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Improved limit to the diffuse flux of ultrahigh energy neutrinos from the
Pierre Auger Observatory
A. Aab,1P. Abreu,2M. Aglietta,3E. J. Ahn,4I. Al Samarai,5I. F. M. Albuquerque,6I. Allekotte,7P. Allison,8A. Almela,9,10
J. Alvarez Castillo,11 J. Alvarez-Muñiz,12 R. Alves Batista,13 M. Ambrosio,14 A. Aminaei,15 L. Anchordoqui,16
S. Andringa,2C. Aramo,14 V. M. Aranda,17 F. Arqueros,17 N. Arsene,18 H. Asorey,7,19 P. Assis,2J. Aublin,20 M. Ave,7
M. Avenier,21 G. Avila,22 N. Awal,23 A. M. Badescu,24 K. B. Barber,25 J. Bäuml,26 C. Baus,26 J. J. Beatty,8K. H. Becker,27
J. A. Bellido,25 C. Berat,21 M. E. Bertaina,3X. Bertou,7P. L. Biermann,28 P. Billoir,20 S. G. Blaess,25 A. Blanco,2
M. Blanco,20 C. Bleve,29 H. Blümer,26,30 M. Boháčová,31 D. Boncioli,32 C. Bonifazi,33 N. Borodai,34 J. Brack,35 I. Brancus,36
A. Bridgeman,30 P. Brogueira,2W. C. Brown,37 P. Buchholz,1A. Bueno,38 S. Buitink,15 M. Buscemi,14
K. S. Caballero-Mora,39 B. Caccianiga,40 L. Caccianiga,20 M. Candusso,41 L. Caramete,42 R. Caruso,43 A. Castellina,3
G. Cataldi,29 L. Cazon,2R. Cester,44 A. G. Chavez,45 A. Chiavassa,3J. A. Chinellato,46 J. Chudoba,31 M. Cilmo,14
R. W. Clay,25 G. Cocciolo,29 R. Colalillo,14 A. Coleman,47 L. Collica,40 M. R. Coluccia,29 R. Conceição,2F. Contreras,48
M. J. Cooper,25 A. Cordier,49 S. Coutu,47 C. E. Covault,50 J. Cronin,51 R. Dallier,52,53 B. Daniel,46 S. Dasso,54,55
K. Daumiller,30 B. R. Dawson,25 R. M. de Almeida,56 S. J. de Jong,15,57 G. De Mauro,15 J. R. T. de Mello Neto,33
I. De Mitri,29 J. de Oliveira,56 V. de Souza,58 L. del Peral,59 O. Deligny,5H. Dembinski,30 N. Dhital,60 C. Di Giulio,41
A. Di Matteo,61 J. C. Diaz,60 M. L. Díaz Castro,46 F. Diogo,2C. Dobrigkeit,46 W. Docters,62 J. C. D’Olivo,11 A. Dorofeev,35
Q. Dorosti Hasankiadeh,30 M. T. Dova,63 J. Ebr,31 R. Engel,30 M. Erdmann,64 M. Erfani,1C. O. Escobar,4,46 J. Espadanal,2
A. Etchegoyen,10,9 H. Falcke,15,65,57 K. Fang,51 G. Farrar,23 A. C. Fauth,46 N. Fazzini,4A. P. Ferguson,50 M. Fernandes,33
B. Fick,60 J. M. Figueira,10 A. Filevich,10 A. Filipčič,66,67 B. D. Fox,68 O. Fratu,24 M. M. Freire,69 B. Fuchs,26 T. Fujii,51
B. García,70 D. Garcia-Pinto,17 F. Gate,52 H. Gemmeke,71 A. Gherghel-Lascu,36 P. L. Ghia,20 U. Giaccari,33
M. Giammarchi,40 M. Giller,72 D. Głas,72 C. Glaser,64 H. Glass,4G. Golup,7M. Gómez Berisso,7P. F. Gómez Vitale,22
N. González,10 B. Gookin,35 J. Gordon,8A. Gorgi,3P. Gorham,68 P. Gouffon,6N. Griffith,8A. F. Grillo,32 T. D. Grubb,25
Y. Guardincerri,55,†F. Guarino,14 G. P. Guedes,73 M. R. Hampel,10 P. Hansen,63 D. Harari,7T. A. Harrison,25 S. Hartmann,64
J. L. Harton,35 A. Haungs,30 T. Hebbeker,64 D. Heck,30 P. Heimann,1A. E. Herve,30 G. C. Hill,25 C. Hojvat,4N. Hollon,51
E. Holt,30 P. Homola,27 J. R. Hörandel,15,57 P. Horvath,74 M. Hrabovský,74,31 D. Huber,26 T. Huege,30 A. Insolia,43
P. G. Isar,42 I. Jandt,27 S. Jansen,15,57 C. Jarne,63 J. A. Johnsen,75 M. Josebachuili,10 A. Kääpä,27 O. Kambeitz,26
K. H. Kampert,27 P. Kasper,4I. Katkov,26 B. Kégl,49 B. Keilhauer,30 A. Keivani,47 E. Kemp,46 R. M. Kieckhafer,60
H. O. Klages,30 M. Kleifges,71 J. Kleinfeller,48 R. Krause,64 N. Krohm,27 O. Krömer,71 D. Kuempel,64 N. Kunka,71
D. LaHurd,50 L. Latronico,3R. Lauer,76 M. Lauscher,64 P. Lautridou,52 S. Le Coz,21 D. Lebrun,21 P. Lebrun,4
M. A. Leigui de Oliveira,77 A. Letessier-Selvon,20 I. Lhenry-Yvon,5K. Link,26 L. Lopes,2R. López,78 A. López Casado,12
K. Louedec,21 L. Lu,27,79 A. Lucero,10 M. Malacari,25 S. Maldera,3M. Mallamaci,40 J. Maller,52 D. Mandat,31 P. Mantsch,4
A. G. Mariazzi,63 V. Marin,52 I. C. Mariş,38 G. Marsella,29 D. Martello,29 L. Martin,52,53 H. Martinez,80 O. Martínez Bravo,78
D. Martraire,5J. J. Masías Meza,55 H. J. Mathes,30 S. Mathys,27 J. Matthews,81 J. A. J. Matthews,76 G. Matthiae,41
D. Maurel,26 D. Maurizio,82 E. Mayotte,75 P. O. Mazur,4C. Medina,75 G. Medina-Tanco,11 R. Meissner,64 V. B. B. Mello,33
D. Melo,10 A. Menshikov,71 S. Messina,62 R. Meyhandan,68 M. I. Micheletti,69 L. Middendorf,64 I. A. Minaya,17
L. Miramonti,40 B. Mitrica,36 L. Molina-Bueno,38 S. Mollerach,7F. Montanet,21 C. Morello,3M. Mostafá,47 C. A. Moura,77
M. A. Muller,46,83 G. Müller,64 S. Müller,30 R. Mussa,44 G. Navarra,3,* J. L. Navarro,38,‡S. Navas,38 P. Necesal,31 L. Nellen,11
A. Nelles,15,57 J. Neuser,27 P. H. Nguyen,25 M. Niculescu-Oglinzanu,36 M. Niechciol,1L. Niemietz,27 T. Niggemann,64
D. Nitz,60 D. Nosek,84 V. Novotny,84 L. Nožka,74 L. Ochilo,1F. Oikonomou,47 A. Olinto,51 N. Pacheco,59
D. Pakk Selmi-Dei,46 M. Palatka,31 J. Pallotta,85 P. Papenbreer,27 G. Parente,12 A. Parra,78 T. Paul,16,86 M. Pech,31
J. Pe¸kala,34 R. Pelayo,87 I. M. Pepe,88 L. Perrone,29 E. Petermann,89 C. Peters,64 S. Petrera,61,90 Y. Petrov,35 J. Phuntsok,47
R. Piegaia,55 T. Pierog,30 P. Pieroni,55 M. Pimenta,2V. Pirronello,43 M. Platino,10 M. Plum,64 A. Porcelli,30 C. Porowski,34
R. R. Prado,58 P. Privitera,51 M. Prouza,31 V. Purrello,7E. J. Quel,85 S. Querchfeld,27 S. Quinn,50 J. Rautenberg,27
O. Ravel,52 D. Ravignani,10 B. Revenu,52 J. Ridky,31 S. Riggi,43 M. Risse,1P. Ristori,85 V. Rizi,61
W. Rodrigues de Carvalho,12 G. Rodriguez Fernandez,41 J. Rodriguez Rojo,48 M. D. Rodríguez-Frías,59 D. Rogozin,30
J. Rosado,17 M. Roth,30 E. Roulet,7A. C. Rovero,54 S. J. Saffi,25 A. Saftoiu,36 F. Salamida,5H. Salazar,78 A. Saleh,67
F. Salesa Greus,47 G. Salina,41 F. Sánchez,10 P. Sanchez-Lucas,38 E. Santos,46 E. M. Santos,6F. Sarazin,75 B. Sarkar,27
R. Sarmento,2R. Sato,48 C. Scarso,48 M. Schauer,27 V. Scherini,29 H. Schieler,30 P. Schiffer,13 D. Schmidt,30 O. Scholten,62,§
H. Schoorlemmer,68 P. Schovánek,31 F. G. Schröder,30 A. Schulz,30 J. Schulz,15 J. Schumacher,64 S. J. Sciutto,63
A. Segreto,91 M. Settimo,20 A. Shadkam,81 R. C. Shellard,82 I. Sidelnik,7G. Sigl,13 O. Sima,18 A. Śmiałkowski,72
R. Šmída,30 G. R. Snow,89 P. Sommers,47 J. Sorokin,25 R. Squartini,48 Y. N. Srivastava,86 D. Stanca,36 S. Stanič,67
J. Stapleton,8J. Stasielak,34 M. Stephan,64 A. Stutz,21 F. Suarez,10 T. Suomijärvi,5A. D. Supanitsky,54 M. S. Sutherland,8
J. Swain,86 Z. Szadkowski,72 O. A. Taborda,7A. Tapia,10 A. Tepe,1V. M. Theodoro,46 J. Tiffenberg,55,†C. Timmermans,57,15
PHYSICAL REVIEW D 91, 092008 (2015)
1550-7998=2015=91(9)=092008(14) 092008-1 Published by the American Physical Society
C. J. Todero Peixoto,92 G. Toma,36 L. Tomankova,30 B. Tomé,2A. Tonachini,44 G. Torralba Elipe,12 D. Torres Machado,33
P. Travnicek,31 R. Ulrich,30 M. Unger,23 M. Urban,64 J. F. Valdés Galicia,11 I. Valiño,12 L. Valore,14 G. van Aar,15
P. van Bodegom,25 A. M. van den Berg,62 S. van Velzen,15 A. van Vliet,13 E. Varela,78 B. Vargas Cárdenas,11 G. Varner,68
R. Vasquez,33 J. R. Vázquez,17 R. A. Vázquez,12 D. Veberič,30 V. Verzi,41 J. Vicha,31 M. Videla,10 L. Villaseñor,45
B. Vlcek,59 S. Vorobiov,67 H. Wahlberg,63 O. Wainberg,10,9 D. Walz,64 A. A. Watson,79 M. Weber,71 K. Weidenhaupt,64
A. Weindl,30 F. Werner,26 A. Widom,86 L. Wiencke,75 H. Wilczyński,34 T. Winchen,27 D. Wittkowski,27 B. Wundheiler,10
S. Wykes,15 L. Yang,67 T. Yapici,60 A. Yushkov,1E. Zas,12 D. Zavrtanik,67,66 M. Zavrtanik,66,67 A. Zepeda,80 Y. Zhu,71
B. Zimmermann,71 M. Ziolkowski,1and F. Zuccarello43
(Pierre Auger Collaboration)¶
1Universität Siegen, Siegen, Germany
2Laboratório de Instrumentação e Física Experimental de Partículas–LIP and Instituto Superior
Técnico–IST, Universidade de Lisboa–UL, Portugal
3Osservatorio Astrofisico di Torino (INAF), Università di Torino and Sezione INFN,
Torino, Italy
4Fermilab, Batavia, Illinois, USA
5Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris 11, CNRS-IN2P3, Orsay, France
6Universidade de São Paulo, Instituto de Física, São Paulo, SP, Brazil
7Centro Atómico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET),
San Carlos de Bariloche, Argentina
8Ohio State University, Columbus, Ohio, USA
9Universidad Tecnológica Nacional–Facultad Regional Buenos Aires, Buenos Aires, Argentina
10Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM),
Buenos Aires, Argentina
11Universidad Nacional Autónoma de Mexico, Mexico, D.F., Mexico
12Universidad de Santiago de Compostela, Spain
13Universität Hamburg, Hamburg, Germany
14Università di Napoli “Federico II”and Sezione INFN, Napoli, Italy
15IMAPP, Radboud University Nijmegen, Netherlands
16Department of Physics and Astronomy, Lehman College, City University of New York, New York, USA
17Universidad Complutense de Madrid, Madrid, Spain
18University of Bucharest, Physics Department, Romania
19Universidad Industrial de Santander, Colombia
20Laboratoire de Physique Nucléaire et de Hautes Energies (LPNHE), Universités Paris 6 et Paris 7,
CNRS-IN2P3, Paris, France
21Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Université Grenoble-Alpes,
CNRS/IN2P3, France
22Observatorio Pierre Auger and Comisión Nacional de Energía Atómica, Malargüe, Argentina
23New York University, New York, New York, USA
24University Politehnica of Bucharest, Romania
25University of Adelaide, Adelaide, S.A., Australia
26Karlsruhe Institute of Technology–Campus South–Institut für Experimentelle Kernphysik (IEKP),
Karlsruhe, Germany
27Bergische Universität Wuppertal, Wuppertal, Germany
28Max-Planck-Institut für Radioastronomie, Bonn, Germany
29Dipartimento di Matematica e Fisica “E. De Giorgi”dell’Università del Salento and Sezione INFN,
Lecce, Italy
30Karlsruhe Institute of Technology–Campus North–Institut für Kernphysik,
Karlsruhe, Germany
31Institute of Physics of the Academy of Sciences of the Czech Republic,
Prague, Czech Republic
32INFN, Laboratori Nazionali del Gran Sasso, Assergi (L’Aquila), Italy
33Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil
34Institute of Nuclear Physics PAN, Krakow, Poland
35Colorado State University, Fort Collins, Colorado, USA
36‘Horia Hulubei’National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania
37Colorado State University, Pueblo, Colorado, USA
38Universidad de Granada and C.A.F.P.E., Granada, Spain
39Universidad Autónoma de Chiapas, Tuxtla Gutiérrez, Chiapas, Mexico
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
092008-2
40Università di Milano and Sezione INFN, Milan, Italy
41Università di Roma II “Tor Vergata”and Sezione INFN, Roma, Italy
42Institute of Space Sciences, Bucharest, Romania
43Università di Catania and Sezione INFN, Catania, Italy
44Università di Torino and Sezione INFN, Torino, Italy
45Universidad Michoacana de San Nicolás de Hidalgo,
Morelia, Michoacán, Mexico
46Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil
47Pennsylvania State University, University Park, USA
48Observatorio Pierre Auger, Malargüe, Argentina
49Laboratoire de l’Accélérateur Linéaire (LAL), Université Paris 11,
CNRS-IN2P3, Orsay, France
50Case Western Reserve University, Cleveland, Ohio, USA
51University of Chicago, Enrico Fermi Institute, Chicago, Illinois, USA
52SUBATECH, École des Mines de Nantes, CNRS-IN2P3, Université de Nantes, Nantes, France
53Station de Radioastronomie de Nançay, Observatoire de Paris, CNRS/INSU, Nançay, France
54Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina
55Departamento de Física, FCEyN, Universidad de Buenos Aires and CONICET, Argentina
56Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil
57Nikhef, Science Park, Amsterdam, Netherlands
58Universidade de São Paulo, Instituto de Física de São Carlos, São Carlos, SP, Brazil
59Universidad de Alcalá, Alcalá de Henares, Spain
60Michigan Technological University, Houghton, Michigan, USA
61Dipartimento di Scienze Fisiche e Chimiche dell’Università dell’Aquila and INFN, Italy
62KVI–Center for Advanced Radiation Technology, University of Groningen, Groningen, Netherlands
63IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
64RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany
65ASTRON, Dwingeloo, Netherlands
66Experimental Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia
67Laboratory for Astroparticle Physics, University of Nova Gorica, Slovenia
68University of Hawaii, Honolulu, Hawaii, USA
69Instituto de Física de Rosario (IFIR)–CONICET/U.N.R. and Facultad de Ciencias Bioquímicas y
Farmacéuticas U.N.R., Rosario, Argentina
70Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM),
and Universidad Tecnológica Nacional–Facultad Regional Mendoza (CONICET/CNEA),
Mendoza, Argentina
71Karlsruhe Institute of Technology–Campus North–Institut für Prozessdatenverarbeitung
und Elektronik, Germany
72University of Łódź,Łódź, Poland
73Universidade Estadual de Feira de Santana, Brazil
74Palacky University, RCPTM, Olomouc, Czech Republic
75Colorado School of Mines, Golden, Colorado, USA
76University of New Mexico, Albuquerque, New Mexico, USA
77Universidade Federal do ABC, Santo André, SP, Brazil
78Benemérita Universidad Autónoma de Puebla, Mexico
79School of Physics and Astronomy, University of Leeds, United Kingdom
80Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), Mexico, D.F., Mexico
81Louisiana State University, Baton Rouge, Louisiana, USA
82Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil
83Universidade Federal de Pelotas, Pelotas, RS, Brazil
84Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics,
Prague, Czech Republic
85Centro de Investigaciones en Láseres y Aplicaciones, CITEDEF and CONICET, Argentina
86Northeastern University, Boston, Massachusetts, USA
87Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas del Instituto Politécnico
Nacional (UPIITA-IPN), Mexico, D.F., Mexico
88Universidade Federal da Bahia, Salvador, BA, Brazil
89University of Nebraska, Lincoln, Nebraska, USA
90Gran Sasso Science Institute (INFN), L’Aquila, Italy
IMPROVED LIMIT TO THE DIFFUSE FLUX OF …PHYSICAL REVIEW D 91, 092008 (2015)
092008-3
91Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo (INAF), Palermo, Italy
92Universidade de São Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil
(Received 18 March 2015; published 26 May 2015)
Neutrinos in the cosmic ray flux with energies near 1 EeV and above are detectable with the Surface
Detector array (SD) of the Pierre Auger Observatory. We report here on searches through Auger data from
1 January 2004 until 20 June 2013. No neutrino candidates were found, yielding a limit to the diffuse flux
of ultrahigh energy neutrinos that challenges the Waxman-Bahcall bound predictions. Neutrino identi-
fication is attempted using the broad time structure of the signals expected in the SD stations, and is
efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as
for “Earth-skimming”neutrino interactions in the case of tau neutrinos. In this paper the searches for
downward-going neutrinos in the zenith angle bins 60°–75° and 75°–90° as well as for upward-going
neutrinos, are combined to give a single limit. The 90% C.L. single-flavor limit to the diffuse flux of
ultrahigh energy neutrinos with an E−2spectrum in the energy range 1.0×1017 eV–2.5×1019 eV is
E2
νdNν=dEν<6.4×10−9GeV cm−2s−1sr−1.
DOI: 10.1103/PhysRevD.91.092008 PACS numbers: 95.55.Vj, 95.85.Ry, 98.70.Sa
I. INTRODUCTION
The flux of ultrahigh energy cosmic rays (UHECRs)
above ∼5×1019 eV is known to be suppressed with
respect to that extrapolated from lower energies. This
feature has been seen in the UHECR spectrum [1,2], with
the position of the break being compatible with the
Greisen-Zatsepin-Kuzmin effect [3], i.e. the interaction
of UHECRs with the cosmic microwave background
(CMB) radiation. However, other explanations are possible,
most prominently a scenario where the limiting energy of
the UHECR sources is being observed [4]. Key to dis-
tinguishing between these two scenarios is the determi-
nation of the composition of the UHECRs [5,6], with the
second scenario predicting increasing fractions of primaries
heavier than protons as energy increases [4].
Above ∼5×1019 eV cosmic-ray protons interact with
CMB photons and produce ultrahigh energy cosmogenic
neutrinos of energies typically 1=20 of the proton energy
[7]. Their fluxes are uncertain and at EeV energies they
depend mostly on the evolution with redshift zof the
unknown sources of UHECRs, and on their spectral
features at injection. Protons typically produce more
neutrinos than heavier primaries do [8,9], so measurement
of the neutrino flux gives information on the nature of the
primaries. In this respect the observation of UHE neutrinos
can provide further hints on the dominant scenario of
UHECR production [9], as well as on the evolution with z
of their sources which can help in their identification [9,10].
UHE neutrinos are also expected to be produced in the
decay of charged pions created in the interactions of cosmic
rays with matter and/or radiation at their potential sources,
such as Gamma-Ray Bursts or Active Galactic Nuclei
among others [11]. In fact, at tens of EeV, neutrinos may be
the only direct probe of the sources of UHECRs at
distances farther than ∼100 Mpc.
A breakthrough in the field was the recent detection with
the IceCube experiment of three neutrinos of energies just
above 1 PeV, including a 2 PeV event which is the highest-
energy neutrino interaction ever observed, followed by tens
of others above ∼30 TeV representing a ∼5.7σexcess above
atmospheric neutrino background [12]. The measured flux is
close to the Waxman-Bahcall upper bound to the UHE
neutrino flux [13], although with a steeper spectrum [14].
In the EeVenergy range, i.e. about 3 orders of magnitude
above the most energetic neutrinos detected in IceCube,
neutrinos have so far escaped detection by existing experi-
ments. These can be detected with a variety of techniques
[15], among them with arrays of particle detectors at ground.
In this paper we report on the search for EeV neutrinos in
data taken with the Surface Detector array (SD) of the
Pierre Auger Observatory [16]. A blind scan of data from
1 January 2004 up to 20 June 2013 has yielded no neutrino
candidates and an updated and stringent limit to the diffuse
flux of UHE neutrino flux has been obtained.
II. SEARCHING FOR UHE NEUTRINOS IN AUGER
The concept for identification of neutrinos is rather
simple. While protons, heavier nuclei, and even photons
interact shortly after entering the atmosphere, neutrinos can
initiate showers quite deep in the atmosphere. At large
zenith angles the atmosphere is thick enough so that the
electromagnetic component of nucleonic cosmic rays gets
absorbed and the shower front at ground level is dominated
*Deceased.
†Now at Fermilab, Batavia, Illinois, USA.
‡Now at CERN, Geneva, Switzerland.
§Also at Vrije Universiteit Brussels, Belgium.
¶auger_spokespersons@fnal.gov
Published by the American Physical Society under the terms of
the Creative Commons Attribution 3.0 License. Further distri-
bution of this work must maintain attribution to the author(s) and
the published article’s title, journal citation, and DOI.
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
092008-4
by muons (“old”shower front). On the other hand, showers
induced by neutrinos deep in the atmosphere have a
considerable amount of electromagnetic component at
the ground (“young”shower front). The Surface
Detector array of the Pierre Auger Observatory is not
directly sensitive to the muonic and electromagnetic
components of the shower separately, nor to the depth at
which the shower is initiated. In the ∼1600 water-
Cherenkov stations of the SD of the Pierre Auger
Observatory, spread over an area of ∼3000 km2, separated
by 1.5 km and arranged in a triangular grid, the signals
produced by the passage of shower particles are digitized
with flash analog to digital converters (FADC) with 25 ns
resolution. This allows us to distinguish narrow signals in
time induced by inclined showers initiated high in the
atmosphere, from the broad signals expected in inclined
showers initiated close to the ground.
Applying this simple idea, with the SD of the Pierre
Auger Observatory [16] we can efficiently detect inclined
showers and search for two types of neutrino-induced
showers at energies above about 1 EeV:
(1) Earth-skimming (ES) showers induced by tau neu-
trinos (ντ) that travel in a slightly upward direction
with respect to ground. ντcan skim the Earth’s crust
and interact relatively close to the surface inducing a
tau lepton which escapes the Earth and decays in
flight in the atmosphere, close to the SD.
Typically, only Earth-skimming ντ-induced
showers with zenith angles 90°<θ<95° may be
identified.
(2) Showers initiated by any neutrino flavor moving
down at large angles with respect to the vertical that
interact in the atmosphere close to the surface detector
array through charged-current (CC) or neutral-current
(NC) interactions. We include here showers induced
by ντinteracting in the mountains surrounding the
Pierre Auger Observatory. Although this latter proc-
ess is exactly equivalent to the “Earth-skimming”
mechanism, it is included in this class because such
showers are also going downwards. In the following
we will refer to all these types of showers as
“downward-going”(DG) ν-induced showers.
With the aid of Monte Carlo simulations we have
established that this search can be performed effi-
ciently as long as it is restricted to showers with zenith
angles θ>60°. Due to the characteristics of these
showers depending on the zenith angle, the search in
this channel was performed in two angular subranges:
(a) “low”zenith angle (DGL) corresponding to 60°<
θ<75° and (b) “high”zenith angle (DGH)
with 75°<θ<90°.
A. General procedure
The identification of potential neutrino-induced showers
is based on first selecting those events that arrive in rather
inclined directions, and then selecting among them those
with FADC traces that are spread in time, indicative of the
early stage of development of the shower and a clear
signature of a deeply interacting neutrino triggering the SD.
First of all, events occurring during periods of data
acquisition instabilities [17] are excluded. For the remain-
ing events the FADC traces of the triggered stations are first
“cleaned”to remove accidental signals [18] induced mainly
by random atmospheric muons arriving closely before or
after the shower front. These muons are typically produced
in lower energy showers (below the energy threshold of the
SD of the Auger Observatory) that arrive by chance in
coincidence with the triggering shower. A procedure to
select the stations participating in the event described in
[18,19] is then applied, with the event accepted if the
number of accepted stations Nst is at least three (four) in the
Earth-skimming (downward-going) selections.
From the pattern (footprint) of stations at ground a length
Lalong the arrival direction of the event and a width W
perpendicular to it characterizing the shape of the footprint
are extracted [18]. The ratio L=W ∼1in vertical events,
increasing gradually as the zenith angle increases. Very
inclined events typically have elongated patterns on the
ground along the direction of arrival and hence large values
of L=W. A cut in L=W is therefore a good discriminator of
inclined events. Another indication of inclined events is
given by the apparent speed Vof the trigger from a station i
to a station j, averaged over all pairs ði; jÞof stations in the
event. This observable denoted as hViis obtained from the
distance between the stations after projection along Land
from the difference in trigger times of the stations. In
vertical showers hViexceeds the speed of light since all
triggers occur at roughly the same time, while in very
inclined events hViis concentrated around the speed of
light. Moreover its root-mean-square [rmsðVÞ] value is
small. For downward-going events only, a cut on the
reconstructed zenith angle θrec is applied [19].
Once inclined showers are selected the next step is to
identify young showers. A Time-over-Threshold (ToT)
trigger1is usually present in SD stations with signals
extended in time, while narrow signals induce other local
triggers. Also the Area-over-Peak ratio (AoP), defined as the
ratio of the integral of the FADC trace to its peak value,
normalized to the average signal produced by a single muon,
provides an estimate of the spread-in-time of the traces, and
serves as an observable to discriminate broad from narrow
shower fronts. In particular, a cut on AoP allows the rejection
of background signals induced by inclined hadronic show-
ers, in which the muons and their electromagnetic products
1This trigger is intended to select sequences of small signals in
the FADC traces spread in time. It requires at least 13 bins in 120
FADC bins of a sliding window of 3μs above a threshold of
0.2Ipeak
VEM (the peak value of the signal expected for a vertical muon
crossing the station), in coincidence in 2 out of 3 photomultiplier
tubes (PMTs) [17].
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are concentrated within a short time interval, exhibiting AoP
values close to the one measured in signals induced by
isolated muons. These observables are used by themselves in
the search for νcandidates, or combined in a linear Fisher-
discriminant polynomial depending on the selection as
described later in this paper.
As a general procedure and to optimize the numerical
values of the cuts and tune the algorithms needed to
separate neutrino-induced showers from the much larger
background of hadronic showers, we divided the whole
data sample (1 January 2004–20 June 2013) into two parts
(excluding periods of array instability). A selection depen-
dent fraction of the data ∼20%, along with Monte Carlo
simulations of UHE neutrinos, is dedicated to define the
selection algorithm, the most efficient observables and the
value of the cuts on them. These data are assumed to be
overwhelmingly constituted of background showers. The
applied procedure is conservative because the presence of
neutrinos in the training data would result in a more severe
definition of the selection criteria. The remaining fraction
of data is not used until the selection procedure is
established, and then it is “unblinded”to search for
neutrino candidates. We used real data to train the selec-
tions instead of Monte Carlo simulations of hadronic
showers, the primary reason being that the detector sim-
ulation may not account for all possible detector fluctua-
tions that may induce events that constitute a background to
UHE neutrinos, while they are contained in data. It is
important to remark that this is the same selection pro-
cedure and training period as in previous publications
[18,19], which is applied in this paper to a larger data set.
Regarding the Monte Carlo simulations, the phase space
of the neutrino showers reduces to three variables: the
neutrino energy Eν, the incidence zenith angle θand the
interaction depth Din the atmosphere for downward-going
neutrinos, or the altitude hcof the τdecay above ground
in the case of Earth-skimming neutrinos. Showers were
simulated with energies from logðEτ=eVÞ¼17 to 20.5 in
steps of 0.5, zenith angles from 90.1° to 95.9° in steps of
0.01 rad (ES) and from 60° to 90° in steps of 0.05 rad (DG).
The values of hcrange from 0 to 2500 m (in steps of 100 m)
whereas Dis uniformly distributed along the shower axis in
steps of 100 gcm
−2.
We have described the general procedure to search for
Earth-skimming ντand downward-going ν-induced show-
ers. However the two searches (ES and DG) differ in
several aspects that we describe in the following sections.
B. Earth-skimming (ES) neutrinos
With Monte Carlo simulations of UHE ντpropagating
inside the Earth, we have established that τleptons above
the energy threshold of the SD are efficiently produced only
at zenith angles between 90° and 95°. For this reason, in the
Earth-skimming analysis we place very restrictive cuts to
select only quasihorizontal showers with largely elongated
footprints: L=W > 5and hVi∈½0.29;0.31mns
−1with
rmsðVÞ<0.08 mns
−1(see Table I).2
In the ES selection, the neutrino identification variables
include the fraction of stations with ToT trigger and having
AoP >1.4for data prior to 31 May 2010 [18]. This fraction
is required to be above 60% of the triggered stations in the
event. The final choice of the values of these cuts was made
by requiring zero background events in the training data
sample, corresponding to 1% of the events recorded up to
that date. For data beyond 1 June 2010 a new methodology
and a new set of efficient selection criteria was established
based on an improved and enlarged library of ES simulated
ντevents and on a larger period of training data. In
particular, we used the average value of AoP (hAoPi) over
all the triggered stations in the event as the main observable
to discriminate between hadronic showers and ES neutri-
nos. The new methodology allows us to place the value of
the cut on hAoPiusing the tail of its distribution as obtained
in real data (which was seen to be consistent with an
exponential shape as shown in Fig. 1). This tail was fitted
and extrapolated to find the value of the cut corresponding
to less than 1 expected event per 50 yr on the full SD array.
As a result, an event is tagged as a neutrino candidate
if hAoPi>1.83 (see Table Iand Fig. 1). The new
<AoP>
1 1.5 2 2.5 3 3.5 4 4.5
Events
-1
10
1
10
2
10
3
10
Training data
Search data
τ
νMonte Carlo
<AoP> > 1.83
candidate region
τ
ν
FIG. 1 (color online). Distributions of hAoPi(the variable used
to identifiy neutrinos in the ES selection for data after 1 June
2010) after applying the inclined shower selection in Table I.
Gray-filled histogram: the data in the training period. Black
histogram: data in the search period. These two distributions are
normalized to the same number of events for comparison
purposes. Blue histogram: simulated ES ντevents. The dashed
vertical line represents the cut on hAoPi>1.83 above which a
data event is regarded as a neutrino candidate. An exponential fit
to the tail of the distribution of training data is also shown as a red
dashed line (see text for explanation).
2The axis of Earth-skimming showers traveling in the upward
direction does not intersect the ground, contrary to the case for
downward-going showers. For this reason, we exploit the proper-
ties of the footprint generated by the shower particles that deviate
laterally from the shower axis and trigger the SD water-
Cherenkov stations.
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
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methodology is not applied to the data prior to 31 May
2010 since that data period was already unblinded to search
for UHE neutrinos under the older cuts [18].
Roughly ∼95% of the simulated inclined ντevents
producing τleptons above the energy threshold of the
SD are kept after the cut on hAoPi. The search for neutrinos
is clearly not limited by background in this channel.
C. Downward-going (DG) neutrinos
In the high zenith angle range of the downward-going
analysis (DGH) the values of the cuts to select inclined
events are obtained in Monte Carlo simulations of events
with θ>75°. Due to the larger angular range compared to
Earth-skimming ντ, less stringent criteria are applied, namely
L=W > 3,hVi<0.313 mns
−1,rmsðVÞ=hVi<0.08 plus a
further requirement that the reconstructed zenith angle
θrec >75°(see[19] and Table Ifor full details).
In the low zenith angle range (DGL) corresponding to
60°<θ<75°, L=W,hViand rmsðVÞ=hViare less effi-
cient in selecting inclined events than the reconstructed
zenith angle θrec, and for this reason only a cut on θrec is
applied, namely 58.5°<θrec <76.5°, which includes some
allowance to account for the resolution in the angular
reconstruction of the simulated neutrino events.
After the inclined shower selection is performed, the
discrimination power is optimized with the aid of the
multivariate Fisher discriminant method [20]. A linear
combination of observables is constructed which optimizes
the separation between background hadronic inclined
showers occurring during the downward-going training
period, and Monte Carlo simulated ν-induced showers. The
method requires as input a set of observables. For that
purpose we use variables depending on the dimensionless
Area-over-Peak (AoP) observable—as defined above—of
the FADC traces.
In the DGH channel, due to the inclination of the shower
the electromagnetic component is less attenuated at the
locations of the stations that are first hit by a deep inclined
shower (early stations) than in the stations that are hit last
(late stations). From Monte Carlo simulations of ν-induced
showers with θ>75° we have established that in the first
few early stations the typical AoP values range between 3
and 5, while AoP tends to be closer to 1 in the late stations.
Based on this simple observation and as already reported
in [19], we have found a good discrimination when the
following ten variables are used to construct the linear
Fisher discriminant variable F: the AoP and ðAoPÞ2of the
four stations that trigger first in each event, the product of
the four AoPs, and a global parameter that measures the
asymmetry between the average AoP of the early stations
and those triggering last in the event (see [19] for further
details and Table I).
The selection of neutrino candidates in the zenith angle
range 60°<θ<75° (DGL) is more challenging since the
electromagnetic component of background hadronic show-
ers at ground increases as the zenith angle decreases
because the shower crosses less atmosphere before reach-
ing the detector level. Out of all triggered stations of an
event in this angular range, the ones closest to the shower
core exhibit the highest discrimination power in terms of
AoP. In fact it has been observed in Monte Carlo simu-
lations that the first triggered stations can still contain some
electromagnetic component for background events and, for
this reason, it is not desirable to use them for discrimination
purposes. The last ones, even if they are triggered only by
muons from a background hadronic shower, can exhibit
large values of AoP because they are far from the core
where muons are known to arrive with a larger spread in
time. Based on the information from Monte Carlo simu-
lations, the variables used in the Fisher discriminant
TABLE I. Observables and numerical values of cuts applied to select inclined and young showers for Earth-skimming and downward-
going neutrinos. See text for explanation.
Selection Earth-skimming (ES)
Downward-going
high angle (DGH)
Downward-going
low angle (DGL)
Flavours and interactions ντCC νe;νμ;ντCC & NC νe;νμ;ντCC & NC
Angular range θ>90°θ∈ð75°;90°Þθ∈ð60°;75°Þ
N° of stations (Nst)Nst ≥3Nst ≥4Nst ≥4
Inclined showers
θrec >75°θrec ∈ð58.5°;76.5°Þ
L=W > 5L=W > 3
hVi∈ð0.29;0.31Þmns
−1hVi<0.313 mns
−1
rmsðVÞ<0.08 mns
−1rmsðVÞ=hVi<0.08
Young showers
Data: 1 January 2004–31 May 2010
≥60% of stations with
ToT trigger and AoP >1.4Fisher discriminant based
on AoP of early stations
≥75% of stations close to
shower core with ToT trigger
and
Fisher discriminant based
on AoP of early stations
close to shower core
Data: 1 June 2010–20 June 2013
hAoPi>1.83
AoPmin >1.4if Nst ¼3
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analysis are the individual AoP of the four or five stations
(depending on the zenith angle) closest to the core, and
their product [21]. In the DGL analysis it is also required
that at least 75% of the triggered stations closest to the core
have a ToT local trigger [21].
Once the Fisher discriminant Fis defined, the next step
is to define a numerical value Fcut that efficiently separates
neutrino candidates from regular hadronic showers. As was
done for the variable hAoPiin the Earth-skimming analy-
sis, Fcut was fixed using the tail of the distribution of Fin
real data, which is consistent with an exponential shape in
all cases. An example is shown in Fig. 2. The tail was fitted
and extrapolated to find the value of Fcut corresponding to
less than 1 expected event per 50 yr on the full SD array
[19,21]. Roughly ∼85% (∼60%) of the simulated inclined ν
events are kept after the cut on the Fisher variable in the
DGH (DGL) selections. The smaller efficiencies for the
identification of neutrinos in the DGL selection are due to
the more stringent criteria in the angular bin θ∈ð60°;75°Þ
needed to reject the larger contamination from cosmic-ray
induced showers.
III. DATA UNBLINDING AND EXPOSURE
CALCULATION
A. Data unblinding
No events survived when the Earth-skimming and
downward-going selection criteria explained above and
summarized in Table Iare applied blindly to the data
collected between 1 January 2004 and 20 June 2013. For
each selection the corresponding training periods are
excluded from the search. After the unblinding we tested
the compatibility of the distributions of discriminating
observables in the search and training samples.
Examples are shown in Fig. 1for the hAoPivariable in
the Earth-skimming analysis, and in Fig. 2for the Fisher
variable in the DGH analysis. In particular fitting the tails
of the corresponding distributions to an exponential, we
obtained compatible parameters within 1σstatistical
uncertainties.
B. Exposure calculation
1. Neutrino identification efficiencies
The selection criteria in Table I, were also applied to
neutrino-induced showers simulated with Monte Carlo, and
the identification efficiencies ϵES;ϵDGH;ϵDGL for each
channel—defined as the fraction of simulated events
passing the cuts—were obtained.
A large set of Monte Carlo simulations of neutrino-
induced showers was performed for this purpose, covering
the whole parameter space where the efficiency is expected
to be sizable. In the case of Earth-skimming ντinduced
showers, the efficiency depends on the energy of the
emerging τleptons Eτ, on the zenith angle θand on the
altitude of the decay point of the τabove ground. These
efficiencies are averaged over azimuthal angle and the τ
decay channels. The maximum efficiency that can be
reached is 82.6%, the 17.4% remaining corresponds to
the channel in which the τdecays into a μwhich is unlikely
to produce a detectable shower close to ground. In the case
of downward-going neutrinos the identification efficiency
depends on neutrino flavor, type of interaction (CC or NC),
neutrino energy Eν, zenith angle θ, and distance D
measured from ground along the shower axis at which
the neutrino is forced to interact in the simulations.
The identification efficiencies depend also on time,
through the changing configuration of the SD array that
was growing steadily since 2004 up to 2008, and because
the fraction of working stations—although typically above
95%—is changing continuously with time. Also the con-
tinuous monitoring of the array reveals a slight evolution
with time of the optical properties of the water-Cherenkov
stations (see below). Although the number of working
stations and their status are monitored every second and as
a consequence the SD configuration is known with very
good accuracy at any instant of time, in practice, to
avoid having to cope with an impractically large number
of configurations, different strategies were devised to
calculate in an accurate and less time-consuming manner
the actual identification efficiencies (as explained in
[18,19,21]).
Fisher value
-10 -5 0 5 10
Events
-1
10
1
10
2
10
3
10
4
10
Fisher > 3.28
candidate regionν
Training data
Search data
νMonte Carlo
FIG. 2 (color online). Distributions of the Fisher variable Fin
inclined events selected by the “Inclined showers”DGH criteria
in Table I, before applying the “Young showers”cuts. In
particular the distribution of events with number of triggered
tanks 7≤Nst ≤11 is shown. Gray-filled histogram: data in the
training period corresponding to ∼23% of the whole data sample
between 1 January 2004 and 20 June 2013. Black line: data in the
search period. The distributions are normalized to the same
number of events for comparison purposes. Blue line: simulated
DGH νevents. The dashed vertical line represents the cut on
F>3.28 above which a data event is regarded as a neutrino
candidate. The red dashed line represents an exponential fit to the
tail of the training distribution (see text for explanation).
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
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The evolution of the optical properties of the water-
Cherenkov stations was taken into account in an effective
way in the calculation of the exposure. The main effect of
this evolution is a decrease with time of the decay time of
the light as obtained from the monitoring data that revealed
a continuous decrease of ∼10% from 2004 until the end of
the data period used in this work (20 June 2013). This
induces a reduction of the AoP and, as a consequence, the
trigger efficiency changes with time. These changes were
accounted for in the calculation of the exposure by dividing
the whole data set into three separate periods and assuming
that in each of them the decay time of the light in the tank
remained approximately constant as seen in data. A
conservative approach was adopted by choosing constant
values of the light decay time below the actual curve in the
three periods.
2. Combination of selections
In previous publications [18,19,21] the fraction of
ν-induced Monte Carlo events identified as neutrino can-
didates was obtained by applying each particular set of
selection criteria (ES, DGH, DGL) only to its correspond-
ing set of simulated showers (ES, DGH or DGL). In this
paper the fraction of selected events is further increased by
applying the three sets of criteria to each sample of
simulated showers (ES, DGH, DGL) regardless of channel.
With this procedure the fraction of identified Monte Carlo
events is enhanced as, for instance, an ES simulated shower
induced by a ντmight not fulfill the requirements of the ES
selection, but might still pass the DGH or DGL criteria, and
hence contribute to the fraction of identified events. The
enhancement in the fraction of events when applying this
“combined”analysis depends on the particular set of
Monte Carlo simulations. For instance applying the three
criteria to the DGH Monte Carlo sample identifies a
fraction of neutrino events ∼1.25 larger than when the
DGH criteria are applied alone, the enhancement coming
mainly from events with three stations rejected by the DGH
criteria but accepted by ES. The application of the three
criteria to the ES Monte Carlo sample however results in a
smaller enhancement ∼1.04.
3. Exposure calculation
For downward-going neutrinos, once the efficiencies
ϵDGðEν;θ;D;tÞare obtained, the calculation of the expo-
sure involves folding them with the SD array aperture and
the νinteraction probability at a depth Dfor a neutrino
energy Eν. This calculation also includes the possibility that
downward-going ντinteract with the mountains surround-
ing the Observatory. Integrating over the parameter space
except for Eνand in time over the search periods and
summing over all the interaction channels yields the
exposure [19,21].
In the Earth-skimming channel, ϵESðEτ;θ;X
dÞare also
folded with the aperture, with the probability density
function of a tau emerging from the Earth with energy
Eτ(given a neutrino with energy Eνcrossing an amount of
Earth determined by the zenith angle θ), as well as with the
probability that the τdecays at an altitude hc[18].An
integration over the whole parameter space except for Eν
and time gives the exposure [18].
The exposures EES,EDGH and EDGL obtained for the
search periods of each selection are plotted in Fig. 3along
with their sum Etot. The exposure to Earth-skimming
neutrinos is higher than that to downward-going neutrinos,
partially due to the longer search period in the Earth-
skimming analysis, and partially due to the much larger
neutrino conversion probability in the denser target of the
Earth’s crust compared to the atmosphere. The larger
number of neutrino flavors and interaction channels that
can be identified in the DGH and DGL analysis, as well as
the broader angular range 60°<θ<90° partly compen-
sates the dominance of the ES channel. The ES exposure
flattens and then falls above ∼1019 eV as there is an
increasing probability that the τdecays high in the
atmosphere producing a shower not triggering the array,
or even that the τescapes the atmosphere before decaying.
At the highest energies the DGH exposure dominates. The
DGL exposure is the smallest of the three, mainly due to
the more stringent criteria needed to apply to get rid of the
larger background nucleonic showers in the zenith angle
bin 60°<θ<75°.
The relative contributions of the three channels to
the total expected event rate for a differential flux
behaving with energy as dNνðEνÞ=dEν∝E−2
νare
ES∶DGH∶DGL ∼0.84∶0.14∶0.02 respectively, where the
event rate is obtained as
[eV]
ν
E
17
10 18
10 19
10 20
10
s sr ]
2
Exposure [ cm
14
10
15
10
16
10
17
10
18
10
Combined (1 Jan 04 - 20 Jun 13)
Earth-Skimming
< 90 deg.θDownward-going 75 <
< 75 deg.θDownward-going 60 <
FIG. 3 (color online). Combined exposure of the SD of the
Pierre Auger Observatory (1 January 2004–20 June 2013) as a
function of neutrino energy after applying the three sets of
selection criteria in Table Ito Monte Carlo simulations of UHE
neutrinos (see text for explanation). Also shown are the individual
exposures corresponding to each of the three selections. For the
downward-going channels the exposure represents the sum over
the three neutrino flavors as well as CC and NC interactions. For
the Earth-skimming channel, only ντCC interactions are relevant.
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Nevt ¼ZEν
dNν
dEν
ðEνÞEtotðEνÞdEν:ð1Þ
C. Systematic uncertainties
Several sources of systematic uncertainty have been
considered. Some of them are directly related to the
Monte Carlo simulation of the showers, i.e., generator of
the neutrino interaction either in the Earth or in the
atmosphere, parton distribution function, air shower devel-
opment, and hadronic model.
Other uncertainties have to do with the limitations on the
theoretical models needed to obtain the interaction cross
section or the τenergy loss at high energies. In the Earth-
skimming analysis the model of energy loss for the τis the
dominant source of uncertainty, since it determines the
energy of the emerging τs after propagation in the Earth;
the impact of this on the downward-going analysis is much
smaller since τenergy losses are only relevant for ντ
interacting in the mountains, a channel that is estimated to
contribute only ∼15% to the DGH exposure [19].
The uncertainty on the shower simulation, which stems
mainly from the different shower propagation codes and
hadronic interaction models that can be used to model the
high energy collisions in the shower, contributes signifi-
cantly in the ES and DG channels.
The presence of mountains around the Observatory—
which would increase the target for neutrino interactions in
both cases—is explicitly simulated and accounted for when
obtaining the exposure of the SD to downward-going
neutrino-induced showers, and as a consequence does
not contribute directly to the systematic uncertainties.
However, it is not accounted for in the Earth-skimming
channel and instead we take the topography around the
Observatory as a source of systematic uncertainty.
In the three channels the procedure to incorporate the
systematic uncertainties is the same. Different combina-
tions of the various sources of systematic uncertainty
render different values of the exposure and a systematic
uncertainty band of relative deviation from a reference
exposure (see below) can be constructed for each channel
and for each source of systematic uncertainty. For a given
source of uncertainty the edges of the ES, DGH and DGL
bands are weighted by the relative importance of each
channel as given before and added linearly or quadrati-
cally depending on the source of uncertainty. In Table II
we give the dominant sources of systematic uncertainty
and their corresponding combined uncertainty bands
obtained in this way. The combined uncertainty band
is then incorporated in the value of the limit itself through
a semi-Bayesian extension [22] of the Feldman-Cousins
approach [23].
In the calculation of the reference exposure the ν-nucleon
interaction in the atmosphere for DG neutrinos (including
CC and NC channels) is simulated with HERWIG [24].
In the case of ντCC interactions, a dedicated, fast and
flexible code is used to simulate the τlepton propagation in
the Earth and/or in the atmosphere. The τdecay is
performed with the TAUOLA package [25]. In all cases
we adopted the ν-nucleon cross section in [26]. In a second
step, the AIRES code [27] is used to simulate the
propagation in the atmosphere of the particles produced
in the high energy νinteraction or in the τlepton decay. The
types, energies, momenta and times of the particles reach-
ing the SD level are obtained. The last stage is the
simulation of the SD response (PMT signals and FADC
traces). This involves a modification of the “standard”
sampling procedure in [28] to regenerate particles in the SD
stations from the “thinned”air shower simulation output,
which was tailored to the highly inclined showers involved
in the search for neutrinos. Light production and propa-
gation inside the station is based on GEANT4 [29] with the
modifications to account for the evolution of the light decay
time explained above. These two latter changes roughly
compensate each other, with the net result being a few
percent decrease of the exposure with respect to that
obtained with the standard thinning procedure and a
constant average value of the light decay-time.
IV. RESULTS
Using the combined exposure in Fig. 3and assuming a
differential neutrino flux dNðEνÞ=dEν¼k·E−2
νas well as
aνe∶νμ∶ντ¼1∶1∶1flavor ratio, an upper limit on the
value of kcan be obtained as
k¼Nup
REνE−2
νEtotðEνÞdEν
:ð2Þ
The actual value of the upper limit on the signal events
(Nup) depends on the number of observed events (0 in our
TABLE II. Main sources of systematic uncertainties and their
corresponding combined uncertainty bands (see text for details)
representing the effect on the event rate defined in Eq. (1). The
uncertainty due to “Simulations”includes: interaction generator,
shower simulation, hadronic model, thinning and detector sim-
ulator. The uncertainty due to “τenergy-loss”affects the ES
channel and also the DGH but only to ντwith θ≳88° going
through the mountains surrounding the Pierre Auger Observatory.
However it does not affect the DGL channel. The topography
around the Observatory is not accounted for in the ES channel
and is taken as a systematic uncertainty that would increase the
event rate.
Source of systematic Combined uncertainty band
Simulations ∼þ4%,−3%
νcross section and τE-loss ∼þ34%,−28%
Topography ∼þ15%,0%
Total ∼þ37%,−28%
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
092008-10
case) and expected background events (conservatively
assumed to be 0), as well as on the confidence level
required (90% C.L. in the following). Using a semi-
Bayesian extension [22] of the Feldman-Cousins approach
[23] to include the uncertainties in the exposure we obtain3
Nup ¼2.39. The single-flavor 90% C.L. limit is
k90 <6.4×10−9GeV cm−2s−1sr−1:ð3Þ
The limit applies in the energy interval ∼1.0×
1017 eV–2.5×1019 eV where the cumulative number of
events as a function of neutrino energy increases from 5%
to 95% of the total number, i.e. where ∼90% of the total
event rate is expected. It is important to remark that this is
the most stringent limit obtained so far with Auger data,
and it represents a single limit combining the three channels
where we have searched for UHE neutrinos. The limit to the
flux normalization in Eq. (3) is obtained integrating the
denominator of Eq. (2) in the whole energy range where
Auger is sensitive to UHE neutrinos. This is shown in
Fig. 4, along with the 90% C.L. limits from other experi-
ments as well as several models of neutrino flux production
(see caption for references). The denominator of Eq. (2) can
also be integrated in bins of energy, and a limit on kcan
also be obtained in each energy bin [30]. This is displayed
in Fig. 5where the energy bins have a width of 0.5 in
log10 Eν, and where we also show the whole energy range
where there is sensitivity to neutrinos. The limit as
displayed in Fig. 5allows us to show at which energies
the sensitivity of the SD of the Pierre Auger
Observatory peaks.
The search period corresponds to an equivalent of 6.4
years of a complete Auger SD array working continuously.
The inclusion of the data from 1 June 2010 until 20 June
2013 in the search represents an increase of a factor ∼1.8in
total time quantified in terms of equivalent full Auger years
with respect to previous searches [18,19]. Further improve-
ments in the limit come from the combination of the three
[eV]
ν
E
17
10 18
10 19
10 20
10 21
10
]
-1
sr
-1
s
-2
dN/dE [ GeV cm
2
E
-9
10
-8
10
-7
10
-6
10
-5
10
Single flavour, 90% C.L.
IceCube 2013 (x 1/3) [30]
Auger (this work)
ANITA-II 2010 (x 1/3) [29]
modelsνCosmogenic
p, Fermi-LAT best-fit (Ahlers '10) [33]
p, Fermi-LAT 99% CL band (Ahlers '10) [33]
p, FRII & SFR (Kampert '12) [31]
Waxman-Bahcall '01 [13]
17
10 18
10 19
10 20
10 21
10
]
-1
sr
-1
s
-2
dN/dE [ GeV cm
2
E
-9
10
-8
10
-7
10
-6
10
-5
10
Single flavour, 90% C.L.
IceCube 2013 (x 1/3) [30]
Auger (this work)
ANITA-II 2010 (x 1/3) [29]
modelsνCosmogenic
Fe, FRII & SFR (Kampert '12) [31]
p or mixed, SFR & GRB (Kotera '10) [9]
Waxman-Bahcall '01 [13]
[eV]
ν
E
FIG. 4 (color online). Top panel: Upper limit (at 90% C.L.) to
the normalization of the diffuse flux of UHE neutrinos as given in
Eqs. (2) and (3), from the Pierre Auger Observatory. We also
show the corresponding limits from ANITAII [31] and IceCube
[32] experiments, along with expected fluxes for several cosmo-
genic neutrino models that assume pure protons as primaries
[33,34] as well as the Waxman-Bahcall bound [13]. All limits and
fluxes converted to single flavor. We used Nup ¼2.39 in Eq. (2)
to obtain the limit (see text for details). Bottom panel: Same as top
panel, but showing several cosmogenic neutrino models that
assume heavier nuclei as primaries, either pure iron [33] or mixed
primary compositions [9].
17
10 18
10 19
10 20
10 21
10
]
-1
sr
-1
s
-2
dN/dE [ GeV cm
2
E
9−
10
8−
10
7−
10
6−
10
5−
10
Single flavour, 90% C.L.
IceCube 2013 (x 1/3) [30]
Auger (this work)
ANITA-II 2010 (x 1/3) [29]
modelsνCosmogenic
p, Fermi-LAT best-fit (Ahlers '10) [33]
p, Fermi-LAT 99% CL band [33]
p, FRII & SFR (Kampert '12) [31]
Fe, FRII & SFR (Kampert '12) [31]
p or mixed, SFR & GRB (Kotera '10) [9]
Waxman-Bahcall '01 [13]
[eV]
ν
E
FIG. 5 (color online). Upper limit to the normalization of the
diffuse flux of UHE neutrinos (at 90% C.L. and in bins of width
0.5 in log10Eν—see text for details) from the Pierre Auger
Observatory (straight steps). We also show the corresponding
limits from ANITAII [31] (dot-dashed line) and IceCube [32]
(dashed line) experiments (with appropriate normalizations to
take into account the energy bin width, and to convert to single
flavor), along with expected fluxes for several cosmogenic
neutrino models [9,33,34] as well as the Waxman-Bahcall bound
[13] (all converted to single flavor).
3To calculate Nup we use POLE þþ [22]. The signal efficiency
uncertainty is ∼0.19 with an asymmetric band (see Table II). This
yields a value of Nup ¼2.39 slightly smaller than the nominal
2.44 of the Feldman-Cousins approach.
IMPROVED LIMIT TO THE DIFFUSE FLUX OF …PHYSICAL REVIEW D 91, 092008 (2015)
092008-11
analyses into a single one, using the procedure explained
before that enhances the fraction of identified neutrinos
especially in the DGH channel.
In Table III we give the expected total event rates for
several models of neutrino flux production.
Several important conclusions and remarks can be stated
after inspecting Figs. 4and 5and Table III:
(1) The maximum sensitivity of the SD of the Auger
Observatory is achieved at neutrino energies around
EeV, where most cosmogenic models of νproduc-
tion also peak (in a E2
ν×dN=dEνplot).
(2) The current Auger limit is a factor ∼4below the
Waxman-Bahcall bound on neutrino production in
optically thin sources [13]. The SD of the Auger
Observatory is the first air shower array to reach that
level of sensitivity.
(3) Some models of neutrino production in astrophysi-
cal sources such as Active Galactic Nuclei (AGN)
are excluded at more than 90% C.L. For the model
#2 shown in Fig. 14 of [35] we expect ∼7neutrino
events while none was observed.
(4) Cosmogenic νmodels that assume a pure primary
proton composition injected at the sources and strong
(FRII-type) evolution of the sources are strongly
disfavored by Auger data. An example is the upper
line of the shaded band in Fig. 17 in [33] (also
depicted in Figs. 4and 5), for which ∼4events are
expected and as a consequence that flux is excluded at
∼98% C:L:Models that assume a pure primary
proton composition and use the GeV γ-ray flux
observations by the Fermi-LAT satellite detector as
an additional constraint, are also disfavored. For
instance for the model shown as a solid line in the
bottom right panel of Fig. 5 in [34] (also depicted in
Figs. 4and 5in this work), corresponding to the best-
fit to the cosmic-ray spectrum as measured by HiRes,
we expect ∼3.2events. As a consequence that model
is excluded at more than 90% C.L. For this particular
model we also show in Figs. 4and 5the 99% C.L.
band resulting from the fitting to the HiRes spectrum
down to Emin ¼1019 eV. The Auger limit is also
approaching the solid line in the upper left panel of
Fig. 5 in [34], a model that assumes extragalactic
protons above Emin ¼1017.5eV [37],forwhich∼1.6
events are expected (see Table III). The Auger direct
limits on cosmogenic neutrinos are also constraining
part of the region indirectly bounded by Fermi-LAT
observations.
(5) The current Auger limit is less restrictive with the
cosmogenic neutrino models represented by the gray
shaded area in the bottom panel of Fig. 4(∼0.5to
∼1.4events are expected as shown in Table III)
which brackets the lower fluxes predicted under a
range of assumptions for the composition of the
primary flux (protons or mixed), source evolution
and model for the transition from Galactic to
extragalactic cosmic rays [9] The same remark
applies to models that assume pure-iron composition
at the sources. A tenfold increase in the current
exposure will be needed to reach the most optimistic
predictions of cosmogenic neutrino fluxes if the
primaries are pure iron, clearly out of the range of
the current configuration of the Auger Observatory.
(6) A large range of exotic models of neutrino
production [36] are excluded with C.L. larger
than 99%.
(7) In IceCube, neutrino fluxes in the 30 TeV to 2 PeV
energy range have shown a ∼5.7σexcess compared
to predicted atmospheric neutrino fluxes [12].A
refinement of the IceCube search technique to
extend the neutrino sensitivity down to 10 TeV
[14] yielded a power-law fit to the measured flux
without cutoff given by dN=dE ¼Φ0ðEν=E0Þ−γ
with Φ0¼2.06 ×10−18 GeV−1cm−2s−1sr−1,E0¼
105GeV, and γ¼2.46. If this flux is extrapolated
to 1020 eV it would produce ∼0.1events in Auger.
ACKNOWLEDGMENTS
The successful installation, commissioning, and oper-
ation of the Pierre Auger Observatory would not have been
possible without the strong commitment and effort from the
TABLE III. Number of expected events Nevt in Eq. (1) for several theoretical models of UHE neutrino production (see Figs. 4and 5),
given the combined exposure of the surface detector array of the Pierre Auger Observatory plotted in Fig. 3. The last column gives the
Poisson probability expð−NevtÞof observing 0 events when the number of expected events is Nevt given in the second column.
Diffuse flux Neutrino model
Expected number of events
(1 January 2004–20 June 2013)
Probability of
observing 0
Cosmogenic—proton, FRII [33] ∼4.0∼1.8×10−2
Cosmogenic—proton, SFR [33] ∼0.9∼0.4
Cosmogenic—proton, Fermi-LAT, Emin ¼1019 eV [34] ∼3.2∼4×10−2
Cosmogenic—proton, Fermi-LAT, Emin ¼1017.5eV [34] ∼1.6∼0.2
Cosmogenic—proton or mixed, SFR & GRB [9] ∼0.5–1.4∼0.6–0.2
Cosmogenic—iron, FRII [33] ∼0.3∼0.7
Astrophysical ν(AGN) [35] ∼7.2∼7×10−4
Exotic [36] ∼31.5∼2×10−14
A. AAB et al. PHYSICAL REVIEW D 91, 092008 (2015)
092008-12
technical and administrative staff in Malargüe. We are very
grateful to the following agencies and organizations for
financial support: Comisión Nacional de Energía Atómica,
Fundación Antorchas, Gobierno de la Provincia de
Mendoza, Municipalidad de Malargüe, NDM Holdings
and Valle Las Leñas, in gratitude for their continuing
cooperation over land access, Argentina; the Australian
Research Council; Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq), Financiadora de Estudos
e Projetos (FINEP), Fundação de Amparo à Pesquisa do
Estado de Rio de Janeiro (FAPERJ), São Paulo Research
Foundation (FAPESP) Grants No. 2010/07359-6 and
No. 1999/05404-3, Ministério de Ciência e Tecnologia
(MCT), Brazil; Grants No. MSMT-CR LG13007,
No. 7AMB14AR005, and the Czech Science Foundation
Grant No. 14-17501S, Czech Republic; Centre de Calcul
IN2P3/CNRS, Centre National de la Recherche
Scientifique (CNRS), Conseil Régional Ile-de-France,
Département Physique Nucléaire et Corpusculaire
(PNC-IN2P3/CNRS), Département Sciences de l’Univers
(SDU-INSU/CNRS), Institut Lagrange de Paris (ILP)
Grant No. LABEX ANR-10-LABX-63, within the
Investissements d’Avenir Programme Grant No. ANR-
11-IDEX-0004-02, France; Bundesministerium für
Bildung und Forschung (BMBF), Deutsche
Forschungsgemeinschaft (DFG), Finanzministerium
Baden-Württemberg, Helmholtz Alliance for
Astroparticle Physics (HAP), Helmholtz-Gemeinschaft
Deutscher Forschungszentren (HGF), Ministerium für
Wissenschaft und Forschung, Nordrhein Westfalen,
Ministerium für Wissenschaft, Forschung und Kunst,
Baden-Württemberg, Germany; Istituto Nazionale di
Fisica Nucleare (INFN), Ministero dell’Istruzione,
dell’Universitá e della Ricerca (MIUR), Gran Sasso
Center for Astroparticle Physics (CFA), CETEMPS
Center of Excellence, Ministero degli Affari Esteri
(MAE), Italy; Consejo Nacional de Ciencia y Tecnología
(CONACYT), Mexico; Ministerie van Onderwijs, Cultuur
en Wetenschap, Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Stichting voor
Fundamenteel Onderzoek der Materie (FOM),
Netherlands; National Centre for Research and
Development, Grants No. ERA-NET-ASPERA/01/11 and
No. ERA-NET-ASPERA/02/11, National Science Centre,
Grants No. 2013/08/M/ST9/00322, No. 2013/08/M/ST9/
00728 and No. HARMONIA 5–2013/10/M/ST9/00062,
Poland; Portuguese national funds and FEDER funds
within Programa Operacional Factores de
Competitividade through Fundação para a Ciência e a
Tecnologia (COMPETE), Portugal; Romanian Authority
for Scientific Research ANCS, CNDI-UEFISCDI partner-
ship projects Grants No. 20/2012 and No. 194/2012, Grants
No. 1/ASPERA2/2012 ERA-NET, No. PN-II-RU-PD-
2011-3-0145-17 and No. PN-II-RU-PD-2011-3-0062, the
Minister of National Education, Programme Space
Technology and Advanced Research (STAR), Grant
No. 83/2013, Romania; Slovenian Research Agency,
Slovenia; Comunidad de Madrid, FEDER funds,
Ministerio de Educación y Ciencia, Xunta de Galicia,
European Community 7th Framework Program, Grant
No. FP7-PEOPLE-2012-IEF-328826, Spain; Science and
Technology Facilities Council, United Kingdom;
Department of Energy, Contracts No. DE-AC02-
07CH11359, No. DE-FR02-04ER41300, No. DE-FG02-
99ER41107 and No. DE-SC0011689, National Science
Foundation, Grant No. 0450696, The Grainger Foundation,
USA; NAFOSTED, Vietnam; Marie Curie-IRSES/
EPLANET, European Particle Physics Latin American
Network, European Union 7th Framework Program,
Grant No. PIRSES-2009-GA-246806; and UNESCO.
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