011. This search assumed a simplified two-flavor
model (one active, one sterile)and found no evidence of sterile neutrino oscillations, as
detailed in [305]. However, it was pointed out soon after the publication of the ICARUS
results that the limits obtained on
q
m
sin 2
e
2by using a two-flavor approximation (which works
well for a short-baseline experiment)in a long-baseline setup neglects sizable four-flavor
effects, induced by the interference of the new large squared-mass splitting
D
m41
2with the
atmospheric one. The analysis also neglected contributions to the four-flavor oscillation
probabilities arising from the intrinsic ν
e
component of the CNGS beam. It is estimated that
these four-flavor effects weaken the reported ICARUS constraints by up to a factor of 3 [306].
The ICARUS T600 detector has since been moved to Fermilab, where it will be operated as
the ‘Far’detector for Fermilab’s Short-Baseline Neutrino program. ICARUS completed
Figure 54. Fluxes of the different CNGS beam neutrino components at LNGS.
Reproduced from [303]. © 2009 IOP Publishing Ltd and SISSA. All rights reserved.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
82
installation at Fermilab in Spring 2022 (the last section of the cosmic ray tagger and
overburden)and is beginning its first physics run. The prospective ICARUS contributions to
the Fermilab SBN program are detailed in section 6.2.1.1.
4.1.3. Reactor neutrino experiments. A conclusive way to test whether RAA is due to
mixing between active and sterile neutrinos is by searching for baseline-dependent sterile
neutrino-induced spectral variations. In this section, we summarize the results from the
experiments that performed a relative spectral search for 3 +1
¯
n
e
oscillations induced by
active to sterile mixing. Relative oscillation searches curtail the dependence on the reactor
¯
n
e
spectrum model and detection efficiency by comparing the ratio of energy spectrum at
different baselines to the corresponding predicted ratio under the oscillation hypothesis.
Baseline-dependent spectral measurement is done either by using a segmented detector, a
single-volume movable detector, or by the use of multiple detectors placed at different
baselines. At reactor
¯
n
e
energies, since eV-scale neutrinos induce oscillations at meter scales,
Figure 55. Left: OPERA 90% C.L. exclusion region in the Dm41
2and q
mt
sin 2
2
parameter space for the normal (NH, solid line)and inverted (IH, dashed line)hierarchy
of the three standard neutrino masses. The exclusion regions by NOMAD [649]and
CHORUS [650]are also shown. Right: OPERA 90% C.L. exclusion region in the
Dm41
2and qm
sin 2 e
2plane is shown for the normal (NH, solid line)and inverted (IH,
dashed line)hierarchy of the three standard neutrino masses. The plot also reports the
90% C.L. allowed region obtained by LSND [19](cyan)and MiniBooNE combining ν
and ¯
n
mode [32](yellow). The blue and red lines represent the 90% C.L. exclusion
regions obtained in appearance mode by NOMAD [285]and KARMEN2 [20],
respectively. The 90% C.L. exclusion region obtained in disappearance mode by the
MINOS and DayaBay/Bugey-3 joint analysis [324]is shown as green line. The black
star (å)corresponds to the MiniBooNE 2018 best-fit values for the combined analysis
of νand ¯
n
data. Reproduced from [34].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
83
purpose-built experiments place their detectors as close to the reactor as possible, ideally <10
m. Furthermore, experiments built to search for θ
13
are also sensitive to sterile neutrino
oscillations but at lower oscillation frequencies, typically for
D
<m0.1eV
13
22
.
All the experiments discussed in this section use scintillator detectors and the IBD
interaction process, where a characteristic signature is provided by the timing and spatial
coincidence between prompt positron annihilation signal and delayed neutron capture signal
producing two separate flashes (Δt∼μs). Refer to section 2.3 for more details on the IBD
mechanism. Experiments also typically use an external neutron capture agent (other than
hydrogen), either Gadolinium or
6
Li, to increase IBD efficiency by increasing the neutron
capture cross-section.
6
Li has the added benefit of constraining the spatial extent of the
delayed signal since the capture products have high dE/dxin scintillators. In addition to the
delayed coincidence, experiments also use various combinations of active and passive
shielding, detector segmentation, and pulse shape discrimination (PSD)for background
reduction. PSD-capable scintillators generate pulse shapes that are particle-dependent and
could in principle be used for both prompt and delayed selection. Whenever possible,
experiments also measure reactor-off data to constrain reactor-uncorrelated IBD-mimicking
backgrounds. Following is a discussion of the individual reactor experiments that searched for
sterile neutrino-induced oscillations. A list of purpose-built experiments and their features
pertinent to the eV-scale oscillation search can be found in table 12.
4.1.3.1. Short-baseline experiments.DANSS. The Detector of AntiNeutrinos based on
Solid State Scintillator (DANSS)experiment [307]consists of 1 m
3
highly segmented, plastic
scintillator detector with each scintillator bar wrapped in Gd-loaded reflector. Light and signal
readout is performed using wavelength-shifting fibers and a combination of pixel photon
detectors and PMTs operated at room temperature. The experiment samples
¯
n
e
from a 3 GW
th
low enriched uranium (LEU)reactor at Kalinin Nuclear Power Plant in Russia. As opposed to
most other reactor
¯
n
e
experiments, the DANSS detector is located below the reactor core,
benefiting from its 50-meter water equivalent (m.w.e)overburden. The detector is placed on a
lifting platform which enables measurements at the baselines of 10.9 m, 11.9 m, and 12.9 m.
Due to its close proximity to the reactor core, the detector measures a high
¯
n
e
flux of around
4000 events per day.
The DANSS detector was commissioned in 2016 and started taking data in October
2016. The experiment has collected around 4 million signal events over three years at three
different positions. The biggest source of background that constitutes 13.8% of the IBD signal
events is the accidental coincidence background, along with non-negligible cosmogenic
backgrounds and IBD backgrounds from neighboring reactors. The data excludes a large area
in sterile neutrino parameter space (Δm
2
,
qsin 2
ee
2
)and most interestingly excludes the best-fit
point of RAA and Ga experiments at more than 5σlevel as shown in figure 56. Additionally,
the IBD positron spectrum was measured and compared to the simulated Huber-Mueller
spectrum. Although the measured spectrum disagrees with DANSS’s Huber-Mueller-derived
prediction, final oscillation measurements are largely independent of the choice of models due
to the ratios taken at different baselines [307].
NEOS. The Neutrino Experiment for Oscillation at Short baseline (NEOS)aims to
search for light sterile neutrinos by detecting electron antineutrinos (¯
n
e)from a reactor at a
very short baseline. The NEOS detector consists of a liquid scintillator (LS)target (∼1000
liter with ∼0.5% Gd loading by weight), two buffer zones filled with mineral oil where 19 8
inch PMTs per a zone are attached, and a muon veto system. NEOS had been installed in the
tendon gallery of the fifth reactor of the Hanbit Nuclear Power Plant in Korea for two periods,
from Aug. 2015 to May 2016 (NEOS-I)and from September 2018 to October 2020 (NEOS-
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
84
Table 12. Details of the short-baseline experiments that have been specifically built to search for eV-scale sterile neutrinos. Short baselines are
preferable for oscillation searches involving eV-scale sterile neutrinos. HEU reactors are typically ∼10xsmaller than commercial LEU power
reactors and are preferred for eV-scale oscillation searches since they have smaller source positions oscillation washout. Detector segmentation,
capture agent, and pulse shape discrimination capabilities are highly beneficial for background reduction.
Experiment Baseline (m)Reactor Reactor Detector Target Sterile ν
type power (MWth)Size Search Strategy
DANSS [682]11–13 LEU 3000 1 m
3
Segmented PS with Gd coating Multi-site
NEOS [133]24 LEU 2800 1 m
3
Single-volume GdLS +PSD Single-site
Neutrino-4 [498]6–12 HEU 90 2 m
3
Segmented GdLS Multi-site/zone
PROSPECT [134]7–9 HEU 85 4 m
3
Segmented
6
LiLS +PSD Multi-zone
STEREO [656]9–11 HEU 57 2 m
3
Segmented GdLS +PSD Multi-zone
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
85
II). For the NEOS-II, the modifications include newly produced target GdLS and a minor
modification in the muon veto system. With a 24 m baseline from the core of the reactor
(2.8 GW
th
in 100%)about 2000 IBD, ¯
n
+ +
+
pe n
e, events per day are observed. The
signal-to-background ratio is 22 thanks to relatively good overburden (∼20 m.w.e.).
Background contribution from the nearest neighboring reactor (d=256 m)is found to be less
than 1% of the total ¯
n
eflux from the fifth reactor. Calibration data using radioactive sources,
22
Na,
137
Cs,
60
Co, PoBe, and
252
Cf, had been taken regularly.
NEOS-I [133]using 180 (46)live days of reactor-ON (-OFF)data excluded the RAA
best fit at 90% C.L. by comparing the prompt energy spectrum of Daya Bay where the sterile
neutrino oscillation effect is averaged out. The best-fit was found at (sin
2
2θ,Δm
2
)=(0.05,
1.70 eV
2
)with χ
2
/NDF for 3νand 4νare 64.0/61, and 57.5/59, respectively. The
corresponding p-value is estimated to be 22%. The well-known ‘5 MeV excess’was clearly
observed as well in NEOS-I. Recently a joint analysis [308]between NEOS-I and RENO was
performed, yielding a slightly improved result beyond its previous result using early Daya
Bay data. More details on the NEOS-I and RENO joint analysis is discussed in the following
sub-section (section 4.1.3.3).
Neutrino-4. Neutrino-4 is the only reactor neutrino experiment performing relative
spectral comparison that has reported evidence of oscillations. The detector is a 1.8 m
3
Gd-
doped liquid scintillator detector divided into 10 rows each row consisting of 5 sections each
of size 0.225 m ×0.225 m ×0.85 m. The detector samples
¯
n
e
from the 57 MW
th
SM-3 reactor,
and HEU in Dimitrovgrad, Russia. A movable platform enables the detector to sample
baselines from 6 m–12 m. The short reactor on (off)cycles of 8–10 (2–5)days enable the
experiment to perform rapid signal and background measurements.
The detector collected data for five years from 2016 to 2021 with ∼300 events/day. The
latest analyzed dataset consists of 720 (860)calendar days of reactor on (off)data with a
Figure 56. Left panel: exclusion curves at 90% C.L. (filled area)and 90% C.L.
sensitivity contours (dashed line)are shown. Expected regions from RAA and GA are
also shown. Reproduced from [651]. © IOP Publishing Ltd. All rights reserved. Right
panel: exclusion curves for 3 +1 neutrino oscillations in the
qsin 2
214
,Dm14
2parameter
space obtained by NEOS. Reprinted (figure)with permission from [133], Copyright
(2017)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
86
signal-to-background ratio of ∼0.5. The experiment performed a sterile neutrino search in the
L/Espace and observed evidence for 2.9σneutrino oscillation effect with the best-fitat
D
m14
2=7.3 ±0.13(stat)±1.16(syst)and
qsin
214
=0.36 ±0.12(stat)(figure 57).Itis
important to point out that these results are widely debated by several groups [109,309–311].
Additionally, PROSPECT and STEREO experiments [312,313]also individually disfavor
the best-fit point and a significant portion of the Neutrino-4 suggested parameter space.
PROSPECT. The Precision Reactor Oscillation and SPECTrum (PROSPECT)experi-
ment [314,315]is a U.S.-based reactor neutrino experiment installed at short baselines of
6.7–9.2m from the 85 MW High Flux Isotope Reactor (HFIR)at Oak Ridge National
Laboratory. The 4-ton
6
Li-loaded PSD-capable liquid scintillator [316]detector is composed of
a two-dimensional grid of optically isolated segments [312,317]as shown in figure 58.Low
mass, highly reflective, rigid separators [318]were used to achieve segmentation and PMTs
enclosed in mineral oil-filled acrylic housings were installed at either ends of the segments for
signal readout.
The detector shielding was optimized based on the neutron and γray background
measurements performed at HFIR [319]and consisted of top-heavy hydrogenous shielding to
reduce cosmogenic backgrounds and a fixed local lead shield to mitigate reactor-specific
backgrounds. PROSPECT was the first on-surface reactor neutrino experiment to achieve a
signal-to-background (S:B)>1, thanks to the high background suppression enabled by the
detector design.
PROSPECT was commissioned in February 2018 and started collecting data in March.
The first oscillation search result was published in 2018 [134]with a relatively small dataset
of 33 (28)reactors on (off)live days which was followed by a result with a longer dataset
consisting of 96 (73)reactor on (off)live days composed of >50k signal events in 2020. The
oscillation search was done by performing a relative comparison of baseline-dependent
spectra minimizing the dependence on the reactor neutrino model [135].
A combination of the compact HFIR reactor core (a cylinder of diameter 0.435 m and
height of 0.508 m)with the fine detector segmentation (14.5 cm ×14.5 cm cross-section)
enabled high sensitivity to oscillation frequencies of Δm
2
>1eV
2
. PROSPECT observed no
statistically significant indication of
¯
n
e
to sterile neutrino oscillations. Using Feldman–Cousins
Figure 57. Left: 1σ(blue),2σ(green), and 3σ(yellow)suggested regions from the
Neutrino-4 sterile neutrino oscillation search. Right: L/Edistribution of background-
subtracted IBD rates reported by the Neutrino-4 Experiment. Reproduced from [498].
CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
87
technique [320], PROSPECT excluded a significant portion of the RAA suggested parameter
space at 95% CL and the best-fit point at 2.5σas shown in figure 59. A complementary
technique using the Gaussian CLs method [321]also provides similar exclusion.
The PROSPECT detector was decommissioned in 2020 after an unexpected HFIR
downtime. During the course of data taking, it was also observed that a number of segments
have slowly lost functionality due to failures of PMT electronics induced by the ingress of the
liquid scintillator into the PMT housings. Due to these reasons, the results shown above–
corresponding to the full PROSPECT dataset–are primarily dominated by statistics. However,
the collaboration is carrying out two major analysis modifications by leveraging distinctive
detector features. (a)Splitting the data-taking period into multiple time-frames and (b)
allowing the use of segments with single PMTs. The former would allow for an increase in
statistics by allowing segments with non-functioning PMTs to be used for part of the dataset
and the latter increases the S:B by improving particle identification and consequently reduces
the backgrounds. Each of the analysis improvements is individually expected to increase the
effective statistics by ∼50% and enable considerable improvement in the statistical power of
the PROSPECT’s oscillation search.
STEREO. The STEREO experiment [322]is a Gd-doped liquid scintillator detector
located at the ILL in Grenoble, France. The detector uses a high-flux 58 MW
th
research
reactor that consists of highly enriched Uranium. The detector is located 9 m away from the
reactor core and is a segmented detector where the position of different segments of the
detector serves as different baselines varied between 9 and 11 m as shown in figure 60 (left).
The IBD signal events are selected using a cut-based approach where selection cuts on
energy and time variables are optimized by trading off between detection efficiency and
background rejection. Furthermore, antineutrino signal rates separated from the remaining
background using pulse shape discrimination (PSD)where pulses generated from neutrons
have longer tails compared to that of gamma. Hence, a ratio of the pulse tail to total charge is
used to mitigate neutron-related background.
Figure 58. Left: schematic of the PROSPECT detector, shielding, and electronics in the
HFIR Experiment Room. The center of the detector is located at a distance of 7.84 m
from the center of the reactor core (red). Right: Cutout of the PROSPECT active
segmented detector enclosed in the containment and shielding. Also shown is
the vertical local lead shield adjoining the reactor pool wall that was installed to
mitigate the reactor-related backgrounds. The figure was a modified version of the
figure. Reproduced from [533]. © IOP Publishing Ltd. All rights reserved.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
88
The test of sterile neutrino oscillations is performed using ratios of energy spectrum at six
different segments to that of the first segment and therefore making the measurement
independent of absolute normalization and of the prediction of the reactor spectrum. With 273
(520)days of reactor-on (-off)data, STEREO found no evidence for sterile neutrino
oscillations, and the results are compatible with the null oscillation hypothesis. The data
excluded RAA best-fit point at p-value <10
−4
and exclusion curve with 3 +1 neutrino
oscillations scenario is shown in figure 60 (Right).
Figure 59. Results from PROSPECT’s search for
¯
n
e
to sterile neutrino oscillations.
Exclusion contours were drawn using Feldman–Cousins (black)and Gaussian CLs
(red)methods. Green and yellow bands show the 1σand 2σPROSPECT sensitivities to
the sterile neutrino oscillations. Also shown for comparison are the RAA-suggested
parameter space and the best-fit point. Reproduced from [135].CC BY 4.0.
Figure 60. (Left)STEREO setup. 1–6: target cells (baselines from core: 9.4–11.1 m).
Reproduced from [322].CC BY 4.0.(Right)Exclusion contour (red)and exclusion
sensitivity (blue)at 95% C.L. Overlaid are the allowed regions of the RAA (grey)and
its best fit point (star). Reproduced from [313].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
89
4.1.3.2. Medium-baseline experiments.Daya Bay. Daya Bay’s unique configuration makes
it an excellent experiment to search for sterile-active neutrino mixing [132,323–325]. In this
experiment, electron antineutrinos emitted from six 2.9 GW
th
nuclear reactors are detected in
eight identically-designed antineutrino detectors (ADs)placed underground in two near
experimental halls (EHs)and one far hall. The two near halls, EH1, and EH2, are located
∼350–600 m away from the reactors, whereas the far hall, EH3, is located ∼1500–1950 m
from the reactors.
Daya Bay’s latest constraints in the
(
)qDmsin 2 ,
214 41
2parameter space, obtained with a
1230 d data set, are shown in figure 61 [325]. Two complementary analysis methods are used
to set the exclusion contours, one relying on the Feldman–Cousins (FC)frequentist approach
and the other on the CL
s
approach. Daya Bay is most sensitive to
qsin 2
214
in the 10
−3
eV
2
∣∣Dm0.
3
41
2eV
2
region, where a distortion from the standard three-neutrino oscillation
framework would be visible through a relative comparison of the rate and energy spectrum of
reactor antineutrinos in the different EHs. For
∣
∣Dm0.
3
41
2eV
2
, the oscillations are too fast
to be resolved, and the sensitivity arises primarily from comparing the measured rate with the
expectation, resulting in less stringent limits.
Daya Bay ceased operations in December 2020 after collecting data for over 3000 d.
Throughout this time it accumulated the largest sample of reactor antineutrinos to date,
consisting of more than six million events. This sample is still being analyzed and final results
are expected to be released by early 2023. The sizable increase in statistics, combined with
potential reductions in systematic uncertainties, implies that significant improvements over
Figure 61. Left: Feldman–Cousins (FC)90% C.L. and 90% CL
s
exclusion regions from
an oscillation analysis of 1230 d of Daya Bay data. The dashed red line shows the 90%
C.L. median sensitivity along 1σand 2σbands. The excluded region for the original
Bugey-3 limit [652]is shown in green, while the resulting CL
s
contour from Daya Bay
and its combination with the reproduced Bugey-3 results are shown in grey and black,
respectively. Reproduced from [325].CC BY 4.0. Right: RENO’s 95% C.L. exclusion
contour for the oscillation parameters
qsin 2
214
and
∣∣
Dm41
2. The black solid contour
represents an excluded region obtained from spectral distortion between near and far
detectors. The green shaded band represents expected 1σexclusion contours due to a
statistical fluctuation. The blue dotted contour represents its median. Reproduced from
[653].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
90
the existing limits are expected. The new constraints will likely remain the best in the world
for the foreseeable future in the
∣
∣Dm0.
3
41
2eV
2
region, which no experiment in the horizon
is expected to cover at the time of writing.
Double chooz. Double Chooz [326]consists of two nearly identical gadolinium-doped
liquid scintillator detectors located close to the nuclear power plant comprising two 4.25 GW
nuclear reactors. The near (far)detectors are located underground at an overburden of 120 m
(300 m)at a distance of 469 m and 355 m (1115 m and 998 m)from the two reactor cores.
The detector-reactor locations are such that the relative contributions to both the detectors
from the reactors are very similar which helps reduce reactor-related uncertainties.
This analysis includes three datasets amounting to a total 5 year long dataset. The first
(FD-I)dataset consists of 455.21 d of livetime collected with the far detector before the
commissioning of the near detector. The second (FD-II)and third (ND)datasets are collected
during the same period of time and consists of 362.97 d and 257.96 d of livetime respectively.
The livetime for ND is lower than FD-II because of the higher muon rate causing larger
deadtime in the near detector. In order to obtain a measurement independent of absolute flux
predictions, the experiment directly compares the event rates measured in the two identical
detectors which helps in canceling most of the reactor flux and detection efficiency-related
uncertainties. The experiment does not see any indications of sterile neutrino oscillations and
set exclusion limits in similar regions of
D
m14
2as the other θ
13
experiments.
RENO. The RENO collaboration has reported a search result for light sterile neutrino
oscillations. The search is performed using six 2.8 GW
th
reactors and two identical detectors
located at 294 m (near)and 1383 m (far), respectively, from the center of six reactor cores at
the Hanbit Nuclear Power Plant Complex in Yonggwang. The reactor flux-weighted baseline
is 410.6 m for the near detector and 1445.7 m for the far detector, respectively. The near (far)
underground detector has 120 m (450 m)of water equivalent overburden. A spectral
comparison between near and far detectors was performed to search for reactor 3 +1 light
sterile neutrino oscillations [327–331].
The RENO sterile analysis uses roughly 2200 live days of data taken in the period
between August 2011 and February 2018 amounting to 850 666 (103 212)
n
e
candidate events
in the near (far)detector. The details of pull terms and systematic uncertainties are described
in [331]. Exclusion regions at 95% confidence level are set for Δχ
2
>5.99 and are shown in
figure 61. Exclusion contours obtained using the Gaussian CL
s
method [321,332]show
negligible difference with the pictured Δχ
2
method. Figure 61 shows the 95% C.L. exclusion
contour and median sensitivity including 1σband due to statistical fluctuations.
The limit of
qsin 2
214
is mostly determined by a statistical uncertainty, while the
systematic uncertainties dominate in the
∣
∣Dm0.06
41
2eV
2
. The uncertainty of background
is a dominant systematic source in the ∣∣Dm
0
.003 0.06
41
2eV
2
region, and the energy-
scale uncertainty is a major limiting factor in the
∣
∣Dm0.008
41
2eV
2
region. The RENO
result provides the most stringent limits on sterile neutrino mixing at
∣
∣Dm0.00
2
41
2eV
2
using the
n
e
disappearance channel. Adding data taken since 2018 and reducing the above
systematic uncertainties will improve the results significantly.
4.1.3.3. Joint fits of reactor neutrino experiments. As discussed above, the conclusive way to
test whether RAA is due to active-sterile mixing is by searching for sterile neutrino-induced
spectral variations as a function of the baseline. With the exception of the Neutrino-4
experiment, no experiment has claimed to observe statistically significant hints of oscillations.
Nonetheless, modest hints of oscillation in the other experiments have been reported, and it is
worth considering the global fits of these datasets to determine and build a broader context
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
91
from their individual results. A joint analysis [333]using Monte Carlo simulations with data
from a combination of the short-baseline reactor neutrino experiments DANSS, NEOS,
Neutrino-4, PROSPECT, and STEREO shows that the combination of these datasets is
statistically compatible with the three neutrino model. The exclusion curve from this joint fit
is shown in figure 62.
Although a combination of relative reactor neutrino datasets is incompatible with sterile
neutrino-induced oscillations, they are in good agreement with the Gallium Anomaly. This is
primarily driven by the data from BEST and Neutrino-4 experiments which prefer oscillations
with
D
m14
2>5eV
2
—a region where other reactor experiments have minimal sensitivity.
Experiments with sensitivity in the
D
m14
2>5eV
2
are needed to fully address these suggested
regions. This could be achieved by a combination of upcoming reactor experiments (see
sections 6.3)and β-decay experiments (see sections 4.1.6,6.6).
4.1.3.4. Joint analysis with accelerator experiments. It is impossible for a single experiment
to cover all the parameter space of interest to experimentalists and phenomenologists, which
motivates the undertaking of joint analyses carried out by the members of the experimental
collaborations that properly treat systematic uncertainties and their correlations. Of particular
interest is the combination of Daya Bay’s data with those of other reactor experiments
operating at shorter baselines to cover a wide range of
∣
∣Dm41
2values. A case in point is the
joint fit of the Daya Bay and Bugey-3 data presented in [325]that results in the black contour
of figure 61. Furthermore, powerful constraints on sterile-driven neutrino oscillations can also
Figure 62. Left: 2σCL Feldman–Cousins (FC)exclusion curve of the combined reactor
neutrino data. Also overlayed are the 2σexclusion FC curves from solar data, ν
e
−
12
C
scattering data from LSND and KARMEN, 95% C.L. exclusion from the KATRIN
experiment, and 2σgallium suggested region. Right: 1σ,2σ, and 3σCL FC suggested
regions for a combination of gallium anomaly and relative reactor measurements. The
suggested regions are at higher Dm
2
mainly driven by the BEST and Neutrino-4
experiments. Reproduced from [333].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
92
be extracted from combining data from reactor experiments with data from long-baseline
accelerator experiments. In a 3 +1 scenario, reactor experiments primarily measure
∣
∣q=Usin
e422
14
through electron antineutrino disappearance, while long-baseline accelerator
experiments are typically most sensitive to
∣
∣qq=
m
Usin cos
422
24 214
through measurements of
muon (anti)neutrino disappearance. The product of the two matrix elements provides the
amplitude of short-baseline electron neutrino appearance in a primary muon neutrino source:
⎜⎟
⎛
⎝⎞
⎠
∣∣∣ ∣ ()
() ()
=D
nn m
m
--
PUU
mL
E
4sin
4,46
SBL e42422 41
2
e
where ∣∣∣∣ qq q=º
mm
UU
4
sin 2 sin sin 2
ee42422
14 224 2. Possibly the most representative exam-
ples of this type of combination are found in Refs. [324,325], where constraints on θ
14
from
the Daya Bay and Bugey-3 experiments are combined with constraints on θ
24
from the
MINOS/MINOS+experiments to constrain the effective mixing parameter
q
m
sin 2
e
2. This
work culminated in the most stringent constraints to date from disappearance searches on
active to sterile neutrino oscillations and probed the parameter space allowed by the LSND
and MiniBooNE anomalies, as shown in figure 63.
As highlighted in [334], there are attractive opportunities in combining Daya Bay’s data
with other current and future experiments, such as PROSPECT, STEREO, NEOS, and
JUNO-TAO. It is worth noting that the Daya Bay collaboration plans to publicly release its
full data set once all final results have been released [335], allowing such combinations to
occur even well after the collaboration has dissolved. Similarly, following end of data taking
in 2016, the MINOS/MINOS+CL
s
surfaces remain available for use in future combinations.
4.1.4. Atmospheric neutrino experiments.IceCube—neutrino telescopes, such as the
IceCube Neutrino Observatory in the South Pole, play a unique role in searches for new
Figure 63. Comparison of the MINOS, MINOS+, Daya Bay, and Bugey-3 combined
90% CL
s
(left)and 99% CL
s
(right)limits on qm
sin 2 e
2to the LSND and MiniBooNE
90% and 99% C.L. allowed regions, respectively. The limit also excludes the 90% and
99% C.L. regions allowed by a fit to global data by Gariazzo et al where MINOS,
MINOS+, Daya Bay, and Bugey-3 are not included [101,654], and the 90% and 99%
C.L. regions allowed by a fit to all available appearance data by Dentler et al [102]
updated with the 2018 MiniBooNE appearance results [32]. Reproduced from [325].
CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
93
physics associated with the short-baseline anomalies [140,151,152,336]. For atmospheric
neutrino oscillation baselines, the L/Erange of the short-baseline anomalies corresponds to
neutrino energies of order 100 GeV–1 TeV. Because this closely matches the peak of the
detected neutrino flux at IceCube, it is natural to expect any Lorentz invariant (LI, implying
scaling as L/E)phenomenon connected with the short-baseline anomalies [1]may be
meaningfully testable at IceCube.
Sensitivity to certain models is even further enhanced by fortuitous features of this
energy range, notably: (1)For sterile neutrinos with 0.1-10 eV
2
mass splittings, a resonant
matter effect leads to dramatic enhancement of oscillations at ∼1 TeV, leading to sensitivity
far exceeding that for vacuum-like oscillations [337–340];(2)Any new physics model that
invokes non-LI effects scaling positively with Ewill be enhanced at IceCube relative to all
other experiments at lower L/E—these include anomalous decoherence [341–343]and
Lorentz violation [344–346]models; (3)this energy range offers unique access to the ν
τ
appearance sector [337,347]. Other notable features of the IceCube event sample are its
‘broadband’nature, covering five decades of energy of atmospheric neutrinos (10 GeV–1
PeV)and 3.5 decades of baselines (20–12 750 km); high statistical precision, owing to the
high total exposure of a billion-ton detector operating stably for ten years collecting 70,000
atmospheric neutrino events per year, and well-controlled cross section uncertainties due to
the predominance of deep-inelastic scattering interactions. These features have enabled
world-leading sensitivity to the parameters governing three-flavor oscillations as well as non-
standard oscillation models including sterile neutrinos [140,151–153], tests of low-energy
manifestations of quantum gravity [345,348], neutrino decay [150], and NSIs [349–351].
Present generation light sterile neutrino searches at IceCube. IceCube has made
powerful sterile neutrino searches in both high (400 GeV)and low (60 GeV)energy
ranges. The former targets the matter resonance [337,338]expected for Δm
2
∼
(1eV
2
)
splittings, and is one of the world’s most sensitive in the ν
μ
disappearance channel at
eV
2
-scale mass splittings. The latest generation analysis [151,152]uses a sample of 305735
reconstructed ν
μ
events and excludes mixing angles down to
q
~
sin 2
224
0.02 at Δm
2
∼0.2 at
99% CL. At 90% CL the analysis yields a closed contour that may be interpreted as a
statically weak hint of a signal, with a best-fit point at
qsin 2
224
=0.10 and
D
m41
2=4.5 eV
2
.
This result is consistent with the no sterile neutrino hypothesis with a p-value of 8.0%. The
90% CL contour is shown in figure 64, left.
At low energy,sterile neutrino mixing within an extended neutral lepton mixing matrix
enhances the standard oscillation probability proportionally to the matter column density
traversed [352]. The effect is approximately independent of Δm
2
, as oscillation cycles are
irresolvable within detector energy resolution. IceCube has tested for this effect using a multi-
flavor sample over an energy range of 10–60 GeV [140], with the strongest effect expected at
an energy of ∼20 GeV for upgoing muons. The analysis yielded no evidence of anomalous
oscillations, setting a limit on the extended PMNS matrix elements
∣
∣q=
m
Usin
422
24
and
∣
∣qq=
t
Usin cos
422
34 234
, marked IC2017(NO) in figure 64, center.
Next generation sterile neutrino searches at IceCube. The sterile neutrino sensitivity at
IceCube has yet to be exhausted, with near-term improvements expected from event samples
already in hand. At low energies, a sterile neutrino search using the full ten year dataset of
300 000 events with E
ν
100 GeV spanning all flavors is underway [353], promising
unique sensitivity in the |U
μ4
|
2
,|U
τ4
|
2
plane (figure 64, center). At higher energies (400
GeV), attention to date has been focused on searches for ν
μ
disappearance through non-zero
θ
24
, motivated by the necessity of its finite value if sterile neutrino osculations were
responsible for the short-baseline ()(
¯¯
n
nn n
mmee
)anomalies (θ
14
=θ
34
=0 leads to the
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
94
most conservative limits on θ
24
[354]). Efforts are now underway to incorporate the high
energy cascade event sample into these analyses, which includes topologies associated with
ν
e
and ν
τ
CC and all flavor NC interactions. This extension promises sensitivity to both ν
e
and
ν
τ
appearance signatures associated with non-zero θ
14
and θ
34
, respectively. Preliminary
studies [347]of the sensitivity in this channel suggest that ν
τ
appearance signatures are
discoverable for values of θ
34
consistent with world data and IceCube’s existing θ
24
limits;
and that values of θ
14
consistent with reactor [66]and gallium/BEST [136,268,355]
anomalies may yield observable ν
e
appearance signatures. The expected sensitivity of the
combined high energy ν
μ
disappearance and cascade appearance signatures is shown in
figure 64, right. Augmentations of the sterile neutrino searches using machine learning
techniques, starting-event topologies, and improved reconstruction methods are also
underway, expected to provide continuing improvements over the coming Snowmass period.
Super-K. Super-Kamiokande (Super-K, SK)has performed a search for light sterile
neutrinos using approximately 4000 live-days of atmospheric neutrino data [356]. The SK
analysis focuses on light sterile neutrinos with mass-squared differences greater than 0.1 eV
2
.
In the energy range of the Super-K analysis, predominantly below 10 GeV, such a large mass-
square difference implies that the oscillation effects due to light sterile neutrinos are averaged
out. Thus, Super-K analysis is insensitive to the mass-square difference, but only to the
mixing elements. In the Super-K analysis, they choose to constraint the mixing elements:
|U
τ4
|and |U
μ4
|. In principle, Super-K has also sensitivity to |U
e4
|, but this is a subleading
effect. Additionally, the Super-K also is sensitive to the additional CP-violating phases that
appear in the presence of a sterile neutrino. The effect of these CP-violating phases is
subleading but does not always yield conservative results on the mixings and thus the results
should be taken with this caveat [337].
The Super-K analysis found no significant evidence of a light sterile neutrino and
reported constraints on |U
τ4
|and |U
μ4
|for
D
>m0.1 eV ;
41
22concretely they limit |U
μ4
|to less
than 0.041 and |U
τ4
|to be less than 0.18 at 90% C.L. These results are shown in figure 65 and
have been superseded by constraints from ANTARES and IceCube; compare to figure 64.
ANTARES. The ANTARES neutrino telescope [357], a sub-gigaton-scale neutrino
telescope, had been designed and optimized for the exploration of the high-energy universe
by using neutrinos as cosmic probes. However, its energy threshold of about 20 GeV was
sufficiently low to be sensitive to the first atmospheric oscillation minimum. The majority of
Figure 64. Left: results from IceCube’s high-energy muon-neutrino disappearance
search. Reproduced from [151].CC BY 4.0. Middle: results from IceCube low- and
high-energy analyses. Reproduced from [353]. © 2021 IOP Publishing Ltd and Sissa
Medialab. All rights reserved. Right: expected sensitivity with cascades. Reproduced
from [347].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
95
the neutrino events have been recorded with energies between 100 GeV and few TeV, an
energy range rich in signatures of eV-scale sterile neutrinos. This is illustrated in figure 66
which shows the ν
μ
survival probability for maximal mixing of θ
23
and different
combinations of the mixing parameters θ
24
,θ
34
and δ
24
with
()q=
md-
Uesin , 47
i
424
24
()qq=
t
Usin cos . 48
43424
The fast oscillations due to
D
m0.5
41
2eV
2
are unobservable due to the limited energy
resolution of the detector, making
D
m41
2not measurable.
The ANTARES neutrino telescope was located in the Mediterranean Sea, 40 km off the
coast of Toulon, France, at a mooring depth of about 2475 m. The detector was completed in
2008 and took data until February 2022. ANTARES was composed of 12 detection lines,
instrumenting a water volume of about 15 Mtons. ANTARES data collected from 2007 to
2016 with a total detector lifetime of 2830 d have been used to constrain U
μ4
and U
τ4
[358].
A total of 7710 low-energetic atmospheric neutrino candidate events have been selected,
largely dominated by muon-(anti)-neutrino charge-current events, identified thanks to a long-
range up-going muon track. Particular attention was paid to consistent handling of the
complex phase δ
24
in conjunction with the neutrino mass ordering. The limits from the
ANTARES analysis are shown in figure 67. As expected from figure 66 ANTARES is
particularly sensitive if both U
μ4
and U
τ4
are non-zero and improves existing limits from
[140,359]substantially.
After profiling over the other variable, the following limits on the two matrix elements
can be derived:
∣∣ ( ) ( ) ()<
m
U0.007 0.13 at 90% 99% CL, 49
42
∣∣ ( ) ( ) ()<
t
U0.40 0.68 at 90% 99% CL. 50
42
Figure 65. Constraint on |U
τ4
|and |U
μ4
|for D>m0.1 eV
41
22obtained by Super-K.
Reprinted (figure)with permission from [356], Copyright (2015)by the American
Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
96
4.1.5. Radioactive source experiments.BEST. The baksan experiment on sterile transitions
(BEST)[355]was proposed to probe the possibility of the short-baseline electron neutrino
disappearance using the same process studied by GALLEX and SAGE, equation (6). The
disappearance of neutrinos was suggested as an explanation of the deficit in observed events
measured by the previous radioactive source experiments (see section 3.3.3).
Although the main experimental idea is the same, the BEST configuration provides for
simultaneous measurements at two different baselines. In this case, a spherical vessel (inner
target)is located inside a cylindrical container (outer target), both filled with liquid gallium
(the detector). The radioactive source (
51
Cr)is placed inside the sphere, as shown in figure 68.
Here again, the emitted neutrinos interact with the detector through reaction equation (6),
and the produced
71
Ge atoms are extracted and counted for each vessel separately [360]. The
ratio of the measured rate of
71
Ge production at each distance to the expected one considering
the cross section and experimental efficiencies are presented in table 13 [361]. Recall that the
cross section of the reaction in equation (6)is used in the calculation of these ratios, and
BEST used the Bahcall results [76], including conservative uncertainties [136]. The ratios are
4.2σand 4.8σless than unity, respectively, supporting the gallium anomaly observed by other
experiments.
BEST performed an analysis of these results in the framework of short-baseline electron
neutrinos disappearance due to neutrino oscillation governed by the survival probability in
equation (7), using ∣∣( ∣∣
)
q=-UUsin 2 4 1
ee
24242
. The study leads to the allowed regions
shown in figure 69, corresponding to 1σ,2σ, and 3σconfidence levels (left plot), with the
best-fitat(
q
sin 2
2,Δm
2
)=(0.42, 3.3 eV
2
). When combined with the results from GALLEX
and SAGE (table 3), the allowed regions are the ones illustrated in the right plot of figure 69,
where correlated cross section uncertainties were considered. In this case, the best fitis
located at
(
)(qD=msin 2 , 0.34, 1.25
22
eV
2
)[361].
Some of the calculations of the cross section of the process equation (6)appear to
decrease the significance of the gallium anomaly related to the GALLEX and SAGE
experiments (section 3.3.3); nonetheless, the results are still consistent with a possible short-
Figure 66. Survival probability of vertically up-going ν
μ
at ANTARES as a function of
neutrino energy for different values of mixing angles θ
24
,θ
34
and δ
24
with D=m41
2
0.5
eV
2
,·D= -
m2.5 10
31
23eV
2
and q=sin 2 1
223 . Reproduced from [358].
CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
97
baseline electron neutrino disappearance produced by active to sterile neutrino oscillations.
On the other hand, the measurements by BEST are in agreement with the former source
experiments and confirm the gallium anomaly with larger significance.
4.1.6. Beta spectrum searches. High precision beta spectroscopy enables searches for
sterile neutrinos from the sub-eV- up to the MeV-scale. Exploiting the kinematics of the weak
process, these experiments offer a clean probe of the coupling of the electron flavor neutrino
to the different mass states. The electron flavor neutrino emitted in β-decay does not have a
well-defined mass but is rather an admixture of the neutrino mass eigenstates. The existence
of a hypothetical sterile neutrino(s)implies the electron flavor neutrino mayalso contain a
small admixture of (at least)a new fourth neutrino mass eigenstate, m
4
.
The β-decay spectrum, R
β
(E)will be altered:
() ( ) ( ) ( )qq=+
bb
bb
RE REm REmcos , sin , 51
ss
2224
2
composed of both the spectrum corresponding to the traditional electron-weighted neutrino
mass m
β
(from the three active neutrinos)and a spectrum associated with m
4
. The maximal
energy of each spectrum contribution is E
0
−m
i
, with the largest neutrino mass resulting in the
lowest endpoint energy. The amplitudes of the two decay branches are given by
qcos
s
2
and
qsin
s
2
, respectively, where θ
s
is the active-to-sterile mixing angle. The resulting signature of a
sterile neutrino is thus a kink-like distortion of the measured spectrum at an energy of E
0
−m
4
.
Spectral measurements across a broad energy range therefore enable searches for kink
features and thus sterile neutrinos. Although not an L/E oscillation signature, detection would
Figure 67. 90% (left)and 99% (right)CL limits for the 3 +1 neutrino model in the
parameter plane of
∣
∣q=
m
Usin
422
24
and
∣
∣qq=
t
Usin cos
422
34 224
obtained by
ANTARES (black lines), and compared to the ones published by IceCube/DeepCore
[140](red)and Super-Kamiokande [359](blue). The dashed lines are obtained for NH
and δ
24
=0°while the solid lines are for an unconstrained δ
24
(ANTARES)or for IH
and δ
24
=0°(IceCube/Deepcore)respectively. The colored markers indicate the best-
fit values for each experiment. The 1D projections after profiling over the other variable
are also shown for the result of this work. Reproduced from [358].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
98
Figure 68. BEST detector configuration. Two Ga target volumes detect neutrino
interactions from a
51
Cr source. Reproduced from [136].CC BY 4.0.
Table 13. Ratio of observed to predicted
71
Ge event rates as measured by BEST using
51
Cr with its inner and outer targets.
Inner Outer
0.79 ±0.05 0.77 ±0.05
Figure 69. Allowed regions obtained in the
qsin 2
2
–Dm41
2parameter space from the
analysis of the BEST results only (left)and from the BEST results combined with
results from GALLEX and SAGE (right). Reproduced from [361].CC BY 4.0. Note
that here
∣∣( ∣∣
)
q=-UUsin 2 4 1
ee
24242
.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
99
be an unambiguous detection of sterile neutrinos subject to drastically different systematics.
As a complementary probe, these searches exclusively probe the sterile neutrino hypothesis,
and not other physics explanations of the existing anomalies. For eV-scale sterile neutrinos,
this signature naturally appears in the region of interest for direct neutrino mass measurements
studying the beta endpoint.
4.1.6.1. Historical context. The flexibility of the beta spectrum method has led to its use in
placing strong constraints on sterile neutrinos. These limits span more than six decades in
m
4
—from 1.5 eV up to 2.5 MeV—and down to
q~
-
sin 10
24
(see figure 70). Isotopes
placing the strongest constraints across this energy range include
3
H[362–365],
187
Re [366],
63
Ni [367],
35
S[368],
64
Cu [369],
144
Ce-
144
Pr [370],
7
Be [371], and
20
F[372].
Tritium endpoint searches for direct neutrino mass study have enjoyed great success,
leveraging the sophisticated detector and source development for that science. Both KATRIN
[364,365]and Troitsk [362,363]have derived eV-scale limits from the primary neutrino
mass physics data. Additionally, dedicated searches away from the endpoint open up a wider
range to keV masses. The progress of the ongoing KATRIN experiment for eV steriles is
described in detail below (section 4.1.6.2), with discussion of sensitivity to keV steriles with
an upgraded detector later (section 6.6.1). At higher mass, the BeEST experiment has
obtained the strongest limits to steriles up to 0.85 MeV based on their Phase II prototype
[371], heralding the advent of new technologies with significant improvements in sensitivity;
BeEST is discussed later in the context of their full sensitivity (section 6.6.3).
4.1.6.2. KATRIN. The Karlsruhe Tritium Neutrino experiment (KATRIN)[373–375]
provides a high-precision electron spectrum measurement of tritium β-decay,
¯
n++
+-
HHee
33 e(endpoint E
0
=18.57 keV, half-life t
1/2
=12.32 yr). KATRIN is
designed to improve the sensitivity on the effective neutrino mass, m
β
, to 0.2–0.3 eV (90%
CL). Based on the science measurement campaigns taken in 2019 [376,377], KATRIN can
constrain the mass and mixture of a sterile neutrino that would manifest itself as a distortion
of the β-electron spectrum. The signature is a kink-like feature, as shown in a simulation
presented in figure 71. The first light sterile neutrino result is based on data from KATRIN’s
Figure 70. Landscape of historical limits on sterile neutrino from beta spectrum
searches. Results from the last decade are highlighted in color and labeled.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
100
first high-purity tritium campaign, which ran from April to May, 2019, at an average source
activity of 2.45 ×10
10
Bq [378]. An updated result is based on KATRIN’s second campaign,
which ran from October to November, 2019, achieving a source activity of 9.5 ×10
10
Bq [364].
The integral β-electron spectrum is scanned repeatedly in the range of [E
0
−90 eV, E
0
+
135 eV]by applying non-equidistant HV settings to the spectrometer electrode system. Each
scan lasted 2 h. At each HV set point, the transmitted electrons are counted. Figure 71 shows the
measurement time distribution. Stable scans are selected with an overall scanning time of 522 h
(campaign one)and 744 h (campaign two). Detector variations are minimized by gathering
events from the 117 most similar pixels and combining them into a single effective pixel
analysis. The resulting spectra, R(〈qU〉), include a combined 5.2 ×10
6
expected tritium events
on a flat background. Even for the campaign one search, which exhibited lower source rates and
higher backgrounds, a high signal-to-background ratio was achieved, rapidly increasing from 1
at 〈qU〉=E
0
−12 eV to >70 at 〈qU〉=E
0
−40 eV. In the campaign two search, the highest
signal-to-background ratio improves to 235 at 〈qU〉=E
0
−40 eV. The modeled experimental
Figure 71. (a)Electron spectrum of KATRIN data R(〈qU〉)over the interval [E
0
−40
eV, E
0
+50 eV]from all 274 campaign 1 tritium scans and the three-neutrino mixing
best-fit model R
calc
(〈qU〉)(line). The integral β-decay spectrum extends to E
0
on top of
aflat background R
bg
.1-σstatistical errors are enlarged by a factor 50. (b)Simulation
of an arbitrary sterile neutrino imprint on the electron spectrum. The ratio of the
simulated data without fluctuation, including a fourth neutrino of mass m
4
=10 eV and
mixing |U
e4
|
2
=0.01, to the three-neutrino mixing model is shown (red solid line).
(c)Integral measurement time distribution. Reproduced from [378].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
101
spectrum R
calc
(〈qU〉)is the convolution of the differential β-spectrum R
β
(E)with the response
function f(E−〈qU〉), and an energy-independent background rate R
bg
:
(⟨ ⟩) · ( ) · ( ⟨ ⟩) ( )
ò
=-+
b
RqU ANREfEqUERd, 52
calc s T bg
where A
s
is the tritium signal amplitude. N
T
denotes the number of tritium atoms in the source
multiplied with the accepted solid angle of the setup ()pq
D
W=-41cos2
max , with
q
=
50.4
max , and the detector efficiency (0.95). The function f(E−〈qU〉)describes the
transmission probability of an electron as a function of its surplus energy E−〈qU〉. KATRIN
extends the experimental modeling and statistical analysis to constrain both the sterile
neutrino mass squared m4
2and its mixing amplitude |U
e4
|
2
, following the same strategy as for
the m
β
analysis [379]. In the 3 +1 active-sterile neutrino model extension the electron
spectrum, R
β
, is replaced by ()(∣∣)()∣∣()=- +
bb bbb
R
Em m U REm U REm,, 1 , ,
ee44
22424
2,
where Uis the extended 4 ×4 unitary matrix,
()
bb
R
Em,
2
is the differential electron spectrum
associated with decays the include active neutrinos in the final state, and
()
b
R
Em,
4
2
describes
the additional spectrum associated to decays involving a sterile neutrino of mass m
4
.
The observable integral spectrum R
calc
is henceforth modeled with six free parameters:
the four original parameters (A
s
,E
0
,R
bg
,n
m2)[376],m4
2and |U
e4
|
2
. This extended model
R
calc
(〈qU〉)is then fitted to the experimental data R(〈qU〉).
In order to mitigate bias, the full analysis is first conducted on a Monte Carlo (MC)data
set before turning to the actual data. The fitofR(〈qU〉)with R
calc
(〈qU〉)is performed by
minimizing the standard χ
2
-estimator. In a ‘shape-only’fit, both E
0
and A
s
are left
unconstrained. To propagate systematic uncertainties, a covariance matrix is computed after
performing
(
)
10
4
simulations. The sum of all matrices encodes the total uncertainties of
R
calc
(〈qU〉), including HV set-point-dependent correlations. The χ
2
-estimator is then
minimized to determine the best-fit parameters, and the shape of the χ
2
-function is used to
infer the uncertainties. The fit range [E
0
−40 eV, E
0
+50 eV]is chosen such that statistical
uncertainties on |U
e4
|
2
dominate over systematic uncertainties in the whole range of m4
2
considered [376,379]. The experimental result agrees well with the sensitivity estimates and
are displayed in figure 72. They are showing no evidence for a sterile neutrino signal and are
compared with short-baseline neutrino oscillation experiments measuring the electron (anti-)
neutrino survival probability (())qDPm,sin 2ee
41
22. An estimation of KATRIN’sfive-year
(1000 live-day)sensitivity is also presented.
4.2. Dark sectors in scattering and in the beam
The MiniBooNE low energy excess has traditionally been interpreted as a potential hint of
neutrino oscillations at short baseline driven by a new sterile state. However, simple inter-
pretations (e.g. 3 +1 models)are in tension with other oscillation measurements (see the
discussion in the sections above), in particular searches for muon flavor disappearance driven
by the same Δm
2
. Given this tension, it is natural to consider other possible new physics
explanations for the LEE. These new physics explanations must have detector signatures and
production mechanisms which are consistent with the existing MiniBooNE measurements.
The measured angular distribution of the events in the LEE constrains the allowed
interaction channels in the detector. For concreteness, let us suppose that the LEE is due to
some new particle X. Simple signatures involving elastic scattering on electrons (e.g. Xe
−
→
Xe
−
)or fully visible decays (e.g. X→e
+
e
−
)produce events which are very forward,
inconsistent with the measurement which features a broad angular distribution. While there is
a highly significant forward component to the excess, especially apparent in the 2021
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
102
MiniBooNE LEE result, the excess remains significant across a broad range of angles, and
one cannot simply presume that the forward excess is due to new physics while the rest of the
excess is due to background underestimation. Considering semi-visible decays (e.g.
g¢+XX )lessens the disagreement somewhat, but such models are still strongly dis-
favored, with either too many forward events or too many backward events depending on the
Xmass. In light of these constraints, the only class of models which can adequately reproduce
the LEE angular distribution are those involving inelastic scattering, similar to the neutrino-
nucleus scattering in the standard sterile neutrino interpretation.
4.2.1. Beam dump searches. Neutrino experiments as well as dedicated electron or proton
beam dump experiments can search for dark sector particles by looking for the decays or
scatterings of states produced at the target station. This technique has been extensively
explored in the literature in the search for light dark matter and mediators [380–383].
Measurements at LSND and MiniBooNE provide competitive limits in several light dark
sectors.
Of particular relevance are the results of the MiniBooNE-DM run. MiniBooNE ran in a
beam dump configuration where the proton beam was aimed directly at the downstream beam
dump instead of onto the neutrino production target. In this mode, charged meson decay in
flight was suppressed, reducing the ‘background’neutrino flux and enhancing sensitivity to
new physics. No excess of events was observed in beam dump mode, implying that any new
physics production modes that have a simple scaling with the number of protons on target like
neutral meson decays or continuum processes (i.e. bremsstrahlung)are ruled out because they
should produce a signature in beam dump mode. This leaves production from charged meson
decay in flight as the only viable production mode for new particles that can explain the LEE.
Figure 72. 95% confidence level exclusion curves in the (()qDmsin 2 ,
ee
241
2)plane
obtained from the analysis of KATRIN data with fixed m
ν
(m
β
)=0. The green contours
denote the 3 +1 neutrino oscillations allowed at 95% confidence level by the reactor
and gallium anomalies [66]. KATRIN data improve the exclusion of the high Dm41
2
values with respect to DANSS, PROSPECT, and STEREO reactor measurements
[134,655,656]. Mainz [657]and Troitsk [658]exclusion curves [659]are also
displayed for comparison. An estimation of KATRIN’sfinal sensitivity is represented
by the dotted line. Reproduced from [364].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
103
New physics explanations of the MiniBooNE LEE based on inelastic scattering
signatures in the detector are favored due to the compatibility with the measured angular
distribution of the excess. The MiniBooNE-DM results imply that such processes should be
initiated by either neutrinos or new particles produced in charged meson decays at the
target [224].
4.2.2. Neutrino–electron scattering measurement. Models that can explain the LSND or
MiniBooNE anomaly through the production of new particles that decay to electromagnetic
showers can be constrained by measurements of neutrino–electron (ν−e)scattering. Since
single photons and collimated e
+
e
−
pairs appear as single showers, they can be searched for
by looking for in the photon-like sidebands of this measurement. In [217], the authors propose
a technique to constrain e
+
e
−
explanations of LSND and MiniBooNE using data from
MINERνA and CHARM-II. These experiments were located in the NuMI and CERN SPS
beams, respectively, and therefore cover a much broader and higher-energy neutrino flux than
LSND and MiniBooNE (see left panel of figure 73).
In the dark photon model discussed in section 3.2, the HNL decays to overlapping e
+
e
−
predict new signals in the large-dE/dxsideband of ν−escattering, with moderate values of
Eθ
2
. The energy deposition dE/dx,defined as the deposited energy in the first centimeters of a
electromagnetic shower, helps discriminate between electron-like showers from photon-like
showers, which have typically twice the energy deposited per cm than the former. The
variable Eθ
2
,defined as the shower energy times the square of the shower angle with respect
to the neutrino beam, is also used to reduce backgrounds since in the boosted electron in ν−e
scattering obeys Eθ
2
<2m
e
, while backgrounds, mostly from π
0
decay and ν
e
CCQE, can
have much broader angular distributions. For the dark sector signatures, the resulting
overlapping e
+
e
−
pairs can be quite forward, especially when the dark photon is light.
Examples of the dark sector predictions at MINERνA as a function of dE/dxand at CHARM-
II as a function of Eθ
2
are shown in figure 73.
Since the backgrounds have large uncertainties and the search is not tailored to the dark
sector signals, the sensitivity is not enough to rule out all explanations of the MiniBooNE
excess. However, due to the higher-energies at MINERνA and CHARM-II, explanations with
large HNL masses, often preferred due to the broader angular distributions at MiniBooNE,
Figure 73. Left: the neutrino flux at MiniBooNE, MINERνA, and CHARM-II are
shown as shaded regions. In lines the upscattering cross section for producing heavy
neutrinos through coherent and incoherent
¢
Zscattering is shown. Right: The single
shower event spectra as a function of dE/dxat MINERνA(top)and of Eθ
2
at CHARM-
II (bottom). Dashed lines indicate analysis cuts. Reproduced from [217].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
104
can be robustly excluded. In figure 73, the limits are shown in the mixing of the HNL with
muon neutrinos, |U
μ4
|
2
, and their mass m
4
. Other parameters like kinetic mixing òand the
dark sector coupling α
D
, as well as the dark photon mass
¢
m
Zare fixed. Two curves are shown
for each experiment: a solid curve for the nominal choice of background uncertainty, and a
dashed curve corresponding to the case where uncertainties were inflated by a factor of a few
(see caption). For MINERνALE(ME), this corresponds to 30% (40%)background
normalization uncertainty in the nominal case and 100% uncertainty in the conservative case.
For CHARM-II these correspond to 3% and 10%, respectively. The uncertainties at CHARM-
II are constrained by the sideband at large Eθ
2
.
Future measurements, including antineutrino-electron scattering at MINERνA can
improve on the limits discussed above. The limits can also be recasted onto models with
photon final states, like those discussed in figure 3.2.1. Finally, HNLs produced via scalar
mediators are less constrained by this technique since the upscattering cross section decreases
at higher energies.
4.2.3. Searches for long-lived particles. The possibility that meson decays produce long-
lived HNLs in neutrino beams is strongly constrained by direct searches at T2K [384],
MicroBooNE [385], and ArgoNeuT [386], as well as by other past-generation experiments
such as PS-191 [387](recently re-evaluated in [388]and [389]), CHARM [390], CHARM-II
[391], and NuTeV [392]. The constraints are placed on minimal models with a single HNL N
that interacts with the weak bosons only, with interaction strength suppressed by small mixing
angles U
αN
.Atfirst sight, this model differs from the light sterile neutrino only for the mass of
the additional neutrino, which is supposed to be in the 10–500 MeV range. However, this
difference results in a radically different phenomenology. Because these new particles are so
much heavier than the standard neutrinos, no oscillation is possible: the HNL mixes with the
other neutrinos but loses coherence immediately with the rest of the wave packet. As a result,
in the minimal scenario, in which no other particle or interaction is present aside from one or
more HNLs, the HNL is produced in the beam through mixing and decays in the detector. The
available decay channels depend on the mass and include e
+
e
−
ν,eμν,eπ,μ
+
μ
−
ν,μπ.
However, this minimal model is ruled out by a combination of Big Bang Nucleosynthesis,
which provides a lower bound on the mixing parameters [393], and experiments with neutrino
beams, which lead to upper bounds, with no available parameter space in between these
bounds (left plot in figure 75).
In particular, the T2K Near Detector ND280, a modular detector able to resolve details of
interactions track and identify individual final state particles, sets the best limits on these
models. For this analysis, the three TPCs filled with gaseous argon provide a low-density
decay volume for the HNLs, with zero background from neutrino interactions, as illustrated in
the left plot in figure 76. The limits have been derived through a search with little expected
background and zero observed events in every analysis channel [394], later extended and
combined with BBN constraints [388].
This model becomes more interesting if new interactions are present. These new
interactions allow new decay modes, hence shortening the lifetime and relaxing BBN limits.
For example, if the HNL possesses a magnetic moment, it could decay electro-
magnetically into νγ. For magnetic moments of the order of PeV, this model could explain the
MiniBooNE anomaly [205]. However, this explanation is constrained by short-baseline
experiments, like MicroBooNE and ND280 (right plot in figure 75). Thanks to the high
density of the liquid argon, MicroBooNE identifies single photons through conversion to
e
+
e
−
pairs. ND280 is instead sensitive to the branching ratio into off-shell photons, which
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
105
results in a genuine e
+
e
−
pair. In this case, the rate is lower by a factor of 100 but benefits
from a zero background search.
Upscattering recasts. As discussed in sections 3.2, HNLs can be short-lived if they
interact via additional forces via a dark photon or scalar, for instance. In these models, the
lifetime of the HNL can range from tens of meters to sub-mm, depending on the choice of
parameters. In this regime, standard neutrinos scattering on nuclei can produce a HNL, as
illustrated in the right panel of figure 76. This particle propagates inside the detector and
Figure 74. The MINERνA and CHARM-II constraints in the parameter space of the
HNL mixing with muons as a function of its mass, at 90% C.L. Solid lines show the
nominal constraints, while dashed ones show constraints with inflated systematic errors
on the background. The arrows on the vertical lines indicate where more than a given
percentage of the total excess events at MiniBooNE are predicted in the forward-most
angular bin. Reproduced from [217].CC BY 4.0.
Figure 75. Left: exclusion plot for the minimal scenario, showing the mixing with the
muon flavour versus the HNL mass. Right: exclusion plot for the non-minimal scenario
where HNLs possess a magnetic moment. It shows the mixing with the muon flavour
versus the magnetic dipole moment for an HNL mass of 250 MeV. The region of
interest to explain the MiniBooNE excess is shown in green [205]. The dark grey
region is taken from or extrapolated by [660]. Reproduced from [388].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
106
subsequently decays into an e
+
e
−
pair plus another neutrino. Searches for e
+
e
−
final states at
neutrino detectors can be used to constraint this possibility. In particular, the near detector of
T2K, ND280, and the MicroBooNE detector have both been used to search for the decay of
long-lived particles into e
+
e
−
In the scenario of a dark photon heavier than the HNL, lifetimes range between a few cm
to several meters. In this case, a dark neutrino would be produced in the Pi0 detector (POD),a
very dense detector composed of high-Zmaterials such as lead, which lies upstream with
respect to the TPCs. The production is particularly copious as the process is coherent, thus
scaling with Z
2
and benefiting the high Zmaterials. In the scenario of a dark photon lighter
than the HNL, the decay proceeds through an on-shell dark photon, resulting in a larger decay
width and shorter lifetimes, sub-millimetre. In this case, the HNL is produced and decays at
the same point in the detector. The fine-grained detectors (FGD)of ND280 come into play for
this study. This plastic scintillator is dense enough to make the rate for production through
upscattering significant while allowing precise tracking and identification of the e
+
e
−
pair.
Because of the larger density, backgrounds from the beam or photons that convert inside the
FGD are present. On the other hand, the invariant mass of the e
+
e
−
pair is an excellent
quantity to discriminate this background as it peaks around the dark photon mass because of
the on-shell decay - making this analysis a peak search. Explanations of MiniBooNE under
this model are not entirely ruled out yet [395], but the next generation of analyses, together
with an upgrade to the detector [296]and a much larger dataset [396]that will be collected by
T2K, are expected to probe the entire parameter space of interest.
4.3. Conventional explanations and other searches
Partly motivated by the lack of a single interpretation that can simultaneously explain all
observed experimental anomalies, the possibility that the anomalies represent a collection of
conventional explanations (or that in combination with new physics)has also been discussed;
see, e.g. [36], in which the possibility that the MiniBooNE anomaly is a combination of
underestimated backgrounds is explored. In this case it was shown that no combination of
varying the known backgrounds can completely explain the MiniBooNE LEE, it can
potentially reduce the significance to 3σif several less well-known backgrounds saturate their
prescribed errors.
Key among the anomalies is the MiniBooNE low-energy excess, where it has been shown
repeatedly that the excess shape at low energy is incompatible with 3+Nlight sterile neutrino
oscillations, raising the question whether this excess is due to another effect. Furthermore, as
Figure 76. Left: schematic representations of an HNL decaying in flight in one of the
ND280 GArTPCs, as considered in [388,394]. Right: the HNL is produced in the
dense layers of lead through upscattering and subsequently decays in one of the
GArTPCs as considered in [395].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
107
this energy region is dominated by non-ν
e
backgrounds, conventional interpretations for the
excess that do not rely on new physics or introduce electrons into the MiniBooNE detector
have been raised. The majority of these rest on the known fact that MiniBooNE—as a
Cherenkov detector—had no ability to distinguish a single photon from a single electron, and
in particular target the various photon backgrounds irreducibly contributing to and dom-
inating the MiniBooNE observed ν
e
CCQE rate at low energy.
In the reactor sector, the experimental search for sterile neutrinos were primarily motivated
by the anomalously low rates of fluxes measured by the past reactor neutrino experiments.
Overestimated
¯
n
e
rates based on mismodeled reactor models, against which the fluxes were
compared, could also explain the observed discrepancy without invoking new BSM particle
physics.
4.3.1. Constraints on single-photon production. The majority of conventional interpretations
to the MiniBooNE excess propose that the excess is due to mis-identified photons from
various neutrino interactions that produce photons and no charged lepton in the final state. In
MiniBooNE, these mis-identified backgrounds are primarily contributed by π
0
production,
due to reconstruction inefficiencies (where one photon from the π
0
decay may be missed)or
more rare processes such as NC single-photon production through Δ(1232)resonance
production and subsequent radiative decay. Many of these processes can and have been
constrained in situ at MiniBooNE. This was the case for the rate and momentum-dependence
of misidentified NC π
0
decays, which were constrained by a high-statistics measurement of
events with two reconstructed electromagnetic shower Cerenkov rings, representing the two
photons from NC π
0
decay. Similarly, the ‘dirt’background component in MiniBooNE,
which was NC π
0
-dominated, was directly constrained by a high-statistics measurements of
events close to the detector boundary. These processes were further studied and disfavored as
the source of the MiniBooNE anomaly by studying both the radial distribution of the excess
as well as the timing of the events relative to the known beam bunch timing [33]. On the other
hand, photons from the radiative decay of the Δ(1232)baryon produced in neutrino NC
interactions (NC Δ→Nγ, where N=p,n)were an irreducible background in MiniBooNE.
This background was not constrained in situ, but rather the rate was constrained indirectly
through its correlation with the NC π
0
measured rate (which proceeds predominantly via Δ→
Nπ
0
decay).
The MicroBooNE collaboration has recently performed a direct search for single-photon
events coming from neutrino-induced NC production of the Δ(1232)baryon resonance with
subsequent Δradiative decay [248]. As discussed in section 3.3.1,Δdecay is expected to be
the dominant source of single-photon events in neutrino-argon interactions below 1 GeV.
Although Δradiative decay is predicted in the SM, and measurements of photoproduction
[397]and virtual Compton scattering [398]are well described by theory, this process has
never been directly observed in neutrino scattering. In a fit to the radial distribution of the
MiniBooNE data with statistical errors only, an enhancement of NC Δ→Nγby a
normalization factor of 3.18 (quoted with no uncertainty)was found to provide the best fit for
the observed excess, and in good spectral agreement with the observed excess across a
number of reconstructed kinematic variables [33]. The MicroBooNE collaboration searched
directly for an excess of this magnitude, interpreted as an overall enhancement to the
theoretically-predicted NC Δ→Nγrate.
MicroBooNE utilized the strength of LArTPC neutrino detectors to search for this excess
of single-photons from the Δdecay, with and without a proton track present in the interaction
(referred to as 1γ1pand 1γ0pfinal states). The presence of the reconstructed track in the 1γ1p
selection allowed for the tagging of the neutrino interaction vertex, and subsequent
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
108
reconstruction of the photon conversion distance in argon, which led to improved background
rejection compared to the 1γ0pselection, where the lack of associated hadronic activity
prevented neutrino vertex tagging.
The analysis used approximately half of the total collected MicroBooNE data to date
(6.9 ×10
20
POT). It selected and simultaneously fitted the 1γ1pand 1γ0psamples together
with two additional, mutually exclusive but highly correlated samples with high NC π
0
purity.
These high-statistics NC π
0
samples effectively constrained the rate and systematic
uncertainty of NC π
0
production in argon, which was the dominant background to the
1γ1pand 1γ0pselections.
MicroBooNE observed no evidence for an excess of NC Δradiative decay, as shown in
figure 77. The measurement ruled out the normalization enhancement factor of 3.18 as an
explanation to the MiniBooNE low-energy excess at 94.8% CL (1.9σ), in favor of the
nominal prediction for NC Δ→Nγ. Note that this was a model-dependent test of the
MiniBooNE excess, and therefore does not necessarily apply universally to any photon-like
interpretation. Those include, e.g. coherent single-photon production, which is expected to be
a rarer process in MicroBooNE than NC Δ→Nγ, or BSM processes that manifest as single-
photon events, such as co-linear e
+
e
−
from the decay of new particles. Those will be the
target of dedicated follow-up MicroBooNE analyses, as well as model-independent single-
photon searches.
4.3.2. Reactor flux models. As discussed in section 2.3, modeling the reactor
¯
n
e
flux is quite
challenging. State-of-the art models used to compare against measured IBD yields employed
the conversion approach and relied on β-decay measurements performed at ILL in the 1980s.
The presence of mistakes in these beta-decay measurements, as well as incorrect assumptions
present in the conversion process, could lead to mis-modeled reactor
¯
n
e
fluxes. Recent
¯
n
e
and
β-decay measurements have played a crucial role in further exploring flux prediction issues as
a possible source of the RAA.
Daya Bay [255]and RENO [256]experiments—leveraging their IBD yield measure-
ments as a function of evolving fission fractions in the reactors—were able to perform
simultaneous IBD yield measurements of
235
U and
239
Pu. While continuing to observe the
same time-integrated IBD yield deficit that defines of the RAA, these results also showed that
while
239
Pu yields are in good agreement with the models,
235
U is at 0.925 ±0.015 (>3σ)of
Figure 77. Summary of MicroBooNE’sNCΔ→Nγsingle-photon searches for both
with (left)and without (right)an associated proton. Reproduced from [248].CC BY 4.0.
No evidence of an enhanced NC Δ→Nγrate is observed.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
109
the modeled yield as shown in figure 78. While these results are in slight tension (∼1σ)with
the average
235
U IBD yields from the pure
235
U measurements done using HEU reactors
[399], they are in approximate agreement (∼0.5σ)with the modern
235
U yield measured by
the STEREO experiment [400]. It is also worth noting that summation-predicted IBD yields
are in good agreement with the Daya Bay’sflux evolution measurements [44,254].
To test the possibility of mis-modeled IBD yields in the conversion model, Kopeikin et al
[401]performed simultaneous β-decay spectrum measurements of
235
U and
239
Pu at the
Kurchatov Institute, generating a conversion prediction, referred to as the KI Model that uses
completely different primary inputs than those used by the Huber model. While the
measurement was designed to achieve an extremely high degree of correlation between
235
U
and
239
Pu measurements, it exhibited lower statistical precision than the ILL measurements of
the 1980s. The KI model found a consistently higher ratio of
235
Uto
239
Pu β-decay rates over
the full energy range compared to the ILL measurements as shown in figure 79. Potential bias
in βdecay measurements have also been pointed out in a separate study [402].
These new conversion prediction results, together with the
¯
n
e
flux evolution
measurements from Daya Bay and RENO and the summation-conversion flux evolution
mis-matches mentioned in section 3.3.2 collectively suggest mis-modeled
235
U IBD yields as
a major contributor to the RAA. This collective picture is well-illustrated in figure 80, which
shows predictions and
¯
n
e
-based measurements of IBD yields for the dominant fission isotopes
235
U and
239
Pu, given in terms of a ratio with respect to the Huber–Mueller conversion
prediction. Conversion predictions based on the ILL beta measurements (Huber–Mueller and
the HKSS model discussed in section 3.3.2)appear to deviate from all other measurements
and predictions. Huber-Mueller models show substantial deficits with respect to direct IBD
Figure 78. IBD yields of
235
U and
239
Pu from Daya Bay (blue), RENO (red), and a
combined fit to Daya Bay and RENO. Horizontal and vertical black lines show the
predicted IBD yields for
239
Pu and
239
Pu respectively based on the Huber-Mueller
(HM)model. While
239
Pu yields agree with the model within 1σ,a>3σdiscrepancy
can be noticed in
235
U yields. Reproduced from [404].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
110
yield measurements, whereas discrepancies between EF and KI models with respect to the
data are not large enough to claim the existence of any anomaly whatsoever.
It is important to stress that while these flux-based indications are fairly clear in their
suggestion of flux prediction issues in the Huber-Mueller model and cast doubt on a pure
sterile neutrino interpretation of the RAA, this global flux picture still leaves substantial room
for short-baseline sterile oscillation phenomena at reactors. As previously mentioned in
section 3.3.2, it is likely that the error bars assigned to most, if not all, predictions in figure 80
are under-estimated, leaving ample room for sterile oscillation amplitudes around the 20%
level or lower. Moreover, multiple studies show that hybrid models containing both incorrect
flux predictions and sterile neutrinos also provide a good fit to global IBD yield datasets
[403,404]; some of these scenarios produce best-fit oscillation-induced deficits well in excess
of 10%. In light of this degeneracy between incorrect flux predictions and constant
oscillation-induced deficits, short-baseline reactor measurements capable of directly probing
the deficit’sL/Echaracter are the better bet for cleanly elucidating the the role played by
short-baseline sterile oscillations in the reactor sector.
4.3.3. MicroBooNE ν
e
CC measurement. MicroBooNE has additionally performed a search
that explicitly tests the nature of the MiniBooNE excess in a physics-model-agnostic way.
Specifically, MicroBooNE has carried out three independent analyses to investigate whether
the MiniBooNE observed low-energy excess can be described by an effective enhancement of
ν
e
CC scattering at low energy given by unfolding the MiniBooNE observed excess
distribution. This unfolding predicts a factor of 5–7 enhancement of ν
e
CC interactions below
500 MeV in true neutrino energy.
The data used in this search correspond to approximately half the data set collected by
MicroBooNE during its entire operational run time in the Fermilab BNB. The search was
carried out by three separate analyses, each targeting different exclusive and inclusive ν
e
CC
final states, and using separate reconstruction paradigms and signal selections. The ν
e
final
states explicitly targeted by MicroBooNE include a pion-less final state topology with one
electron and with 0 or N>1 protons as part of the visible hadronic final state; a CCQE-like
Figure 79. Ratio of the cumulative βspectra for
235
Uand
239
Pu as measured at ILL [661]
(blue)and at KI [662](red). KI sees consistently lower ratios than ILL. Reprinted (figure)
with permission from [401],Copyright(2021)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
111
final state topology with one electron and with only 1 proton as part of the visible hadronic
final state; and a CC-inclusive final state topology with one electron and with any number of
charged pions or protons as part of the visible hadronic final state. While probing different
event topologies with distinct event reconstruction and selection methods, the three
independent analyses still share several common aspects, including the signal model, a
Geant4-based simulation of the neutrino beam, the detector response model, and a tuned
variation of the GENIE v3 event generator incorporating the most up to date knowledge of
neutrino scattering in the <1 GeV energy range. The results from each of the three analyses
are presented in detail in [279,281,282], and are summarized in [280]. The final observed
and predicted distributions from each search are reproduced in figure 81, with the observed
data to Monte Carlo ratios shown in figure 82.
While statistics-limited, the three mutually-compatible analyses collectively reported no
excess of low-energy ν
e
candidates, and were found to be either consistent with or modestly
lower than the predictions for all ν
e
event classes, including inclusive and exclusive hadronic
final-states, and across all energies. With the exception of the pion-less, zero-proton selection,
which was the least sensitive to a simple model of the MiniBooNE low-energy excess,
MicroBooNE rejected the hypothesis that an enhancement of ν
e
CC interactions at low energy
Figure 80. Best-fit points and 95 % CL, and 99 % CL contours of
235
U and
239
Pu IBD
yields obtained using integrated rates (red), evolution measurements by Daya Bay and
RENO (purple), and combined integrated rates and evolution measurements (gray). The
axes correspond to r
i
(
R
HKSS
as described above)for
235
U and
239
Pu along x and y
direction respectively. Predictions from HM, EF, and HKSS models are shown in cyan,
orange, and blue contours respectively. Black dashed line represents r
235
=r
239
.Itis
clear from the plot that while the measured IBD yields agree with the predictions from
the EF (ab inito)model for both isotopes, only
239
Pu agrees with the HM and HKSS
models—both of which are conversion models relying on ILL βspectra measurements
—pointing towards an issue with the conversion approach-based
235
U predictions.
Reproduced from [110].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
112
is fully responsible for the MiniBooNE low-energy excess at >97% CL for both exclusive
and inclusive event classes. Additionally, MicroBooNE disfavored generic ν
e
interactions as
the primary contributor to the excess, with a 1σ(2σ)upper limit on the inclusive ν
e
CC
contribution to the excess of 22% (51%).
It should further be noted that while these searches do not explicitly test the possibility of
light sterile neutrino oscillations, a recent MicroBooNE publication [278], as well as
independent phenomenological studies, have further analyzed the observed data within that
context, including ν
e
appearance and/or ν
e
disappearance. The results of those are
summarized in section 4.1.2.1.
5. Astrophysical and cosmological indirect probes
It has been known for a long time that astrophysical observations can provide powerful
constraints on BSM physics. Stellar evolution arguments have long been invoked to constrain
couplings between light BSM particles and SM particles [405]. In particular, the success of a
core-collapse supernova and the synthesis of heavy elements via the r-process therein maybe
turned into an argument for or against sterile neutrino states (see, e.g. [1]). In the past two
decades, however, the strongest astrophysical statements on light sterile neutrinos have come
from cosmological measurements, i.e. those observations that probe the Universe on the
largest length scales. We discuss in this section the relevant theoretical arguments and the
most recent observational constraints.
Figure 81. MicroBooNE’s four targeted ν
e
CC spectra. Reproduced from [280].
CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
113
5.1. Cosmology
The standard hot big bang model predicts that the three generations of SM neutrinos are held
in a state of thermodynamic equilibrium with other SM particles via the weak interaction in
the first second post-big bang. At temperatures below about 20 MeV, the dominant equili-
brating interactions are
¯
()
nn
nn
nn nn
+-
ee
ee
,
,
.53
As the Universe expands and cools, these interactions become less frequent. When the
Universe cools to a temperature of
()
1
MeV, the interaction rate per neutrino Γdrops below
the Hubble expansion rate H. From this point onwards, the neutrinos are said to be
‘decoupled’from the thermal plasma. The typical energy of the neutrino ensemble at
decoupling is E∼3T?m
ν
, i.e. the ensemble is largely ultra-relativistic at decoupling.
Because of this, the neutrinos retain to a high degree of accuracy their relativistic Fermi–Dirac
phase space distribution parametrized by a temperature and possibly a nonzero chemical
potential.
Shortly after neutrino decoupling, the e
+
e
−
plasma becomes non-relativistic at T∼0.5
MeV. Here, kinematics favor the annihilation of e
+
e
−
pairs. The energy released in this
process ‘reheats’the photon population. The neutrino population, however, does not feel this
reheating, because they have already decoupled: in other words, the weak interaction pro-
cesses are no longer efficient at transporting the energy released from the annihilation to the
neutrino sector. The net effect is that the neutrinos emerge from the annihilation event a little
colder than the photons. Assuming (i)ideal gases, (ii)instantaneous neutrino decoupling, and
(iii)ultra-relativistic electrons/positrons at neutrino decoupling, one can show using entropy
conservation arguments
Figure 82. Summary of MicroBooNE ν
e
CC measurements. Reproduced from [280].
CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
114
⎛
⎝⎞
⎠()=
ng
TT
4
11 ,54
13
where T
ν
and T
γ
are the neutrino and the photon temperatures, respectively, after e
+
e
−
annihilation.
equation (54)is generally taken to define the standard neutrino temperature after e
+
e
−
annihilation. In reality, however, dropping any one of the three aforementioned assumptions
can result in percent-level corrections to the relation. These corrections are commonly
absorbed into the definition of the effective number of neutrinos N
eff
via
⎛
⎝⎞
⎠()
r
pr==
nng
NTN
7
120
7
8
4
11 .55
eff
24eff
43
Here, ρ
ν
is the actual total neutrino energy density after e
+
e
−
annihilation (but still deep in the
radiation domination era when the neutrinos are ultra-relativistic),thequantity
(
)pn
T7 120
24
denotes the energy density in one family of thermally-distributed relativistic neutrinos with a
temperature T
ν
defined in equation (54),andρ
γ
is the actual energy density in the photon
population, i.e. what eventually becomes the cosmic microwave background (CMB)radiation.
Precision calculations of the SM prediction of N
eff
find
=
N
3.0440 0.000
2
eff
SM [406,407],
including the effects summarized in table 14.
125
The effective number of neutrinos N
eff
is of interest to cosmology primarily because
energy density in relativistic particles affect directly the Hubble expansion expansion rate
during the radiation domination era. In the epoch after e
+
e
−
annihilation, the expansion rate is
given by
Table 14. Leading-digit contributions from various SM corrections, in order of
importance, that make up the final -
N
3
eff
SM (adapted from [407]). The largest, m
e
/T
d
correction results from dropping the assumption of an ultra-relativistic electron-posi-
tron population; finite-temperature quantum electrodynamics corrections (FTQED)to
the QED equation of state (EoS)enter at ()
e2and
()
e
3, where eis the elementary
electric charge; the non-instantaneous decoupling+spectral distortion correction is
defined relative to an estimate of
N
eff
SM
in the limit of instantaneous decoupling
assuming T
d
=1.3453 MeV [683]; and Type (a)FTQED corrections to the weak rates
refer to neutrino–electron scattering rates corrected with thermal masses. Reproduced
from [407]. © 2021 IOP Publishing Ltd and Sissa Medialab. All rights reserved.
Standard-model corrections to
N
eff
SM
Leading-digit contribution
m
e
/T
d
correction +0.04
()
e2FTQED correction to the QED EoS +0.01
Non-instantaneous decoupling+spectral distortion −0.005
()
e
3FTQED correction to the QED EoS −0.001
Neutrino flavor oscillations +0.0005
Type (a)FTQED corrections to the weak rates 10
−4
125
Note that because the parameter N
eff
is defined in relation to the neutrino energy density in an epoch when the
neutrinos are ultra-relativistic, there is no ambiguity in the definition (equation (55)) even if the neutrinos should
become non-relativistic at a later time because of their nonzero masses, provided the masses do not exceed the eV
scale.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
115
() ( ) ( )
prr=+
gn
Ht G8
3,56
2
where Gis the gravitational constant. With the photon energy density ρ
γ
having been
measured to better than 0.1% accuracy by the FIRAS instrument on board COBE [408,409],
constraints on H(t)in the early universe can be interpreted as bounds on the ratio ρ
ν
/ρ
γ
and
hence N
eff
.
From a particle physics standpoint, a thermal population of light sterile neutrinos is one
possible cause of a N
eff
that differs from the standard
N
eff
SM
value. However, it is important to
emphasize that, as far as the Hubble expansion rate H(t)is concerned, any thermal back-
ground or non-thermal population (e.g. from decays)of non-photon light particles such as
axions, majorons, or even gravitons will contribute to N
eff
. Such scenarios have been con-
sidered by many authors, including Refs. [410–416]. Likewise, any process that alters the
thermal abundance of neutrinos (e.g. a low reheating temperature)or affects directly the
expansion rate itself (e.g. a time-dependent gravitational constant G)can mimic a non-
standard N
eff
value. Yet another way to change N
eff
is to tinker with the photon energy density
itself (via, e.g. interaction with millicharged particles [417]or late kinetic decoupling of the
dark matter [418]), while preserving the neutrino energy density.
In the case of a non-standard N
eff
due to a BSM light particle, the mass of the new particle
can also impact on the evolution of cosmological density perturbations via its role as a ‘hot
dark matter’; the mathematical description of this effect goes beyond the Hubble expansion
rate (equation (56)).
In the following, we describe first how a thermal population of light sterile neutrinos can
arise in the early universe through a combination of neutrino flavor oscillations and scattering
with other SM particles. We then discuss the various signatures of light sterile neutrinos in
cosmological observables such as the light elemental abundances from big bang nucleo-
synthesis (BBN), the CMB anisotropies and the large-scale structure (LSS)distribution, con-
straints from current observations, as well as various proposals on how to get around them.
5.1.1. Light sterile neutrino thermalization. If a sterile neutrino state mixes sufficiently
strongly with any of the active neutrino states, a thermal population of light sterile neutrinos
that adds to N
eff
can be produced prior to neutrino decoupling via a combination of active-
sterile neutrino oscillations and collisions (i.e. elastic and inelastic scattering)with the
primordial plasma of SM particles. Roughly speaking, as the Universe cools, an initial
population comprising only active neutrinos can begin to oscillate into sterile neutrinos once
the oscillation frequency, given by Δm
2
/(2E), becomes larger than the Hubble expansion rate
H(t). The role of collisions is then to force a neutrino into a flavor eigenstate and hence
‘measure’the flavour content of the ensemble. Since the probability of measuring a sterile
flavor is nonzero, signifying that an active neutrino has turned into a sterile state, collisions
also play the role of refilling any gap in the active neutrino distribution vacated by the
oscillation process. This effect and the region of parameter space leading to thermalization of
the sterile neutrino was found by the early works of, e.g. [419–422]If sterile neutrinos do
become thermalized, then we expect them to have the same temperature as the active
neutrinos.
Nowadays, light sterile neutrino thermalization in the early universe can be computed
precisely, using a generalized Boltzmann formalism developed in [423,424]which tracks the
flavor evolution of a neutrino ensemble under the influence of neutrino oscillations and
scattering. Schematically, the generalized Boltzmann equation for the one-particle reduced
density matrix of the neutrino ensemble, ñ(t,p), in the Friedmann-Lemaître–Robertson–
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
116
Walker (FLRW)universe of standard hot big bang cosmology is given by
[][] ()
-¶=- +

pH i, , 57
tp
where ∂
t
and ∂
p
are partial derivatives with respect to the cosmic time tand physical
momentum prespectively, His the Hubble expansion rate,
[
]º-

,denotes a
commutator between the flavor oscillations Hamiltonian
and ñ, and the collision integrals
[
]
encapsulate all non-unitary (scattering)effects on ñ. In the fully CP symmetric case, one
set of density matrix ñ(t,p)suffices to describe the evolution of the whole neutrino ensemble
including antineutrinos. If however the system is CP asymmetric, we will need to introduce a
separate one-particle reduced density matrix
¯(
)
tp,
for the antineutrino ensemble. Here, we
follow the convention of [423], and define the density matrices using the ”transposed
notation, e.g. for a 3 active+1 sterile system one would have
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
() ¯()
¯¯ ¯ ¯
¯¯ ¯ ¯
¯¯ ¯ ¯
¯¯ ¯ ¯
()==
mt
mmmmtm
ttmttt
mt
mt
mmm tm m
tmt tt t
mt








tp tp,,,.58
ee e e es
es
es
se s s ss
ee e e se
es
es
es s s ss
This convention enables the equations of motion to be expressed in a more compact form.
Working in the flavor basis, the oscillations Hamiltonian under this convention is
⎡
⎣
⎢⎤
⎦
⎥
( ()) [ ( ()) ( ()) () ()]
(()) (()) (()) (()) () () ()
†
¯¯
¯¯
¯
= + - + -
+++++
nn
nn


ptTt UU
pGTt Tt t t
Gp Tt Tt Tt Tt
m
tt
m
,, 22
22 4
3,59
Fℓ ℓ
Fℓℓℓℓ
WZ
22
which contains a vacuum and an in-medium part. The vacuum part consists of the neutrino
squared-mass difference matrix
and the vacuum mixing matrix U, with the ‘+’sign
pertaining to neutrinos and the ‘−’sign to the antineutrinos. The in-medium part proportional
to the Fermi constant G
F
, i.e. the ‘matter potential’, contains a CP symmetric and a CP
asymmetric correction to the neutrino dispersion relation. The CP asymmetric part is similar
to the usual matter potential found in, e.g. the Sun, with the matrix
¯
-
ℓℓ
denoting the
asymmetry in the number density of charged leptons; in a 3 +1 system
ℓ
would take the
form
()( ) ()
ò
p
º=
mt mt
pp f f f n n n
1
2d diag , , , 0 diag , , , 0 , 60
ℓee
2
2
where f
ℓ
(p,T)is the (equilibrium)occupation number of the charged lepton ℓ. A similar
expression exists also for
¯
ℓ
. Typically, the charged-lepton asymmetries are of order 10
−10
,
so this
¯
-
ℓℓ
term is not strictly a necessary ingredient. Observe however the additional
term proportional to ¯
-
nn
, where
()
ò
p
º
n
pp S S
1
2d, 61
aa
2
3
and similarly for ¯
n
. This CP asymmetric term describes neutrino self-interaction in the
presence of a large (>10
−5
)neutrino asymmetry. Current cosmological data constrain
neutrino asymmetries only to ()
-
10 2[425], so the presence of a sizeable ¯
-
nn
term is an
interesting possibility. In standard calculations of light sterile neutrino thermalization,
however, this asymmetry is set to zero. The quantity S
a
is a diagonal matrix that projects out
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
117
only the active neutrino states, since sterile states are by definition interaction-less. In a 3 +1
system it takes the form S
a
=diag(1, 1, 1, 0).
In the CP symmetric portion of the in-medium terms, m
W
and m
Z
denote respectively the
Wand Zboson mass, while the terms
ℓ
and
ℓare momentum-integrals of some
combinations of the charged-lepton energy
() ( )º+
E
ppm
ℓℓ
2212and occupation number
f
ℓ
(p,T), and ¯
ℓ,
¯
ℓ
are their antiparticle counterparts. For a 3 +1 system, we have
()()()
ò
prrrº=
mmttmt
pp E f E f E f
1
2d diag , , , 0 diag , , , 0 , 62
ℓe
ee
2
2
⎜⎟
⎛
⎝⎞
⎠()()
ò
p
º=
mmttmt
pp p
Efp
Efp
EfPPP
1
6d diag , , , 0 diag , , , 0 , 63
ℓ
e
ee
2
2
22 2
where ρ
ℓ
and P
ℓ
are, respectively, the energy density and pressure of the charged lepton ℓ.
Lastly, n
is the equivalent of equation (62)for an ultra-relativistic neutrino gas,
()
ò
p
º
n
pp S S
1
2d, 64
aa
2
3
where S
a
is again a diagonal matrix that projects out only the active neutrino states.
Note that the
+
ℓℓ
term in equation (59)differs from its usual presentation found in,
e.g. equation (2.2)of [426], which has
+
ℓℓ
replaced with
(
)43 ℓ. First reported in [427],
the former is in fact the more general result, while
(
)43 ℓapplies strictly only when the
charged leptons are ultra-relativistic.
The collision integral
[
]
incorporates in principle all weak scattering processes
wherein at least one neutrino appears in either the initial or final state. All published
calculations to date, however, account only for 2 →2 processes involving (i)two neutrinos
and two charged leptons anyway distributed in the initial and final states, and (ii)neutrino–
neutrino scattering. Then, schematically,
[
]
comprises 9D momentum-integrals that, at tree
level, can be systematically reduced to 2D integrals of the form
[( )] ( ) () ( )
ò
µP

pt G p p ppptF,dd,,;, 65
F
2
23 23
where Πis a scalar function representing the scattering kernel, and Fis a phase space matrix
including quantum statistics.
The vast majority of existing works on light sterile neutrino thermalization solve the
above set of equations of motion for a 1 active+1 sterile system. Because of the complexity of
the collision integrals
[
]
, a variety of approximations have been introduced to simplify the
integrals and hence speed up the computation [424,428–432], although of course it is also
possible to solve the collision integrals exactly if percent-level precision is required [432].
The publicly available code LASAGNA [433]solves a 1 +1 system and also allows for the
possibility of a CP asymmetry. On the other hand, multi-flavor (i.e. 3 +1)effects have been
considered in [434]using the momentum-averaged approximation and in [166]using a multi-
momentum approach. Most recently, a publicly available multi-flavor code FortEPiaNO
[426]has also become available, which is capable of solving a system with up to 3 active+3
sterile species, although it does not provide the CP asymmetric case.
Irrespective of how exactly the system is solved (3+1, 1 +1, approximate or exact
collision integrals, etc), however, the general conclusion is that the active-sterile neutrino
squared mass difference and mixing required to explain the short-baseline anomalies will
inevitably lead to a fully thermalized light sterile neutrino population with a temperature
similar to that of the active neutrinos. In other words, in terms of the N
eff
parameter, we expect
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
118
the canonical light sterile neutrino solution to the short-baseline anomalies to lead to N
eff
∼4.
Figure 83 and 84 show the prediction for N
eff
as a function of the mixing parameters in a
1+1 and 3 +1 scheme respectively. We discuss in the next section the observable
consequences of this light sterile neutrino population.
5.1.2. Observable consequences. Three standard cosmological probes are sensitive to the
presence of a light sterile neutrino population primarily through its contribution to increasing
N
eff
and hence the Hubble expansion rate, and/or through its nonzero mass and hence its role
as a ‘hot dark matter’. We describe these probes below.
5.1.2.1. Big bang nucleosynthesis. The discussion of light element formation from protons
and neutrons via the process of big bang nucleosynthesis (BBN)(see [435]for a recent
review)usually begins at a temperature around T∼0.7 MeV, when the weak processes
¯()
n
n
+« +
+« +
-
+
ne p
pe n
,
66
e
e
become inefficient compared with the Hubble expansion rate and equilibrium can no longer
be maintained. When these process go out of equilibrium, the ratio of neutron-to-proton
number density also freezes out, to a value given by
⎜⎟
⎛
⎝⎞
⎠()=-
-
n
n
mm
T
exp , 67
n
p
np
fr fr
where T
fr
is the freeze-out temperature, and m
n,p
are the neutron and proton masses. For T
fr
;
0.7 MeV, this ratio evaluates approximately to 1/6. Free neutron decay over a lifetime of
about 880 s, however, will reduce it to a smaller number by the end of BBN.
Figure 83. The change in the effective number of neutrinos, Dº -NNN
eff eff eff
SM,ata
temperature T=0.1 MeV from active-sterile neutrino oscillations in a 1 +1 system,
where δm
2
is the squared mass difference and θis the effective mixing angle between
the active and the sterile state. Reproduced from [432].CC BY 3.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
119
In standard BBN, the formation of elements commences at a temperature controlled by
the baryon-to-photon ratio η, when the energy in the photon bath per baryon has become
sufficiently low such that newly formed nuclei are no longer immediately broken apart. For η
Figure 84. The final effective number of neutrinos from active-sterile neutrino
oscillations in a 3 +1 scheme, under the constraint
∣∣
å=-Ulog 13
i
10 42
. Reproduced
from [426]. © 2019 IOP Publishing Ltd and Sissa Medialab. All rights reserved.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
120
∼6×10
−10
, this temperature is around T∼0.1 MeV. The first element to be formed is
Deuterium, followed by the production of heavier nuclei. Of particular note is Helium-4,
whose mass fraction is defined as
()º+
Yn
nn
4,68
p
np
He 4
where n
He4
is the number density of
4
He. Because
4
He has the largest binding energy amongst
the light elements, the bulk of all initially available neutrons will eventually end up bound in
Helium-4 nuclei, i.e. we expect n
He 4
;n
n
/2. Then, to estimate Y
p
from equation (68)we
simply need to note that the neutron-to-proton ratio typically drops to about 1/7 at the end of
BBN via neutron decay. From this we find Y
p
;0.25.
Besides Helium-4 mass fraction, small amounts of Deuterium and
3
He (D/H∼
3
He/H
∼O(10
−5
)), as well as traces of
6
Li and
7
Li, are expected to remain. Unlike for
4
He, however,
there are no simple ways to estimate their abundances, and we must rely on solving a set of
Boltzmann equations to track their number densities. Several publicly available codes can
perform this task, including AlterBBN [436,437],PArthENoPE [438,439], and PRIMAT
[435]. In standard BBN, barring experimental uncertainties in the nuclear reaction rates and
the free neutron lifetime, the baryon-to-photon ratio ηalone enters these Boltzmann equations
and is hence the sole free parameter in the determination of the elemental abundances.
A non-standard neutrino sector can alter this picture in two different ways. Firstly, as can
be seen in equation (66), electron neutrinos participate directly in the CC weak interactions
that determine the neutron-to-proton ratio. If because of non-standard physics these neutrinos
should end up at T1 MeV with an energy spectrum that departs strongly from an
equilibrium relativistic Fermi–Dirac distribution with zero chemical potential, then the
equilibrium of the processes (equation (66)) could shift to a different point and in so doing
alter the neutron-to-proton ratio. A particularly well studied example in this regard is the case
of a nonzero electron neutrino chemical potential μ
e
, which shifts the neutron-to-proton ratio
at weak freeze-out in a manner well described by
⎜⎟
⎛
⎝⎞
⎠()
m
=-
--
n
n
mm
TT
exp . 69
n
p
np e
fr fr fr
The effects of more general distortions to the ν
e
and/or
¯
n
e
energy spectra on n
n
/n
p
need to be
computed numerically using a Boltzmann code.
Secondly, neutrinos of all flavors influence the expansion rate of the Universe prior to
and during BBN through their energy densities via equation (56). Therefore, if because of
new physics the total neutrino energy should be larger than the standard
N
eff
SM
, the freeze-out
of the processes (equation (66)) would occur at a higher temperature. This in turn pushes up
the neutron-to-proton ratio via equation (67)and hence the Helium-4 mass fraction as well via
equation (68). Figure 85 shows the Deuterium, Helium-4 and Lithium-7 abundances
computed using PArthENoPE [438,439], as a function of the baryon density ω
b
, the excess
number of relativistic degrees of freedom
ºD º -
N
NNN
seff eff eff
S
M
, and the electron
neutrino degeneracy parameter ξ≡μ
e
/T.
For the specific problem of a light sterile neutrino with mixing parameters compatible
with hints from terrestrial experiments, only the second effect is relevant. This is because the
relatively large mass-squared difference and mixing between the active and the sterile
neutrino states essentially guarantee full thermalization of the sterile species prior to the
decoupling of the active neutrinos (see figures 83 and 84). In other words, ΔN
eff
;1 and the
phase space distribution of the sterile states follows closely the equilibrium relativistic Fermi–
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
121
Dirac distribution of the active neutrinos. This also implies equipartition amongst the four
neutrino flavors, such that any further active-sterile flavor oscillations after neutrino
decoupling will not cause the ν
e
phase space distribution to deviate from a thermal
distribution. Thus, to constrain such light sterile neutrino scenarios, we only need to extend
standard BBN with one extra free parameter, namely, N
eff
. We emphasize, however, that more
general cases of active-sterile neutrino mixing would require that we determine the ν
e
energy
spectrum as well, in order to determine the full effect of light sterile states on the light
elemental abundances.
Current BBN constraints. Current astrophysical observations put the Helium-4 mass fraction
at Y
p
=0.2449 ±0.0040 [440], the Deuterium abundance at D/H=(2.527 ±0.030)×10
−5
[441], and the Lithium-7 abundance at
7
Li/H=(1.58 ±0.3)×10
−10
[442], while the Helium-3
abundance is constrained to
3
He/H<(1.1 ±0.2)×10
−5
[443]. Of these, only the D/HandY
p
measurements have sufficient precision to probe N
eff
during the BBN epoch. How D/HandY
p
probe N
eff
can be seen in figure 86, which shows in the top panel the 68.27% and 95.45%
contours in the (Ω
b
h
2
,N
eff
)-plane, where Ω
b
h
2
≡ω
b
is the baryon density, obtained from various
data combinations, and in the bottom panel the corresponding 1D marginalized posterior for N
eff
.
As can be seen, the Helium-4 mass fraction alone is already quite sensitive to N
eff
,
although this measurement is not particularly useful for pinning down the baryon-to-photon
ratio ηand hence the baryon density Ω
b
h
2
. This is because ηhas no strong influence on the
rate at which
4
He is formed, other than setting the initial time of BBN. In contrast, the
Deuterium abundance is strongly sensitive to both N
eff
and η, which do directly affect the
Figure 85. Deuterium, Helium-4 and Lithium-7 abundances, as computed using
PArthENoPE [438,439], as a function of cosmological parameters: ω
b
is the baryon
density, N
s
is our Dº -NNN
eff eff eff
SM, and ξ≡μ
e
/Tis the electron neutrino
degeneracy parameter. Reproduced from [454]. © 2011 IOP Publishing Ltd and
SISSA. All rights reserved.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
122
formation rate. However, because these two measurements have opposite degeneracy
directions on the (Ω
b
h
2
,N
eff
)-plane, in combination they provide a good measurement of both
Ω
b
h
2
and N
eff
. For the latter, [435]finds
() ()=
N
2.88 0.27, 68% CL 70
eff
using the code PRIMAT [435]. Using PArthENoPE [438,439]instead would have yielded a
central value about 2% smaller [435]. Thus, the conclusion here is that current measurements
of primordial elemental abundances are completely consistent with the
=
N
3.0440
eff
SM , and
shows no evidence of any extra relativistic degrees of freedom.
5.1.2.2. Cosmic microwave background and large-scale structure. Unlike BBN, probes of
the Universeʼs inhomogeneities such as the CMB temperature and polarization anisotropies
and the large-scale matter distribution are not sensitive to the flavor content of the neutrino
sector, only to its contribution to the stress-energy tensor. If neutrinos are massless, then the
Figure 86. Top: 68.27% and 95.45% contours in the (Ω
b
h
2
,N
eff
)-plane obtained from
various data combinations. Bottom: 1D marginalized posterior for N
eff
. Reprinted from
[435], Copyright (2018), with permission from Elsevier.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
123
N
eff
parameter as defined in equation (55)alone characterizes their effects on the Universeʼs
evolution. If neutrinos are massive, then, in addition to N
eff
and the neutrino masses, in
principle it is also necessary to know the exact form of the neutrino momentum distribution in
order to solve the evolution equations for the inhomogeneities exactly. However, unless the
deviations from a thermal relativistic Fermi–Dirac spectrum is of order unity, it suffices to
specify only the temperature of the distribution, as late-time cosmological probes are currently
not very sensitive to spectral distortions in the neutrino sector. For this reason, most existing
analyses characterize the neutrino sector, including light sterile neutrinos produced as
described in section 5.1.1, only in terms of the neutrino mass spectrum and the N
eff
parameter.
The light sterile states are assumed to share the same temperature as the standard active
neutrinos.
One interesting variation to the above is the case in which an excess >
N
N
eff eff
SM is due to
a thermalized particle species that has temperature different from the standard neutrino
temperature and/or has a different spin statistics, e.g. a thermalized bosonic particle species
such as an axion that follows the Bose–Einstein distribution. If this new particle is massless,
then again it suffices to describe its phenomenology in terms of its contribution to N
eff
alone.
If however the particle species is massive, then in addition to its mass, its temperature also
plays a role in determining the ‘hotness’of the resulting hot dark matter, where the relation
between the hot dark matter’s temperature and abundance is fixed by the particle’s spin
statistics.
Cosmic microwave background primary anisotropies. The CMB primary anisotropies
refer to the temperature and polarization fluctuations imprinted on the last scattering surface.
These are sensitive to the physics of the early universe up to the time of photon decoupling (T
∼0.1 eV or redshift z∼1000), and differ from the secondary anisotropies which are
additional spatial fluctuations gathered by the CMB photons as they free-stream from the last
scattering surface to the observer and hence sensitive to late-time/low-redshift physics.
The effects of a non-standard N
eff
value on the CMB primary anisotropies and its
associated parameter degeneracies with the present-day Hubble expansion rate H
0
and
physical matter density ω
m
in the context of ΛCDM cosmology have been discussed
extensively in, e.g. [1,444]. Broadly speaking, if the particles that make up N
eff
are ultra-
relativistic at the time of CMB formation, then a non-standard N
eff
can manifest itself in the
following ways:
1. The redshift of matter-radiation equality z
eq
controls the ratio of radiation to matter at the
time of photon decoupling and hence the evolution of the potential wells. This in turn
affects the peak height ratios of the CMB temperature anisotropy spectrum. With seven
acoustic peaks measured by the Planck mission [445], the equality redshift z
eq
has been
measured to percent level precision in ΛCDM-type cosmologies. As a probe of N
eff
,
however, we note that
()
w
w
=+-
g
z
N
1
0.227 1, 71
eq m
eff
where ω
γ
is the present-day photon energy density. In other words, N
eff
is exactly
degenerate with the physical matter density ω
m
, and measuring z
eq
alone does not
determine N
eff
.
2. The angular sound horizon θ
s
, which determines the CMB acoustic peak positions, is
another quantity sensitive to N
eff
.Defined as θ
s
≡r
s
/D
A
, where r
s
is the sound horizon at
photon decoupling and D
A
is the angular diameter distance to the last scattering surface,
the parameter dependence of θ
s
in ΛCDM cosmologies is as follows,
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
124
()
()
*
ò
q
µW
-
W+-W
-
,72
s
a
a
aa
m
12
1d
1
2m3m
where Ω
m
≡ω
m
/h
2
,his the reduced Hubble expansion rate defined via H
0
=100hkm
s
−1
Mpc
−1
,a
*
is the scale factor at photon decoupling, and we have held z
eq
and the
baryon density ω
b
fixed. This relation implies that while θ
s
constrains the parameter
combination ω
m
/h
2
, it does not constrain ω
m
and hindividually. Since there already
exists an exact degeneracy between N
eff
and ω
m
through z
eq
(see equation (71)), this
additional (ω
m
,h)-degeneracy through θ
s
immediately sets up a three-way degeneracy
between N
eff
,ω
m
, and h, which needs to be broken by some other means. In more
complex models, degeneracies between N
eff
and a nonzero spatial curvature Ω
k
or a non-
canonical dark energy equation of state are also possible.
3. The angular diffusion scale θ
d
≡r
d
/D
A
, where r
d
is the diffusion scale at photon
decoupling, characterizes the scale at which the CMB temperature anisotropy power
spectrum becomes suppressed due to diffusion damping (or Silk damping). The
phenomenon of diffusion damping occurs at the CMB damping tail, i.e. at multipoles ℓ
1000, and was first measured by the Atacama Cosmology Telescope [446]and the South
Pole Telescope [447], and now by the Planck CMB mission [445].
For fixed z
eq
,ω
b
and a
*
, the angular diffusion scale has a parameter dependence
() ()
q
qµWH,73
dsm0
214
where θ
s
is the angular sound horizon of equation (72). Thus, a simultaneous
measurement of θ
d
,θ
s
, and z
eq
by a CMB mission such as Planck immediately constitutes
a measurement of
w
µW H
mm
0
2and hence N
eff
. Figure 87 shows the signature of N
eff
in
the CMB damping tail.
Large-scale matter distribution. There are many different ways to quantify and probe the
large-scale matter distribution. The most basic quantity, however, is the present-day matter
power spectrum P(k).
The broad-band shape of the large-scale matter power spectrum in ΛCDM-type
cosmologies by two quantities: the comoving wavenumber at matter-radiation equality
()
() ()
º
´W+
--
kaHa
zh4.7 10 1 Mpc , 74
eq eq eq
4meq 1
which fixes the location of the ‘turning point’of P(k), and the baryon-to-matter density
fraction
()
w
w
ºf,75
b
b
m
which determines the suppression in power at k>k
eq
due to baryon acoustic oscillations
(BAO). In addition, the matter power spectrum has small-amplitude oscillatory features which
are the manifestation of the BAO themselves. These oscillatory features originate in the same
early universe physics as the acoustic peaks in the CMB anisotropy power spectra, and when
analyzed together with CMB data, can act as a powerful standard ruler for distance
measurements.
If some of the neutrinos are massive and become non-relativistic at late times, then they
can constitute a fraction of the present-day dark matter content. However, this neutrino dark
matter is ‘hot’, in the sense that the neutrinos, although non-relativistic, come with a
significant thermal velocity dispersion, which tends to hinder its gravitational clustering on
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
125
small scales. In terms of the present-day large-scale matter power spectrum, keeping the total
matter density fixed but replacing some of the cold dark matter with neutrino hot dark matter
suppresses P(k)at k-values larger than the free-streaming wave number by an amount
dependent on the neutrino fraction
()
w
ww
º=
å
n
nn
fm94 eV .76
mm
Thus, neutrino masses also influence the overall shape of the matter power spectrum.
Since it is already possible to pin down z
eq
,Ω
m
, and ω
m
using the CMB primary
anisotropies, measurements of the matter power spectrum P(k)generally do not improve the
constraint on N
eff
in the simplest ΛCDM+N
eff
fit. However, it must be noted that after the
Figure 87. Signature of N
eff
in the damping tail of the CMB TT power spectrum. Top:
here, the cosmological parameters have been adjusted such that the baryon density
Ω
b
h
2
, the redshift of matter-radiation equality z
eq
, the angular sound horizon θ
s
, and the
normalisation at ℓ=200 are fixed for all N
eff
cases shown. Middle: like the top panel,
but with the spectrum normalisation fixed at ℓ=400 instead. Bottom: like the middle
panel, but here the Helium-4 fraction Y
p
is also allowed to vary such that all N
eff
cases
end up with roughly the same angular diffusion scale θ
d
. Reprinted (figure)with
permission from [444], Copyright (2013)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
126
formation of the CMB primary anisotropies, these fluctuations are gravitationally lensed by
the intervening matter distribution as the CMB photons propagate from the last scattering
surface to the observer, contributing to the so-called CMB secondary anisotropies at
multipoles ℓ500. In other words, any CMB anisotropy signal at ℓ500 will always
include some information about P(k), and this is particularly useful for the purpose of
constraining the neutrino mass sum ∑m
ν
.
Current CMB and LSS constraints. In a standard ΛCDM parameter inference, estimating
cosmological parameter values from the CMB and related observations involve varying six
free parameters related to cosmology: the baryon density ω
b
, the cold dark matter density ω
c
,
the Hubble parameter h, the spectral index n
s
and amplitude A
s
of the primordial curvature
perturbation, and the optical depth to reionization τ. Analyses of the Planck CMB data also
require that we vary of order 20 nuisance parameters to model the foregrounds and
instrumental systematics. These are later marginalized.
To constrain radiation excess, at minimum we need to add N
eff
as a free parameter to this
list. Doing so the Planck collaboration finds [445]
()()=+
-
+
N
3.00 95% CL, Planck TT lowE , 77
eff 0.53
0.57
()()=+
-
+
N
2.92 95% CL, Planck TTTEEE lowE , 78
eff 0.37
0.36
()()=+++
-
+
N
3.11 95% CL, Planck TT lowE lensing BAO , 79
eff 0.43
0.44
()()=+++
-
+
N
2.99 95% CL, Planck TTTEEE lowE lensing BAO , 80
eff 0.33
0.34
using various combinations of the Planck temperature and E-polarization measurements
(TTTEEE and lowE), the lensing potential extracted from the Planck temperature maps, as
well as the BAO measurements from 6dFGS [448], SDSS-MGS [449], and BOSS DR12
[450]. As can be seen, in all cases, the inference returns an estimate of N
eff
that is remarkably
consistent with the SM prediction of N
eff
=3.0440.
Since the CMB anisotropies are also sensitive to the large-scale matter distribution at low
redshifts because of the weak gravitational lensing signal inherent in all CMB power
spectrum, one can also derive a constraint on the neutrino mass sum ∑m
ν
from the Planck
CMB data at the same time as we constrain N
eff
. In a 8-parameter ΛCDM+N
eff
+∑m
ν
fit, the
Planck collaboration finds [445]
()
()
=+++
å<
n
-
+
N
m
2.96 95% CL, Planck TTTEEE lowE lensing BAO ,
0.12 eV.
81
eff 0.33
0.34
Note that the fit assumes three degenerate neutrino mass eigenstates of equal abundances. The
role of N
eff
is merely to dial up or down the abundances, which is why N
eff
can go below the
standard value of
=
N
3.0440
eff
SM . This combined fit is to be compared with the N
eff
constraint quoted in equation (80)in a 7-parameter fit of the same data combination, which
has the same error bars (about 11%)and a central value off only by 2%. It is also interesting to
compare it with the constraint obtained on the neutrino mass sum ∑m
ν
from 7-parameter
ΛCDM+∑m
ν
fit[445]
()()
å<+++
n
m0.13 eV 95% CL, Planck TT lowE lensing BAO , 82
()()
å<+++
n
m0.12 eV 95% CL, Planck TTTEEE lowE lensing BAO , 83
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
127
which is identical to the upper limit obtained from the 8-parameter fit(equation (81)). Thus,
one can conclude from this comparison that there is no strong degeneracy between the N
eff
parameter and the neutrino mass sum ∑m
ν
in the current generation of precision
cosmological data.
What about constraints on the sterile neutrino mass m
s
? The Planck collaboration [445]
also reports a ‘massive sterile neutrino’fit to their data in a scenario in which the three active
neutrinos are assumed to have a fixed minimum mass sum of ∑m
ν
=0.06 eV and the
effective sterile neutrino mass is defined as ()ºW
nn
mh94.1 eV
,sterile
eff ,sterile 2. This effective
mass is related to the physical sterile neutrino mass via
() ()=D
n
-
m
Nm ,84
seff 1,sterile
eff
assuming the sterile states have the same temperature as the SM neutrinos. Imposing the
priors ΔN
eff
0 and m
s
<10 eV, they find the constraints
()
()
<+++
<
n
N
m
3.29 95% CL, Planck TTTEEE lowE lensing BAO ,
0.65 eV. 85
eff
,sterile
eff
Taking ΔN
eff
to be a maximum allowed 0.29, the mass bound corresponds to an upper limit
of m
s
<2.24 eV on the physical sterile neutrino mass. Thus, while cosmological
measurements do constrain m
s
in any interesting way, it cannot completely rule out a 1 eV
light sterile provided thermalization is kept at below the 30% level. In other words, the extent
of thermalization as quantified by the N
eff
parameter remains the limiting factor for the light
sterile neutrino scenario in standard cosmology.
Lastly, we note that while the cosmological bound on N
eff
given in equation (81)is already
strongly indicative that the short-baseline light sterile neutrino is in serious tension with
precision cosmological measurements, it is nonetheless possible to analyse cosmological and
oscillation data together in a consistent way. This has been done most recently in [451],which
considers a 3 +1 scenario, computes the corresponding light sterile neutrino thermalization
using the thermalization code FortEPiaNO [426]and the associated N
eff
with mixing
parameters consistent with laboratory measurements, and feeds the output into a CMB analysis.
Figure 88 shows the constraints on the
(
∣∣)DmU,e
41
242-and
(
∣∣)Dm
mU,
41
242-planes.
5.1.3. Can we evade cosmological constraints? We have seen that the canonical 1 eV-mass
light sterile neutrino motivated by the short baseline anomalies is in strong tension with
cosmological measurements primarily because of the non-detection of a non-standard N
eff
∼
4. However, a criticism often levelled at cosmological constraints is that all parameter
estimation via statistical inference are inherently dependent on the cosmological framework
assumed in the inference exercise. Given the large number of unknowns in cosmology, e.g.
the nature of dark energy, inflation, etc., critics argue that there may exist a corner of this vast
unknown parameter space in which a completely thermalized light sterile neutrino state with a
mass close to 1 eV might be permitted to live.
To investigate this possibility, the Planck collaboration has provided a large number of
analyses of expanded cosmological parameter spaces, often in combination with external,
non-CMB data sets. These are available at the Planck Legacy Archive (https://pla.esac.esa.
int/home). Of particular interest to light sterile neutrinos is the 10-parameter
ΛCDM+N
eff
+∑m
ν
+w
0
+n
run
fit, where w
0
is the equation of state parameter of the dark
energy (w
0
=1 for a cosmological constant), and n
run
is the running of the scalar spectral
index, a parameter related to the initial conditions of the Universe (n
run
=0 in single-field
inflation). Using the usual Planck TTTEEE+lowE+lensing+BAO data combination together
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
128
with the Hubble parameter measurement of [452]and Supernova Ia data from the Pantheon
sample [453], the constraints on N
eff
and ∑m
ν
in this extended parameter fit are
()
()
=
å<
n
-
+
N
m
3.11 95% CL ,
0.16 eV. 86
eff 0.36
0.37
Clearly, while the bound on the neutrino mass sum ∑m
ν
has relaxed somewhat and the
central N
eff
has shifted a little up, relative to the more limited bounds in equations (80)and
(81)the error bars on N
eff
have not weaken significantly, and the canonical light sterile
neutrino is still in tension with precision cosmological measurements in this expanded
parameter space. The upward shift in N
eff
can be attributed to the discrepancy between the
Planck inference of the Hubble expansion rate and the local measurement of [452]. Because
of the degeneracy between N
eff
and H
0
in the CMB primary anisotropies, combining Planck
data with local measurements—the latter of which prefer a higher value of H
0
—tends to
drag up the inferred N
eff
as well. The neutrino mass sum ∑m
ν
, on the other hand, has long
been known to be somewhat degenerate with the dark energy equation of state parameter
w
0
. However, the combination of BAO and Supernova Ia data can lift this degeneracy very
effectively.
Thus, expanding the cosmological parameter space no longer appears to do much for the
light sterile neutrino case (in the sense of allowing a larger N
eff
)the way it once did [454].In
order to get around cosmological constraints, we need to introduce new physics that directly
affects the cosmological phenomenology of the light sterile states. Since the main problem of
the canonical light sterile neutrino is that its thermalization in the early universe raises N
eff
to
an unacceptably large level for BBN and CMB/LSS, all known new physics solutions so far
involve tampering with the thermalization process, in order to maintain N
eff
at as close to the
SM value as possible. A number of ideas have been proposed and explored throughout the
years (though not all are guaranteed to work as desired), including
Figure 88. Left: 2D marginalized 68% and 95% constraints on the mass splitting Dm41
2
and mixing matrix element |U
e4
|
2
from cosmology (blue), from the tritium β-decay
end-point measurements by KATRIN (green), and from neutrinoless double-β-decay
experiments (red). The preferred regions of reactor experiments are also indicated.
Right:cosmological 68% and 95% marginalized constraints on the |U
μ4
|
2
(blue)versus
constraints from the ν
μ
disappearance measurements of IceCube and MINOS+(grey).
Reproduced from [451].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
129
1. Large chemical potentials or, equivalently, number density asymmetries for the active
neutrinos [166–455,457],
2. Secret interactions of the sterile neutrinos [162–164,169,170,458–463], and
3. Low reheating temperature of the Universe [165,464–467].
Large chemical potentials for the active neutrinos. As discussed earlier in section 5.1.1,
in a standard calculation of light sterile neutrino thermalization, the active neutrino
asymmetries, defined as ()
¯
=-
anng
aa
L
nnn
, are assumed to be zero. However, if for some
reason some of these asymmetries are large—usually taken to mean L
α
>10
−5
—then the CP
asymmetric term ()
¯
-
nn
G2Fin the Hamiltonian (equation (59)) can act as a large matter
effect to suppress oscillations between the active and sterile states. If this suppression is
effective before neutrino decoupling, then it is possible to maintain N
eff
at close to the SM
prediction [455]. For active-sterile neutrino mass splittings in the range Δm
2
;0.2 →10 eV
2
,
the minimum neutrino asymmetries required to effect some degree of suppression are L>
10
−4
→5×10
−3
[456]. To significantly suppress thermalization, however, asymmetries as
large as L∼10
−2
are required [166].
Unfortunately, aside from the difficulty in explaining how such large neutrino
asymmetries could have arisen in the first place, this solution also suffers from other
undesirable effects, namely, significant distortion to the ν
e
and
¯
n
e
energy spectra. While it is
possible to suppress active-sterile oscillations with the choice of L∼10
−2
before neutrino
decoupling, beyond this critical point vacuum oscillations will inevitably take over and distort
the active neutrino energy spectra as a result [456].[166]has computed this distortion and its
effect on the light elemental abundances. They find that the larger the neutrino asymmetry
employed to suppress light sterile neutrino thermalization, the larger the spectral distortion
and the resulting Helium-4 mass fraction Y
p
. Thus, while large neutrino asymmetries do
improve the outcome for N
eff
, at the same time they also affect at least one important
observable in an undesirable way. The solution is therefore far from fool-proofed.
Self-interaction or NSI for the sterile neutrino. These solutions also work on the principle
of suppressing sterile neutrino thermalization through the introduction of a non-standard
matter potential for the sterile state in the oscillation Hamiltonian (equation (59)). They differ
primarily in their coupling structures.
References [162–164,458,461,462]consider an interaction of the form
¯()
ng n
=
mm
gPX,87
XsLsint
where the sterile neutrino self-interaction is mediated by a MeV-mass vector boson X. This
leads to the addition of a matter potential to the Hamiltonian (equation (59)) of the form
⎡
⎣
⎢⎤
⎦
⎥()
¯
+
Gp m
22 4
3,88
Xss
X
2
where
()º
G
gm28
XXX
22
,m
X
is the mass of the Xboson, and
sand
¯
s
are defined like n
and ¯
n
in equation (64), but with a projection matrix S
a
=diag(0, 0, 0, 1)that singles out the
sterile state for coupling. The collision integrals
[( )
]
pt,
also need to be modified
appropriately. For g
X
10
−2
and g
X
10 MeV, the new interaction (equation (87)) is able to
suppress sterile neutrino thermalization and hence preserve N
eff
at close to the SM value
without altering BBN predictions. However, at times after neutrino decoupling, the same
interaction also leads to equipartition amongst the active and sterile states. That is, if at
neutrino decoupling the neutrino number densities are (n
e
,n
μ
,n
τ
,n
s
)=(1, 1, 1, 0), the secret
interaction will redistribute it to (3/4, 3/4, 3/4, 3/4). Thus, the mass of sterile state m
s
will
nonetheless contribute to the hot dark matter energy density probed by the CMB anisotropies
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
130
and the large-scale matter distribution, and be subjected a substantially tighter constraint,
about m
s
<0.2 eV, than is implied by equations (85)or (86). This solution is therefore also
not fool-proofed.
On the other hand, [459,460]consider a self-interaction of the mass eigenstate ν
4
mediated by a massless pseudoscalar f:
¯()fn g n=
f
g.89
int 4 54
As with the massive vector boson case above, the secret interaction engenders a matter
potential, which in turn suppresses the production of sterile states. The transition from no to
full thermalization happens in the range of coupling values 10
−6
<g
f
<10
−5
[459]. The
authors further argue that because the secret interaction happens exclusively for the mass
eigenstate ν
4
, the interaction cannot equilibrate the active and sterile states and whatever is the
ΔN
eff
produced at neutrino decoupling is also the only component of the neutrino population
that carries a mass of m
s
;1 eV. Thus, the scenario can easily evade both limits on N
eff
and
m
s
.
Lastly, the solution of [169,170]invokes a coupling of the sterile state to an ultra-light
real scalar field of mass m
f
<5×10
−17
eV that also contributes to the cold dark matter. At
early times, the coupling induces an effective mass for the sterile state, which suppresses
active-sterile oscillations and hence thermalization of the sterile state in much the same way
as the two scenarios discussed above. After neutrino decoupling, the ffield starts to oscillate
coherently. Since unlike the MeV vector boson case the model does not lead to the
equilibration of the active and sterile states, both limits on N
eff
and m
s
can be easily avoided.
Low reheating temperature. Low reheating temperature scenarios [165,464–467]refer to
those cases in which the Universe transitions to radiation domination at temperatures below T
∼10 MeV. This might happen because of a very low inflation energy scale, or because some
non-standard physics causes the Universe to enter a period of matter domination immediately
prior to the most recent phase of radiation domination, and the transition back to radiation
domination takes place at
(
)
~T1
MeV.
A low reheating temperature appears to be a viable way to evade cosmological
constraints on light sterile neutrino states. If reheating occurs at
(
)
~T1
MeV, even the SM
active neutrinos have barely enough time to interact before neutrino decoupling happens.
Depending on how exactly reheating happens, some of the active neutrino species may not
even reach equilibrium number or energy densities. If light sterile neutrino thermalization was
to happen at the same time, the shortage of active neutrinos in the plasma would also slow
down the production rate. For these reasons, it is possible to engineer a scenario in which the
final N
eff
is close to the SM value, while the ratio of sterile to active states remains smaller
than 1 to 3. Naively, this makes it possible to satisfy N
eff
as well as m
s
bounds from CMB
and/or BBN.
In practice, however, whether or not the solution works depends on the details of the
reheating model. Reference [467], for example, finds that if the parent particle responsible for
reheating decays exclusively into electromagnetically interacting radiation, then a low
temperature reheating can indeed render light sterile neutrinos consistent with measurements
of the primordial elemental abundances. If however the parent particle decays mainly into
hadrons, then together with the presence of active-sterile neutrino mixing, the primordial
synthesis of light elements can proceed in a way incompatible with observations for a wide
range of the mass and the hadronic branching ratio of the parent particle.
In addition to low reheating scenarios, cosmological scenarios where entropy is
conserved and the expansion rate is modified can significantly affect light sterile neutrino
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
131
constraints. This includes, for example, scalar-tensor theories, and is discussed in detail in
[465,466], and also in [468](for resonance sterile neutrino production).
6. Future experimental prospects
6.1. Decay-at-rest accelerator experiments
6.1.1. JSNS
2
and JSNS
2
-II. The JSNS
2
(J-PARC Sterile Neutrino Search at the J-PARC
Spallation Neutron Source)[469–471]and its second phase JSNS
2
-II [472], aim to search for
neutrino oscillations with Δm
2
near 1 eV
2
at the J-PARC Materials and Life Science
Experimental Facility (MLF). Figure 89 shows the experimental setup and search
sensitivities. An intense neutrino beam from muon decay at rest is produced by a
spallation neutron target with the 1 MW beam of 3 GeV protons created by a Rapid Cycling
Synchrotron (RCS). Neutrinos come predominantly from μ
+
decay :
¯
m
nn++
m
++
e
e.An
oscillation of
¯
n
m
to
¯
n
e
through the fourth mass eigen-state is searched for by detecting the
Inverse-Beta-Decay (IBD)interaction ¯
n
+ +
+
pe n
e
, followed by gammas from neutron
capture on Gd. The JSNS
2
detector, as the near detector in the JSNS
2
-II setup, contains 17
tonnes of Gd-loaded liquid scintillator and is located 24 meters away from the Mercury target.
The new far detector of JSNS
2
-II, currently under construction, is located outside the MLF
building with a baseline of 48 meters. The far detector contains 32 tonnes of Gd loaded liquid
Figure 89. The experimental setups of the JSNS
2
and JSNS
2
-II and their sensitivities.
Reproduced with permission from [663].CC BY-NC-ND 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
132
scintillator as a neutrino target. Both JSNS
2
and JSNS
2
-II employ a Hydrogen target for the
neutrino source (μdecay-at-rest), and a neutrino detection channel (IBD)identical to LSND.
With improvements made by the short pulsed beam and the neutron capture signal, JSNS
2
and JSNS
2
-II will provide clean and direct tests of the LSND anomaly. JSNS
2
started data
taking in 2020, and accumulated 1.45 ×10
22
Proton-On-Target (POT)by 2021, 13% of the
approved POT by J-PARC, which corresponds to 1 MW beam power for 3 years. An
extensive analysis is ongoing (e.g. [473]). The search sensitivity of JSNS
2
with the full design
POT is shown in the bottom-middle plot of figure 89. The construction of the far detector of
JSNS
2
-II started in September 2021 and the aim is to start data taking in 2023. It will provide
additional sensitivity, especially in the low Δm
2
region with 1 MW beam power for 5 years.
Figure 90 shows a picture of the JSNS
2
detector during the installation in June 2020 and
the construction status of the new far detector of the JSNS
2
-II.
6.1.2. COHERENT at the SNS. The COHERENT collaboration can perform a powerful test
of oscillations of sterile neutrinos by considering NC disappearance. Parameter space favored
by a global fit of oscillation data to a 3 +1 scenario is accessible to COHERENT in the near
future with later data giving a much stronger constraint.
COHERENT measures coherent, elastic neutrino-nucleus scattering (CEvNS)and other
low-energy neutrino scattering processes at the Spallation Neutron Source (SNS)at Oak
Ridge National Lab (ORNL). CEvNS is a neutral current process whose only signature is a
low-energy nuclear recoil which was first measured by COHERENT on CsI in 2017 [474].
The cross section is very large compared to other neutrino scattering cross sections below 50
MeV and is precisely predicted. The SNS is an intense source of πdecay-at-rest neutrinos
with energies 0–53 MeV, ideal for measuring CEvNS. The width of the SNS beam, 360 ns
FWHM, is small compared to the muon lifetime so that the neutrino flux separates in time to a
prompt ν
μ
flux from π
+
→μ
+
ν
μ
and a delayed flux of ¯
n
n
mefrom ¯
m
nnm
++
ee. The ν
μ
flux
is monoenergetic with E
ν
=29.8 MeV. COHERENT builds and commissions several CEvNS
detectors for operation at the SNS at baselines of 19.3 to 28 m. These baselines place
COHERENT detectors at the first oscillation maximum for the ν
μ
flux assuming the global
best fitof
D
m41
2. Since the neutrino flux at the SNS includes both ¯
n
n
mm
and ν
e
, CEvNS
searches can simultaneously search for ν
μ
→ν
s
and ν
e
→ν
s
disappearance with favorable
sensitivity to both θ
14
and θ
24
with the same experiment. Additionally, the largest systematic
uncertainty, the neutrino flux normalization, is correlated between all detectors which
mitigates its effect on a joint fit.
There are plans for three future detectors suitable for searching for sterile neutrinos
through CEvNS disappearance in the near future. The first is an upgrade of the CENNS10
Figure 90. The JSNS
2
detector during the installation (left)and the construction status
of the new far detector of the JSNS
2
-II (right).
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
133
detector which made the first CEvNS measurement on argon [475]. This will be a liquid argon
calorimeter with 610 kg of fiducial mass with a baseline of 28 m. Detector performance is
well understood from experience with CENNS10 operations and data. A 10 kg CsI
scintillation detector at a 19.3 m baseline is also planned. This detector will be undoped and
cooled to 77 K which can dramatically increase light yield while reducing background
scintillation within the crystal [476]. This ensures a low threshold, allowing tests of CEvNS
disappearance with low-energy recoils. Finally, a 50 kg germanium PPC detector at 22 m is
planned as an upgrade to the 17 kg array currently being commissioned at the SNS. The
sensitivity of a joint fit using three years of data from all three detectors to search for a sterile
neutrino through NC disappearance with CEvNS is shown in figure 91. This would test the
parameter space preferred by a global fit at 90% confidence [101].
Into the next decade, ORNL is investing in the SNS, doubling its power and constructing
a new second target station (STS)with one in every four beam spills delivered to the STS to
supplement work at the first target station (FTS). Though the upgrade will not be completed
until the 2030s, it will facilitate a strong search for sterile neutrinos. The two targets would
only be 140 m apart, meaning a large flux of neutrinos from both sources would pass through
each CEvNS detector at the SNS. Similar to two-detector oscillation experiments, this
mitigates systematic uncertainties from neutrino interaction modeling and detector response
by observing neutrinos from a near and far flux source. The dominant remaining uncertainty
comes from π
+
production in each beam target which is small. With this control of
uncertainties, a test of NC disappearance is possible at the 1%-level. Sensitivity to sterile
neutrino oscillations in a 3 +1 framework for a 10 t fiducial argon calorimeter running for
five years, when placed 20 m from the STS and 120 m from the FTS, is shown in figure 91.
Exploiting flux from both targets, this large detector could test
q
m
sin 2
e
2values of 10
−5
at the
global best fit
D
m41
2and could test the LSND and MiniBooNE preferred regions for
D
>m0.04
41
2eV
2
at high confidence.
Figure 91. Sensitivity of COHERENT CEvNS detectors to constrain sterile neutrino
parameter space assuming a 3 +1 model compared to the LSND and MiniBooNE
allowed regions. A global fit to all short-baseline oscillation data is also shown.
Reproduced with permission from [664].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
134
6.1.3. Coherent CAPTAIN-Mills. The physics program of the Coherent Captain Mills (CCM)
Experiment comprises searches for new particles in the weak sector, including Dark Photons,
Axion-like Particles (ALPs), and heavy neutral leptons in the keV to MeV mass range,
extending the coverage of open parameter space for these searches at the order of magnitude
level. Many of these particles are invoked as alternative or additional explanations to
oscillations involving sterile neutrinos as the source of MiniBooNE anomaly. Thus, the
results of CCM from the ongoing run at Los Alamos National Laboratory (LANL)have direct
bearing on phenomenology presented in this white-paper. Here, we describe the CCM
detector, present a relevant CCM search for production of new bosons by charged meson
decays [215]as an example of the impact of the results, and summarize other searches that
can be performed.
The CCM experiment is relatively new to the scene of experiments to understand the
phenomenology of short-baseline anomalies. The experiment was conceived in 2017 and
prototyped using ‘CCM120,’which tested 120 PMTs for the SBND liquid argon (LAr)
experiment. First physics results from CCM120 were recently published [477,478]. In 2019,
the LANL LDRD office and DOE Dark Matter New Initiative program recognized the
relevance of the CCM rare-particle searches to dark matter studies and provided funding for
an upgrade to 200 PMTs for ‘CCM200.’This 5t fiducial-volume (10t total)LAr detector with
50% PMT coverage, seen in figure 92, was completed in Autumn 2021. The detector is
unusual for accelerator-based liquid argon experiments, in that it utilizes only light collection
—no time projection chamber. The detector is being commissioned now, and data totaling
2.25 ×10
22
POT will be collected in three runs between 2022-24, at the Lujan spallation
neutron center. This facility targets 100 microamps on tungsten of 800 MeV protons with 275
ns spills at 20 Hz. This is a prolific source of neutrinos from stopped pion and muon decay,
and, potentially, a source for production of new particles, such as ALPs [479], that can be
observed in CCM200 through interactions or decays. CCM200 is located 90
◦
off-axis and 20
m from the target.
The CCM200 design has a combination of features related to light collection that makes
it powerful and unique. The first is its PMT coverage (8”Hammamatsu R5912-MOD), which
is orders of magnitude higher per unit volume than any LAr TPC experiment. Furthermore,
the large charge dynamic range of the PMT’s and electronics enables the detector to have
reconstructed energy sensitivity from 10 keV to over 200 MeV. The second is the rate of
PMT readout, which provides information at 500 MHz and is synced to the accelerator
Figure 92. The interior of the CCM200 detector. Of the 200 PMTs, 80% are coated
with wavelength shifter (TBP)to shift 128 nm scintillation light to the visible, leaving
20% uncoated (darker, more reflective PMTs in image), aiding discrimination of
Cherenkov light. TPB foils cover the walls. The light-tight interior is surrounded by a
veto region instrumented with PMTs. CCM is now running.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
135
providing 2-ns absolute timing relative to the 275 ns beam pulse. This is key for separating
out early speed of light particles from the prolific beam related neutrons. Third, as can be seen
in the figure 92, 80% of the PMTs are coated with 1,1,4,4-Tetraphenyl-1,3-butadiene (TPB),
while 20% are uncoated. The TPB allows observation of the scintillation light from LAr,
which emits 40 000 photons MeV
−1
in zero electric field–×4 brighter than typical oil-based
liquid scintillator—at 128 nm wavelength, by shifting to the visible to penetrate the PMT
glass. The uncoated tubes, which is unique to the CCM design, allows clean observation of
Cherenkov light. An R&D goal of CCM is to make the first use of observed Cherenkov light
on an event-by-event basis in an analysis to reject backgrounds, since, for a signal, the
direction of the Cherenkov ring is opposite the Lujan target.
These design features make CCM particularly ideal for searches for electromagnetic
signatures of new physics produced in the target, which is a signature of popular explanations
for the short-baseline anomalies. The most popular new-physics explanation has been
oscillations involving sterile neutrinos. CCM can explore the recent large-mixing angle result
from the BEST experiment [136]using ν
e
disappearance for the pion decay-at-rest neutrino
beam, since the threshold for ν
e
-argon scatters is 1.5 MeV. In the longer term, an upgraded
CCM complex can be modified to perform a two-detector search for ν
μ
→ν
e
in the LSND
range that may be motivated by JSNS
2
results [480]. However, recently, community interest
has turned to new particles to explain the observed anomalies. Motivated by this, for this short
review, we are featuring an example of CCM’s new-particle-discovery capability.
As an example of an interesting new model that CCM can address, consider the proposed
explanation of the MiniBooNE Low Energy Excess (LEE)[33]from three-body meson decay
[215]. The diagrams for production of a new scalar or pseudoscalar particles that will interact
in the detector to produce a single photon exchanging a light vector boson (
¢
Z)with the
nucleus are shown in figure 93, left. The allowed region for the LEE is shown in figure 93,
right, and this model (model 1)finds a good fit to both the angular and energy dependence of
the LEE [33]. Another version of this model (model 2)which also can fit the data involves the
emission a light vector boson
¢
Zfrom the pion decay (just like the scalar/pseudoscalar).V
will then produce a photon by exchanging a scalar with the nucleus at the detector. This
model explains the LEE. All these new mediators emerging from the charged pion decays, so
far we have discussed, can be coupled to only quarks.
Figure 93. Left: example diagrams for three-body meson decay producing scalar or
pseudoscalar(axion-like)particles that interact in the detector. Right: allowed regions
for scalers (green)and pseudoscalers (blue)that account for the MiniBooNE low
energy excess, presented as a function of coupling versus new particle mass [215].
Lines: predictions of 10 000, 1000, and 100 signal events in solid, dashed and dotted,
respectively. Reproduced from [215].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
136
CCM will be able to probe both models. The main production channel will be π
0
decay
into gamma and
¢
Z. In model 1,
¢
Zcan be assumed to dominantly decay into a pair of scalars,
which will subsequently produce a photon from the scattering at the detector as needed to
resolve LEE.
¢
Zalso can decay into a photon and the scalar. Here, our assumption is that
¢
Z
does not decay into a pair of visible particles promptly. Under this assumption, figure 93
shows the predicted number of signal events at CCM in the allowed parameter space to
explain the LEE. Therefore, CCM200 has the capability for discovery, if this new physics is
the source of the LEE. Model 2 probes the MiniBooNE anomaly more directly since the same
¢
Zthat emerges from the charged pion decay to address the anomaly also can be produced
from the π
0
decay; therefore no assumption is needed to correlate the LEE and a possible
signal at the CCM. This possibility is under investigation at present.
Outside of models explaining the anomalies, CCM engages in a broad range of new-
physics searches. Limits on leptophobic dark photons from CCM120 [477,478], the
prototype run, will be extended by two orders of magnitude in CCM200. Searches for the
QCD axion can close the last remaining open-window at masses >0.1 MeV [479]. Searches
for ”neutrissimos”–not so heavy neutral heavy leptons–that have focused on >100 MeV
masses to address the LEE are being extended to lower masses in CCM. Although these
searches are not directly tied to explanations of the anomalies, a discovery would inevitably
demand investigation on whether the observed new-physics is related.
In summary, CCM is a small, fast-timescale experiment that is already taking data at
LANL. Its results have the potential to change our thinking about the anomalies.
6.1.4. PIP2-BD: GeV proton beam dump at fermilabʼs PIP-II linac. The completion of the
PIP-II superconducting LINAC at Fermilab as a proton driver for DUNE/LBNF in the late
2020s creates an attractive opportunity to build a GeV proton beam dump facility at Fermilab
dedicated to and designed from the ground up for HEP with excellent sensitivity to eV-scale
sterile neutrinos via neutral current disappearance using the CEvNS reaction (see [481]).
Thus, relative to spallation neutron facilities tailored to neutron physics and optimized for
neutron production operating at a similar proton beam power, a HEP-dedicated beam dump
facility would be designed to suppress rather than maximize neutron production and
implement a beam dump made from a lighter target such as carbon, which can have a pion-to-
proton production ratio up to ∼2 times larger than heavier Hg or W targets. The facility could
also accommodate multiple, 100-ton-scale high energy physics experiments located at
different distances from the beam dump and at different angles with respect to the incoming
proton beam. This flexibility further improves the sensitivity of dark sector and sterile
neutrino searches, by allowing relative measurements at different distances and angles to
constrain uncertainties in expected signal and background rates.
The continuous wave capable PIP-II LINAC at Fermilab can simultaneously provide
sufficient protons to drive megawatt-class
(GeV)proton beams as well as the multi-
megawatt LBNF/DUNE beamline. By coupling the PIP-II LINAC to a new Booster-sized,
permanent magnet or DC-powered accumulator ring, the protons can be compressed into
pulses suitable for a proton beam dump facility with a rich physics program. The accumulator
ring could be located in a new or existing beam enclosure and be designed to operate at 800
MeV but with an upgrade path allowing for future operation in the GeV range. The
accumulator ring would initially provide 100 kW of beam power, limited by stripping foil
heating, and have a ()
-
10 4duty factor. One variant of this accumulator ring would be a
∼100 m circumference ring operating at 1.2 GeV with a pulse width of 20 ns and a duty
factor of ()
-
10 6, which would greatly reduce steady-state backgrounds. Another is an
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
137
accumulator ring coupled to a new rapid cycling synchrotron replacing the Fermilab Booster
with an increased proton energy of 2 GeV and an increased beam power of 1.3 MW [482].
Decay-at-rest neutrinos from a stopped pion beam dump provide an excellent source of
ν
μ
,
¯
n
m
, and ν
e
with a time structure that can separate ν
μ
from
¯
n
m
and ν
e
. CEvNS provides a
unique tool to definitively establish the existence of sterile neutrinos through active-to-sterile
neutrino oscillations [483]. Using CEvNS, we can explore both mono-energetic ν
μ
disappearance with E
ν
=30 MeV and the summed disappearance of ν
μ
,
¯
n
m
, and ν
e
to ν
S
,
which can also put constraints on ν
μ
→ν
e
oscillation parameters in a 3 +1 sterile neutrino
model. We consider here a setup consisting of identical 100-ton LAr scintillation detectors,
located 15 m and 30 m away from a carbon proton beam dump with a 20 keV recoil energy
threshold and an efficiency of 70%. The 100-ton scale scintillation-only detector assumes a
cylindrical volume with a 5 m height and 2.5 m radius, and we perform a full Geant4-based
[484]scintillation photon simulation with wavelength shifting and propagation to PMTs
along the endcaps and side walls of the detector. Based on simulation studies, we assume the
detectors have a position resolution given by
s
=T
40 cm
20 keV in each spatial dimension,
where Tis the nuclear recoil produced by the neutrino interaction within the detector. This
information allows the possibility for a ‘rate+shape’fit using five bins in the reconstructed
neutrino propagation distance with a bin width of 1 m matched to the expected resolution of
the reconstructed neutrino propagation distance. If the prompt ν
μ
can be separated from the
delayed
¯
n
m
and ν
e
, one can exploit the mono-energetic feature of the ν
μ
flux and perform a
joint rate +shape disappearance fit of CEvNS events in the near and far detectors as a
function of reconstructed position.
In calculating the sensitivity, we assume the neutron background in this dedicated facility
could be suppressed to a negligible level for this experiment and that the signal-to-noise ratio
for the remaining steady-state backgrounds is 1:1. In figure 94, we compute the 90%
confidence limits on the ν
μ
→ν
S
mixing parameter
q
m
sin 2
S
2
for a 5 year run of an upgraded
1.2 GeV proton accumulator ring operating with a pulse width of 20 ns, a duty factor of
()
-
10 6, and a 75% uptime, assuming a 9% normalization systematic uncertainty correlated
between the two detectors and Also shown are the 90% confidence limitsa 36 cm path length
smearing. Also shown are the 90% confidence limits for ν
μ
disappearance, ν
e
disappearance,
Figure 94. PIP2-BD 90% confidence limits on active-to-sterile neutrino mixing
compared to existing ν
μ
disappearance limits from IceCube [151]and a recent global fit
[103], assuming a 5 year run (left). Also shown are the 90% confidence limits for ν
μ
disappearance (left),ν
e
disappearance (middle), and ν
e
appearance (right), assuming the
¯
n
m
and ν
e
can be detected with similar assumptions as for the ν
μ
. Reproduced with
permission from [481].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
138
and ν
e
appearance, assuming the
¯
n
m
and ν
e
can be detected with similar assumptions as for
the ν
μ
.
6.1.5. KPIPE at fermilab. The KPIPE experimental concept, outlined in [485], calls for a very
long (120 m)and thin (1.5 m radius)cylindrical detector close to and oriented radially outward
from an intense beam-dump source of monoenergetic 236 Mev ν
μ
from charged-kaon decay-at-
rest (K
+
→μ
+
ν
μ
, with branching ratio of 64%)to achieve sensitivity to short-baseline muon-
neutrino disappearance. The idea is to search for an L/E-dependent oscillation wave using
fixed-Eneutrinos with minimal background and only modest detector requirements.
The KPIPE detector, relying on liquid scintillator and silicon photomultipliers (or PMTs),
is designed to look for 236 MeV ν
μ
n→μ
−
pinteractions, which provide a unique double-
flash coincidence due to the muon decay following the initial prompt event. Mapping these
interactions as a function of distance along the detector pipe, with a nominal, no-oscillation
expectation of a 1/r
2
rate dependence, provides sensitivity to muon-flavor disappearance.
Given a beam dump, decay-at-rest neutrino source, the beam-based ν
μ
background (from
decay-in-flight mesons)to these signal events is expected to be completely sub-dominant, at
the 1-2% level. While cosmics can be considered a concern for such a surface or near-surface
detector, this background can be mitigated by typical accelerator duty factors of ∼10
−6
–10
−5
combined with the short charged kaon lifetime (13 ns). The monoenergetic neutrino source,
combined with low decay-in-flight background and small beam duty factor, means that the
signal-to-background ratio is expected to be well over 50:1 in the scenarios considered. This
large ratio means that the detector requirements, in particular the photocoverage, can be quite
modest. In fact, a preliminary estimate at [486]predicts that the entire KPIPE detector would
cost $5M.
The KPIPE detector was originally envisioned to be paired with the 3 GeV, 730 kW
(currently, with 1 MW planned)J-PARC Spallation Neutron Source. Aside from the primary
proton energy, which is above the kaon production threshold, and the high power, this source
is particularly attractive because the beam timing structure, two ∼80 ns pulses separated by
540 ns at 25 Hz, provides an extremely low duty factor (4×10
−6
), essential for cosmic
background rejection. The drawback of this source, however, is that the 3 GeV primary
proton energy, while above threshold, is somewhat lower than optimal for charged kaon
production per unit power: at 3 GeV, the MARS15 software package [487]predicts 0.007
KDAR ν
μ
/POT. With an increase in proton energy to 8 GeV, for example, the production rate
increases by a factor of 10–0.07 KDAR ν
μ
/POT. Spatial and facility issues, especially in
consideration of the existing materials-science-focused beamlines and experiments, also means
that optimal detector placement, with KPIPE calling for a 120 m long detector with closest
distance of 32 m from the neutrino source, is challenging.
The future Fermilab particle accelerator complex [482], including PIP-II [488]and the
RCS upgrade [489], can provide an optimal beam-dump/stopped-kaon neutrino source for
KPIPE, in terms of beam energy (8 GeV), beam timing (∼10
−5
duty factor), and spatial
considerations (see [490]). Using the detector and Fermilab-accelerator assumptions shown in
table 15, and scaling based on the detailed study in [485], we expect KPIPE could achieve the
sensitivity to short-baseline ν
μ
disappearance shown in figure 95. As can be seen, this
sensitivity surpasses, and is highly complementary to, SBN (6years)at Δm
2
>10 eV
2
for
both scenarios considered and Δm
2
>1eV
2
for the RCS upgrade era case.
6.1.6. IsoDAR. Through tracing
¯
n
e
disappearance continuously across L/Efrom 1 to
∼10 m MeV
−1
, the IsoDAR (Isotope Decay At Rest)experiment uniquely addresses the
fundamental question raised by this white paper: What, if any, new physics phenomenology
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
139
underlies the short-baseline anomalies? Despite the enormous consequences if new physics
is the cause, the question has been unanswered for more than 20 years. Incremental
improvements on our present approaches are likely to yield more of the same confusing
results. IsoDAR represents an entirely new approach–the experiment makes use of a flux from
8
Li βdecay, produced through a 60 MeV proton beam that is targeted on
9
Be to yield
neutrons that enter a surrounding isotopically-pure
7
Li sleeve and capture. When this source is
paired with the 2.3 kton Yemilab liquid scintillator detector (LSC), approximately 1.6 million
IBD events can be reconstructed in 5 years of running. The high statistics, relatively high
energy, E,of
¯
n
e
from
8
Li decay, and the ideal matching baseline, L, due to the size of the LSC,
gives unprecedented capability to study the L/Edependence of short-baseline disappearance
in an agnostic manner, determining its cause without design assumptions that bias toward
specific underlying physics models. Figure 96 illustrates the power of IsoDAR to resolve
various popular proposals for the source of the effect, with a 3 +1 model at top left; 3 +1
with nonzero quantum mechanical wave packet effects at top right; introduction of additional
sterile neutrinos, in this case 3 +2 at bottom left; and introduction of new interactions, in this
case 3 +1+decay, at bottom right. These examples show that IsoDAR can clearly elucidate
the underlying oscillation-related phenomenology of the electron-flavor short-baseline
anomalies, even in the case of physics that produces very complex waveforms.
IsoDAR has received preliminary approval to run at Yemilab in the configuration shown
in figure 97.[491]provides an overview of the technology and installation-plan. In figure 97,
Table 15. Summary of the relevant KPIPE experimental parameter assumptions.
Reproduced with permission from [490].
Experimental assumptions
Detector length 120 m
Active detector radius 1.45 m
Closest distance to source 32 m
Liquid scintillator density 0.863 g cm
−3
Active detector mass 684 tons
Primary proton energy 8 GeV
Target material Hg or W
KDAR ν
μ
yield (MARS15)0.07 ν
μ
/POT
ν
μ
CC σ@ 236 MeV (NuWro)1.3 ×10
−39
cm
2
/neutron
KDAR signal efficiency 77%
Vertex resolution 80 cm
Light yield 4500 photons MeV
−1
Uptime (5 years)5000 h/year
ν
μ
creation point uncertainty 25 cm
PIP-II era assumptions
Proton rate (0.08 MW)1.0 ×10
21
POT/year
Beam duty factor 1.6 ×10
−5
Cosmic ray background rate 110 Hz
Raw KDAR CC event rate 2.7 ×10
4
events/year
RCS upgrade era assumptions
Proton rate (1.2 MW)1.5 ×10
22
POT/year
Beam duty factor 5.3 ×10
−5
Cosmic ray background rate 360 Hz
Raw KDAR CC event rate 4.0 ×10
5
events/year
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
140
the cyclotron that drives the flux production is located at the far right. This novel 5mA H
2
+
ion
accelerator, producing 10 mA of 60 MeV protons, yields an order of magnitude higher proton
beam current than on-market cyclotrons at similar energies. Since the 2013 Snowmass Study,
cyclotron development has culminated in the design described in [492], which presents start-
to-end simulations and prototypes of components now under test [493,494]. As seen in
figure 97, the proton beam is transported from right to left and then bent through 180
◦
to the
target surrounded by the sleeve, hence fast neutrons are directed away from the LSC detector,
shown in green. Substantial R&D and engineering have established successful target, sleeve
and shielding designs [495,496].
IsoDAR@Yemilab is designed to address issues that have arisen during studies of reactor
and MegaCurie source experiments. The
¯
n
e
flux is generated from a single, well understood
isotope, avoiding issues faced by reactor flux modeling. The
¯
n
e
energy range is from about
3–13 MeV, with peak at ∼6 MeV, well beyond environmental backgrounds and backgrounds
from neutron capture. The source creation region is compact (∼41 cm at 1σ)and isotropic.
The experiment has the capability of event-by-event reconstruction, with prompt (e
+
)energy
resolution of 2.3% and vertex resolution of 4 cm at 8 MeV [497], in contrast to MegaCurie
(MCi)source experiments that do not reconstruct event kinematics. Use of the well-known
IBD cross section is also an advantage over the gallium experiments. Lastly, and importantly,
the size of the LSC detector, when combined with the energy range of the source, leads to the
wide L/Erange, allowing precision reconstruction of the oscillation wave across many
cycles.
A simple 3 +1 model is traditionally used for cross-comparison of experimental reach.
The reach of IsoDAR in
qsin 2
ee
2
at 95% CL is presented in table 16, column 2 for a range of
Δm
2
. For comparison, column 3 shows the combined limits at 95% CL from Prospect, RENO
and Daya Bay [111]. The IsoDAR mixing angle reach is ×4(×35)that of the reactor limits at
1(8)eV
2
. For allowed region comparisons for Neutrino-4 [498]and the Gallium experiments
Figure 95. The 90% CL sensitivities of the KPIPE at Fermilab scenarios considered
here, in both the PIP-II and RCS upgrade eras. For reference, we also show the
expected 90% C.L. SBN sensitivity (6 years)[500], existing 90% C.L. MiniBooNE
+SciBooNE limit [274], and 99% allowed region from the Collin et al global fit[100].
Reproduced with permission from [490].
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
141
[136], we use the 2σlower edge in
qsin 2
ee
2
. In the Neutrino-4 case, the allowed region is
narrow in Δm
2
and does not coincide with 8 eV
2
, so we present the mixing angle reach for the
best fit mass splitting of 7.3 eV
2
.
Figure 96. The IsoDAR@Yemilab capability to trace
¯
n
e
disappearance versus L/Efor
IBD interactions. Top left and right present a 3 +1 example without and with
wavepacket effects described in [111]. Bottom left and right are 3 +2and3+1+decay
models for the global best fitpointsin[103]. Orange is the true underlying model. Points
represent the measurement capability. See text for further discussion. Reproduced from
[491]. © 2022 IOP Publishing Ltd and Sissa Medialab. All rights reserved.
Figure 97. Layout of IsoDAR@Yemilab in the Yemilab caverns. The excavation of the
IsoDAR cavern complex is complete. Reproduced from [491]. © 2022 IOP Publishing
Ltd and Sissa Medialab. All rights reserved.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
142
As a result of the novel design, IsoDAR@Yemilab design is able to elucidate
¯
n
e
disappearance across L/Eof 1 to ∼10 m MeV
−1
without guidance from any
phenomenological model. Figure 96 illustrates the complex oscillation waves that are able
to be differentiated in 5 years of running, with efficiency included. The upper plots illustrate
the oscillation wave without (left)and with (right)wavepacket effects as discussed in [111],at
a point where the combined reactor limit and gallium allowed region overlap assuming the
wavepacket model. Comparison of the two plots shows that the distinctive damping due to
wavepacket effects can be observed given IsoDAR’s high statistics. The lower plots present 3
+2 and 3 +1+decay models evaluated at the best fit points from [103]. The value of the
high statistics and excellent reconstruction of IsoDAR is particularly emphasized by the 3 +2
case, where the second predicted modulation is clear due to the capability of using very fine
binning. The orange line indicates the true underlying distribution, while the points with error
bars present the expected measurements, illustrating the loss of information from finite
statistics and bin sizes. The 3 +1(top)and 3 +2 points (bottom right)also include detector
energy and position smearing.
The experiment will also collect ×4 the world’s sample
¯
n
e
-electron elastic scattering
events in 5 years which may help further decipher new physics, depending on the source. In
fact, IsoDAR@Yemilab has an extensive discovery-level physics program beyond searching
for the short-baseline anomalies, including an order of magnitude improvement in NSI
searches through elastic scattering from electrons [497], unique neutrino-based searches for
¢
Z
signatures [497], and exotic non-neutrino searches, such as for neutrons shining through walls
[499]. As such, IsoDAR represents a leap forward for electron-flavor neutrino experiments.
6.2. Decay-in-flight accelerator experiments
6.2.1. Short-baseline experiments
6.2.1.1. The fermilab SBN program. The Short-Baseline Neutrino (SBN)program consists
of three LArTPC detectors located along the BNB at Fermilab: the MicroBooNE detector,
which completed operations in 2021; the ICARUS detector, which began operations in the
BNB in 2021; and the upcoming short-baseline near detector (SBND), which is expected to
begin operations in 2023. This program represents an exciting opportunity for a multi-
baseline search for light sterile neutrino oscillations in multiple exclusive or inclusive
oscillation channels, and a test of the 3 +1 light sterile neutrino oscillation interpretation of
past experimental anomalies at 5σ[500]. In particular, ν
μ
CC measurements across the three
detectors will probe
n
n
mm
oscillations with world-leading sensitivity as shown in figure 98
Table 16. Quantitative comparison of the low
qsin 2
ee
22σreach of electron-flavor
experiments in the Δm
2
range of interest. IsoDAR sensitivity is based on assumptions
in [497]. Combined reactor limits are from PROSPECT, NEOS, and Daya Bay. N/A
indicated Δm
2
is not within 95% CL allowed region. The Neutrino-4 2σreach is
quoted at 7.3 eV
2
.
Δm
2
IsoDAR@Yemilab
Combined Reac-
tor [111]
Neutrino-
4[498]
Gallium
[136]
Sensitivity Limits Allowed Allowed
1eV
2
0.004 0.016 N/A 0.28
2eV
2
0.004 0.07 N/AN/A
4eV
2
0.005 0.13 N/A 0.27
8(7.3)eV
2
0.008 0.28 (0.12)0.28
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
143
(right);ν
e
CC measurements will probe ν
μ
→ν
e
and/or
n
n
ee
oscillations with sensitivity
as shown in figure 98 (left)and 99. Additionally, NC-based oscillation searches have been
proposed, e.g. [501], with unique sensitivity to U
si
under a 3+Nmodel, as well as potentially
U
τi
(for i>3)when combined with ν
e
and ν
μ
CC-based appearance and disappearance
searches.
The power of a multi-baseline and multi-channel search has been shown to be
advantageous not only for 3 +1 searches, but for 3+Nsearches more generally. For example,
[502]has found that SBN is capable of ruling out 85%, 95% and 55% of the 99%-globally-
allowed parameter space region
126
of 3 +1, 3 +2, and 3 +3 light sterile neutrino oscillation
parameters at 5σCL, assuming a null observation, particularly when appearance and
disappearance effects are studied simultaneously (including correlations). This is illustrated in
figure 100, for the 3 +3 scenario. Additionally, it has been pointed out that within the context
of 3+Noscillations with N>1, SBN offers an opportunity for measuring potential CP
violation in the leptonic sector, particularly if future antineutrino beam running is possible
with SBN. In particular, if antineutrino exposure is considered, for maximal values of the
(3+2)CP violating phase f
54
, SBN could be the first experiment to directly observe ∼2σ
hints of CP violation associated with an extended leptonic sector. This is illustrated in
figure 101, for the 3 +2 scenario. Furthermore, a planned analysis using the ICARUS
detector can probe meter-scale oscillations within the detector volume, consistent with sterile
mass splittings ≈7eV
2
and q»sin 2 0.
4
214 , providing a test of the allowed region claimed by
the Neutrino-4 experiment.
Beyond searches for physics associated with eV-scale sterile neutrinos, SBN’s main
physics goals include detailed studies of neutrino-argon interactions at the GeV energy scale,
enabled by millions of neutrino interactions that will be recorded on argon in its high
precision detectors. SBND’s anticipated high statistics, in particular, provide a unique
opportunity for first-ever measurements of rare SM-predicted neutrino interaction processes at
Figure 98. SBN light sterile neutrino sensitivities in the ν
μ
→ν
e
appearance channel
(left)and ν
μ
→ν
μ
disappearance channel (right)according to the SBN proposal [500].
The 3σ(5σ)sensitivities are given by the solid (dotted)red curves. The LSND 90% C.
L. (99% C.L.)allowed region is shown as shaded blue (grey)[19]. The global 3σν
e
(ν
mu
)appearance (disappearance)regions from [102]are shown by the shaded red
region (black line), and the global best fit regions from [101]are shown in green.
Reproduced from [156].CC BY 4.0.
126
Global allowed regions as of 2018.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
144
0.1–1 GeV, including rare photon production processes such as coherent NC single-photon
production, NC Δ→Nγradiative decay, or production and radiative decay of heavier
resonances. Additionally, the high statistics coupled with the unprecedented event
Figure 99. Due to the large intrinsic ν
e
statistics at SBND, SBN is also sensitive to ν
e
disappearance, probing
qsin 2
ee
2at high Δm
2
0.2 eV
2
(assumes θ
24
=0). This
provides a complementary probe of oscillations traditionally probed using reactor
antineutrinos at a much lower (MeV)energy scale. Reprinted (figure)with permission
from [502], Copyright (2017)by the American Physical Society.
Figure 100. SBN’s coverage of globally-allowed 3 +3 light sterile neutrino oscillation
parameters, defined as the fraction of 99%-CL-globally-allowed parameter space that
can be ruled out by SBN at a given CL indicated by the x-axis, assuming a null
observation. Coverage of 3 +1 and 3 +2 globally-allowed parameter space is
provided in [502]. Reprinted (figure)with permission from [502], Copyright (2017)by
the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
145
reconstruction, excellent particle identification, and fine-sampling calorimetry of the SBN
detectors’LArTPC technology opens up invaluable opportunities for new physics searches.
In particular, the capabilities of LAr detectors will allow for greater discrimination
between e
−
,e
+
e
−
,γ, and γγ final states, as well as to identify final state hadron multiplicities.
For models in which new particles are produced in neutrino-nucleus scattering, it will be
possible to search for a hadronic vertex associated with the displaced decay position. The EM
showers in this case may not point back to the original vertex due to missing energy.
Furthermore, for models that explain MiniBooNE with new heavy particles produced in
meson decays, the SBN detectors can also leverage the decays-at-rest of kaons produced in
the NuMI absorber [503].
Reference [156]provides a broad overview of such new physics, including their
signatures in SBN. Here, we limit the discussion to a summary of ones suggested as
interpretations to short-baseline anomalies, extending beyond eV-scale sterile neutrinos:
1. SBN can probe eV-scale sterile neutrinos decaying to active neutrinos and a Majoron or
gauge boson, which would lead to new features in the active neutrino energy spectrum
with respect to 3+Nscenarios.
2. Large extra-dimension models, such as ones proposed as an explanation of the reactor
anomaly, would affect both appearance and disappearance channels at SBN.
3. Resonant ν
μ
→ν
e
oscillations that arise in the presence of a light scalar boson that
couples only to neutrinos and could induce a MSW effect sourced by the cosmic neutrino
background could also be probed with SBN, through the search of ν
μ
→ν
e
transitions
Figure 101. The significance at which SBN can observe CP violation in the (3+2)
sterile neutrino scenario, as a function of true CP violating phase f
54
, for two injected
signals corresponding to the global (3+2)best fit point (red lines)as well as the point
with largest total allowed mixings (blue lines), for a variety of POT in neutrino and
antineutrino running modes at SBN. Reprinted (figure)with permission from [502],
Copyright (2017)by the American Physical Society.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
146
and lack of ν
μ
disappearance (as the latter would be suppressed compared to a vanilla 3
+1 scenario).
4. Violation of Lorentz and CPT symmetry would lead to modifications in the oscillation
probability measurable at SBN, such as direction-dependent effects, neutrino-
antineutrino mixing, annual modulations, and energy dependent effects on observable
mass splittings and mixing angles.
5. Sterile neutrinos and ADRs, also proposed as an explanation of the short-baseline
anomalies, would have a similar phenomenology in SBN to that of the usual 3 +3 sterile
scenario (while evading the constraints from long-baseline and atmospheric neutrino
experiments).
6. Charged current non-standard interactions (CCNSI)in the lepton sector could lead to a
number of observable effects, such as (1)deviations of the SM CC quasi-elastic cross
section, (2)modification of angular and energy distributions due to the presence of new
Lorentz structures, and (3)flavor violation such as ν
μ
n→e
−
p; At SBN, CCNSIs can
lead to an apparent baseline-independent ν
μ
→ν
e
conversion.
7. Dark neutrino sectors connected to the standard neutrino sector, allowing for neutrino
upscattering into a heavy state which could then decay to a light neutrino and a gauge
boson within a detector, followed by the gauge boson decay to visible particles such as
e
+
e
−
could also be measurable at SBN. As shown in figure 102,ane
+
e
−
pair can give
rise to four distinct topologies in LAr, depending on the lifetime of the parent particle and
on the angle between the charged leptons. A variety of signatures could be probed,
including pair production of e
+
e
−
,μ
+
μ
−
or π
+
π
−
induced by neutrino interactions, with
little to no hadronic activity and with the same signal strength at all three detectors, since
there is no L/Edependence.
8. Heavy neutrinos and transition magnetic moment proposed as an explanation of the
LSND/MiniBooNE anomalies would be observable at SBN as anomalously large single-
photon production with small hadronic activity. LArTPC e−γdiscrimination capability
places SBN in a special position to probe these scenarios. Again, the signal strength
would be the same at all three detectors, since there is no L/E dependence in these
models either.
6.2.1.2. nuSTORM. The 2020 Update of the European Strategy for Particle Physics (ESPP)
[504]recommended that muon beam R&D should be considered a high-priority future
initiative and that a programme of experimentation be developed to determine the neutrino
cross-sections required to extract the most physics from the DUNE and Hyper-K long-
baseline experiments. The ENUBET [505–507]and nuSTORM [508,509]collaborations
have begun to work within and alongside the CERN Physics Beyond Colliders study group
[510]and the international Muon Collider Collaboration [511]to carry out a joint, five-year
design study and R&D programme to deliver a concrete proposal for the implementation of
an infrastructure in which:
1. ENUBET and nuSTORM deliver the neutrino cross-section measurement programme
identified in the ESPP and allow sensitive searches for physics beyond the SM to be
carried out; and in which
2. A 6D muon ionisation cooling experiment is delivered as part of the technology
development programme defined by the international Muon Collider Collaboration.
With their existing proton-beam infrastructure, CERN and Fermilab are both uniquely
well-placed to implement ENUBET, nuSTORM, and the 6D-cooling experiment as part of
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
147
the required muon collider demonstrator. The design of ENUBET, carried out within the
framework of a European Research Council funded design study, includes the precise layout
of the kaon/pion focusing beamline, photon veto and timing system as well as the
development and test of a positron tagger together with the required electronics and readout.
The feasibility of implementing nuSTORM at CERN has been studied by the CERN Physics
Beyond Colliders study group while a proposal to site nuSTORM at FNAL was developed for
the last Snowmass study in 2013. The FNAL study focused on the optimisation of the muon
storage ring to provide exquisite sensitivity in the search for sterile neutrinos. In the Physics
Beyond Colliders study, the muon storage ring was optimised to carry out a definitive
neutrino-nucleus scattering programme using stored muon beams with momentum in the
range 1–6 GeV while maintaining its sensitivity to physics beyond the SM.
The study of nuSTORM is now being taken forward in the context of the demonstrator
facility required by the international Muon Collider Collaboration that includes the 6D muon
ionization cooling experiment. The muon-beam development activity is being carried out in
close partnership with the ENUBET collaboration and the Physics Beyond Colliders Study
Group. In consequence we now have the outstanding opportunity to forge an internationally
collaborative activity by which to deliver a concrete proposal for the implementation of the
nuSTORM infrastructure.
On top of the program outlined above, nuSTORM can still provide unprecedented
sensitivity to light sterile neutrinos. In particular, it allows to search for short-baseline
oscillations in ν
e
→ν
μ
appearance, the CPT-conjugate channel of the appearance hypothesis
at LSND. This would be possible due to charge selection of muons in a magnetic field, which
can discriminate the
n
m
produced in μ
+
decays from the ν
e
→ν
μ
oscillations. A detailed study
of nuSTORM’s sensitivity to sterile neutrinos was performed in [512], which focused on a 3.8
GeV muon ring design for siting at FNAL. The study considered a 1.3 kt magnetized iron-
scintillator detector at 2 km from the ring with an exposure of 10
21
POT, corresponding to
≈2×10
18
useful muon decays. The sensitivity curves covered the entire LSND and
MiniBooNE regions of preference at more than 5σ. This impressive sensitivity was achieved
thanks to the muon signature, which is subject to low levels of backgrounds, and the low
systematic uncertainties on the neutrino flux.
Figure 102. The four main topologies of e
+
e
−
LEE models at MicroBooNE: coherent
and incoherent scattering with well-separated or overlapping e
+
e
−
pairs.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
148
Thanks to its unique neutrino beam, nuSTORM is also sensitive to other explanations to
short-baseline anomalies. It would stand out as a unique test of lepton-flavor-violation in
muon decays. Because the beam is derived from μ
+
decays, any exotic branching ratio of the
muon, such as
m
nna
++
ee, would be a striking signature in a near detector with electron-
positron discrimination capabilities, such as in a magnetized, low-density detector. This type
of near detector would also benefit the sensitivity to models with neutrino upscattering to new
dark particles with decays to e
+
e
−
.
6.2.2. Long-baseline experiments
6.2.2.1. DUNE. The DUNE experiment is a next-generation, long-baseline neutrino
oscillation experiment, designed to be sensitive to ν
μ
to ν
e
oscillations. The experiment
consists of a high-power, broadband neutrino beam, a powerful precision multi-instrument
Near detector complex located at Fermi National Accelerator Laboratory in Batavia, Illinois,
574 m away from the neutrino production target, and a massive Liquid Argon Time
Projection Chamber Far detector located at the 4850 ft level of the Sanford Underground
Research Facility (SURF), 1300 km away in Lead, South Dakota, USA. The anticipated total
fiducial mass of the Far detector is 40 kton. The long baseline of 1300 km provides
sensitivity, in a single experiment, to all parameters governing neutrino oscillations. Due to
the high-power proton beam facility, the Near detector consisting of precision detectors
capable of off-axis data taking for improved constraining of systematics, and the massive Far
detector, DUNE provides enormous opportunities to probe BSM phenomena in both new
particle production and interactions, and in neutrino propagation effects.
DUNE expects to begin data taking operations in 2029 with half of the full Far detector,
and start beam data taking operations in 2031 with the 1.2 MW long-baseline neutrino facility
(LBNF)beam, upgradable to 2.4 MW. The LBNF neutrino beam flux sampled on-axis by the
Far detector is shown in figure 103. The wide-band range of energies provided by the LBNF
beam afford DUNE significant sensitivity to probe sterile mixing, which would typically
cause distortions of standard oscillations in energy regions away from the three-flavor ν
μ
→
Figure 103. LBNF neutrino beam fluxes at the DUNE Far detector for neutrino-
enhanced forward horn current (FHC)beam running (left), and antineutrino-enhanced
reverse horn current (RHC)beam running (right). Reproduced from [665].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
149
ν
μ
disappearance maximum. Therefore, DUNE sterile mixing probes reach a broad range of
potential sterile neutrino mass splittings by looking for disappearance of CC and NC
interactions over the long distance separating the ND and FD, as well as over the short
baseline of the ND. The DUNE sterile neutrino mixing studies shown below assume a
minimal 3 +1 oscillation scenario with three active neutrinos and one sterile neutrino, with a
new independent neutrino mass-squared difference,
D
m41
2, and for which the mixing matrix is
extended with three new mixing angles, θ
14
,θ
24
,θ
34
, and two additional phases δ
14
and δ
24
.
Figure 104 shows how the standard three-flavor oscillation probability is distorted at
neutrino energies above the standard oscillation peak when oscillations into sterile neutrinos
are included and the energy ranges DUNE ND and FD are sensitive to those distortions.
The sterile neutrino effects have been implemented in GLoBES via the existing plug-in
for sterile neutrinos and NSI [513]. The DUNE ND plays a very important role in the
sensitivity to sterile neutrinos both directly, for rapid oscillations with
D
>m1
41
2eV
2
where
the sterile oscillation matches the ND baseline, and indirectly, at smaller values of
D
m41
2
where the ND is crucial to reduce the systematic uncertainties affecting the FD to increase its
sensitivity. For these studies, the DUNE ND is assumed to be an identical scaled-down
Figure 104. Regions of L/Eprobed by the DUNE Near and Far detectors compared to
3-flavor and 3 +1-flavor neutrino disappearance and appearance probabilities. The
gray-shaded areas show the range of true neutrino energies probed by the ND and FD.
The top axis shows true neutrino energy, increasing from right to left. The top plot
shows the probabilities assuming mixing with one sterile neutrino with D=m0.0
5
41
2
eV
2
, corresponding to the slow oscillations regime. The middle plot assumes mixing
with one sterile neutrino with D=m0.5
41
2eV
2
, corresponding to the intermediate
oscillations regime. The bottom plot includes mixing with one sterile neutrino with
D=m50
41
2eV
2
, corresponding to the rapid oscillations regime. As an example, the
slow sterile oscillations cause visible distortions in the three-flavor ν
μ
survival
probability (blue curve)for neutrino energies. Reproduced from [514].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
150
version of the FD, with identical efficiencies, backgrounds and energy reconstruction. The full
set of systematic uncertainties employed in the sterile neutrino studies, as well as the
methodology accounting for non-negligible beam-induced baseline spreads between
production target and ND, are described in [514].
By default, GLoBES treats all systematic uncertainties included in the fitas
normalization shifts. However, depending on the value of
D
m41
2, sterile mixing will induce
shape distortions in the measured energy spectrum beyond simple normalization shifts. As a
consequence, shape uncertainties are very relevant for sterile neutrino searches, particularly in
regions of parameter space where the ND, with virtually infinite statistics, has a dominant
contribution. The correct inclusion of systematic uncertainties affecting the shape of the
energy spectrum in the two-detector fit GLoBES framework used for this analysis posed
technical and computational challenges beyond the scope of the study. Therefore, for each
limit plot, we present two limits bracketing the expected DUNE sensitivity limit, namely: the
black limit line, a best-case scenario, where only normalization shifts are considered in a ND
+FD fit, where the ND statistics and shape have the strongest impact; and the grey limit line,
corresponding to a worst-case scenario where only the FD is considered in the fit, together
with a rate constraint from the ND.
For sensitivity to θ
14
, the dominant channels are those regarding ν
e
disappearance. For
simplicity, only the ν
e
CC sample is analyzed and the NC and ν
μ
CC disappearance channels
are not taken into account. This is expected to be improved by using more complex multi-
channel fits in future studies, as highlighted and recommended by [179]. The sensitivity at the
90% C.L., taking into account the systematic uncertainties mentioned above, is shown in
figure 105, along with a comparison to current constraints. For the θ
24
mixing angle, the ν
μ
CC and NC disappearance samples are analyzed jointly. Results are shown in figure 105,
along with comparisons with present constraints.
Figure 105. The left plot shows the DUNE sensitivities to θ
14
from the ν
e
CC samples
at the ND and FD, assuming θ
14
=0, along with a comparison with the combined
reactor result from Daya Bay and Bugey-3. The right plot is adapted from [666]and
displays sensitivities to θ
24
using the ν
μ
CC and NC samples at both detectors, along
with a comparison with previous and existing experiments. In both cases, regions to the
right of the contours are excluded. Reproduced from [514].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
151
Inthecaseoftheθ
34
mixing angle, disappearance in the NC sample, the only contributor to
this sensitivity, is probed. The results are shown in figure 106. Further, a comparison with previous
experiments sensitive to ν
μ
,ν
τ
mixing with large mass-squared splitting is possible by considering
an effective mixing angle θ
μτ
, such that
∣∣∣∣qqqqº=
mt t m
UUsin 2 4 cos sin 2 sin
242424
14 224 234,
and assuming conservatively that
q=cos 1
414
,and q=sin 2 1
224 . This comparison with
previous experiments is also shown in figure 106. The sensitivity to θ
34
is largely independent of
D
m41
2, since the term with
qsin
234
in the expression describing P(ν
μ
→ν
s
), depends solely on the
D
m31
2mass splitting.
Finally, sensitivity to the θ
μe
effective mixing angle, defined as
∣∣∣∣qqqº=
mm
UUsin 2 4 sin 2 sin
ee
242422
14 224, is shown in figure 106, which also displays a
comparison with the allowed regions from LSND and MiniBooNE, as well as with present
constraints and projected constraints from Fermilab’s SBN program.
DUNE will also have the ability to conduct short-baseline sterile probes, for instance, by
searching for anomalous sterile-driven ν
τ
appearance in the Near detector. The τlepton is not
directly observable in the DUNE detectors due to its short 2.9 ×10
−13
s lifetime, and it is
only produced for interactions where the incoming ν
τ
has an energy of ∼3.5 GeV due to the
relatively large τmass of 1776.82 MeV. However, the final states of τdecays, ∼65% into
hadrons, ∼18% into
¯
n
n++
t-
ee
, and ∼17% into ¯
n
mn++
tm
-, are readily identifiable in
the DUNE ND, given the excellent spatial and energy resolution of the ND instruments,
namely, ND-LAr, ND-GAr, and SAND, which are complementary in providing sensitivity to
different decays channels. While within a three-flavor scenario, the DUNE ND baseline is far
too short for ν
μ
→ν
τ
oscillations to occur, ν
τ
originating in sterile-neutrino driven fast
oscillations could be detected. In particular, probing the τ→μdetection channel with high-
energy muons in the final state, which is challenging due to muon containment and
backgrounds, becomes very accessible through the use of the ND-GAr magnetic field and the
SAND detector further downstream, with studies indicating that ND-GAr’s reconstructible
Figure 106. Left: comparison of the DUNE sensitivity to θ
34
using the NC samples at
the ND and FD with previous and existing experiments. Regions to the right of the
contour are excluded. Right: DUNE sensitivities to θ
μe
from the appearance and
disappearance samples at the ND and FD are shown on the top plot, along with a
comparison with previous existing experiments and the sensitivity from the future SBN
program. Regions to the right of the DUNE contours are excluded. Reproduced from
[514].CC BY 4.0.
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
152
muon momentum via curvature extends beyond 15 GeV/c. This sensitivity will be strongly
enhanced when operating LBNF in the high-energy tune, aimed at enriching the available
sample of ν
τ
at the Far detector, while extending sensitivity to anomalous ν
τ
appearance at the
Near detector [515]. Preliminary studies using LBNF’s nominal flux, and including ND-LAr
and ND-GAr, estimate that DUNE’s sensitivities to anomalous ν
τ
appearance may extend
beyond those of previous searches carried out by NOMAD and CHORUS.
6.2.2.2. Hyper-Kamiokande. Hyper-Kamiokande (HK)is a large-scale water Cherenkov
detector with a fiducial volume of about 188 kton which is approximately 8.4 times larger
than Super-Kamiokande. HK is currently under construction in Japan and operations are
scheduled to begin in 2027 together with the upgraded J-PARC neutrino beam. The physics
capabilities of HK cover a broad range of topics including a search for sterile neutrino mixing
[516]. There are various major approaches currently being considered.
While we focus in the following on the sensitivity to sterile neutrino searches, HK can
also investigate other exotic scenarios like the breaking of Lorenz and CPT invariance, as
demonstrated in T2K in [517], and non-standard neutrino interactions, as studied with Super-
K’s atmospheric neutrino observations [518].
Mixing of light sterile neutrino will be investigated with the Hyper-Kamiokande data at a
baseline of 295 km baseline. T2K reported a limit on
qsin
224 for <
-
10 eV
42
D
<´ -
m310eV
41
242
using both CC and NC samples at Super-Kamiokande [299]. More
stringent limit will be set by Hyper-Kamiokade with more than 20 times higher statistics by
the combination of a larger fiducial volume and an upgraded J-PARC neutrino beam.
Hyper-Kamiokande’s near detectors will measure the neutrino beam flux and cross-
section at different baselines. Each detector has the capability to test the existence of sterile
mixing at certain values of L/Ebut it should be noted that the sensitivity will be further
enhanced by combined measurements among the detectors where the ND280 works as a near
detector and give constraint to the IWCD measurement.
The IWCD (Intermediate Water Cherenkov Detector)instrument has sensitivity to sterile
neutrino mixing in the ν
μ
→ν
e
channel with a baseline of ∼1 km and energy of 0.5–1 GeV,
which matches the L/Eat LSND and MinoBooNE. As a remarkable advantage, IWCD can
measure the neutrino flux at different off-axis angles by moving the detector along its vertical
pit. As the energy spectrum changes with the off-axis angle, IWCD can rule out some
potential interpretations by the combination of the measurement, such as feed-down from
high energy due to nuclear effects or unexpected background. The design of the IWCD
detector is still under investigation, but it has potential to test the allowed region given by
LSND, as indicated by the studies from the NuPRISM collaboration [519].
The off-axis ND280 has sensitivity to few eV
2
sterile neutrinos. A first search was
published in [298]. It is anticipated that the upgrades currently being done for T2K, consisting
in one fully active target (Super-FGD), two High-Angle TPCs, and a Time Of Flight system,
and possible further upgrades under study for Hyper-K, will boost the sensitivity of ND280.
Searches for sterile neutrinos with the upgraded ND280 will have several advantages with
respect to [298], including a larger target mass, a lower threshold to reconstruct leptons, better
performances in distinguishing electrons from gammas, and the larger exposure that will be
collected in HK. ND280 has also sensitivity to search for relatively heavy sterile neutrinos
produced by the decay of Kaons produced by the beamline, as demonstrated in [384].
6.2.2.3. ESSnuSB. The ESSnuSB (European Spallation Source Neutrino Super Beam)
experiment [520,521]is a proposed long-baseline neutrino oscillation experiment to use a
neutrino superbeam produced using 2.0 GeV protons from the ESS Linac in Lund, Sweden,
J. Phys. G: Nucl. Part. Phys. 51 (2024)120501 Major Report
153
resulting in a 5 MW beam peaked at E
nu
=0.4 GeV. By sampling this beam at a distance of
540 km from Lund, using a large underground Water Cherenkov detector with a 500 kton
fiducial mass, ESSnuSB will make measurements of the three-flavor oscillation second
maximum, <