Constraints on flavor-diagonal non-standard neutrino interactions from Borexino Phase-II

Abstract

A bstract
The Borexino detector measures solar neutrino fluxes via neutrino-electron elastic scattering. Observed spectra are determined by the solar- ν e survival probability P ee ( E ), and the chiral couplings of the neutrino and electron. Some theories of physics beyond the Standard Model postulate the existence of Non-Standard Interactions (NSI’s) which modify the chiral couplings and P ee ( E ). In this paper, we search for such NSI’s, in particular, flavor-diagonal neutral current interactions that modify the ν e e and ν τ e couplings using Borexino Phase II data. Standard Solar Model predictions of the solar neutrino fluxes for both high- and low-metallicity assumptions are considered. No indication of new physics is found at the level of sensitivity of the detector and constraints on the parameters of the NSI’s are placed. In addition, with the same dataset the value of sin ² θ W is obtained with a precision comparable to that achieved in reactor antineutrino experiments
.

Full text

JHEP02(2020)038
Published for SISSA by Springer
Received:May 11, 2019
Revised:December 19, 2019
Accepted:January 20, 2020
Published:February 5, 2020
Constraints on flavor-diagonal non-standard neutrino
interactions from Borexino Phase-II
The Borexino collaboration
S.K. Agarwalla,1,2,3M. Agostini,4K. Altenm¨uller,4S. Appel,4V. Atroshchenko,5
Z. Bagdasarian,6D. Basilico,7G. Bellini,7J. Benziger,8D. Bick,9G. Bonfini,10
D. Bravo,7,a B. Caccianiga,7F. Calaprice,11 A. Caminata,12 L. Cappelli,10
P. Cavalcante,13,b F. Cavanna,12 A. Chepurnov,14 K. Choi,15 D. D’Angelo,7
S. Davini,12 A. Derbin,16 A. Di Giacinto,10 V. Di Marcello,10 X.F. Ding,17,10
A. Di Ludovico,11 L. Di Noto,12 I. Drachnev,16 K. Fomenko,18 A. Formozov,18,7,14
D. Franco,19 F. Gabriele,10 C. Galbiati,11 M. Gschwender,20 C. Ghiano,10
M. Giammarchi,7A. Goretti,11,33 M. Gromov,14,18 D. Guffanti,26 C. Hagner,9
E. Hungerford,21 Aldo Ianni,10 Andrea Ianni,11 A. Jany,22 D. Jeschke,4
S. Kumaran,6,23 V. Kobychev,24 G. Korga,21,c T. Lachenmaier,20 M. Laubenstein,10
E. Litvinovich,5,25 P. Lombardi,7L. Ludhova,6,23 G. Lukyanchenko,5L. Lukyanchenko,5
I. Machulin,5,25 G. Manuzio,12 S. Marcocci,17,d J. Maricic,15 J. Martyn,26 E. Meroni,7
M. Meyer,27 L. Miramonti,7M. Misiaszek,22 V. Muratova,16 B. Neumair,4
M. Nieslony,26 L. Oberauer,4V. Orekhov,5,26 F. Ortica,28 M. Pallavicini,12 L. Papp,4
¨
O. Penek,6,23 L. Pietrofaccia,11 N. Pilipenko,16 A. Pocar,29 G. Raikov,5G. Ranucci,7
A. Razeto,10 A. Re,7M. Redchuk,6,23 A. Romani,28 N. Rossi,10,e S. Rottenanger,20
S. Sch¨onert,4D. Semenov,16 M. Skorokhvatov,5,25 O. Smirnov,18 A. Sotnikov,18
C. Sun,30,31 Y. Suvorov,5,10,f T. Takeuchi,13 R. Tartaglia,10 G. Testera,12 J. Thurn,27
E. Unzhakov,16 A. Vishneva,18 R.B. Vogelaar,13 F. von Feilitzsch,4M. Wojcik,22
M. Wurm,26 O. Zaimidoroga,18 S. Zavatarelli,12 K. Zuber27 and G. Zuzel22
aPresent address: Universidad Aut´onoma de Madrid, Ciudad Universitaria de Cantoblanco,
28049 Madrid, Spain.
bPresent address: INFN Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy.
cAlso at: MTA-Wigner Research Centre for Physics, Department of Space Physics and Space Technology,
Konkoly-Thege Mikl´os ´ut 29-33, 1121 Budapest, Hungary
dPresent address: Fermilab National Accelerato Laboratory (FNAL), Batavia, IL 60510, U.S.A. .
ePresent address: Dipartimento di Fisica, Sapienza Universit`a di Roma e INFN, 00185 Roma, Italy.
fPresent address: Dipartimento di Fisica, Universit`a degli Studi Federico II e INFN, 80126 Napoli, Italy.
Open Access,c
The Authors.
Article funded by SCOAP3.https://doi.org/10.1007/JHEP02(2020)038

JHEP02(2020)038
1Institute of Physics, Sachivalaya Marg, Sainik School Post, Bhubaneswar 751005, India
2Homi Bhabha National Institute, Training School Complex,
Anushakti Nagar, Mumbai 400085, India
3International Centre for Theoretical Physics, Strada Costiera 11, Trieste 34151, Italy
4Physik-Department and Excellence Cluster Universe, Technische Universit¨at M¨unchen,
85748 Garching, Germany
5National Research Centre Kurchatov Institute, 123182 Moscow, Russia
6Institut f¨ur Kernphysik, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany
7Dipartimento di Fisica, Universit`a degli Studi e INFN, 20133 Milano, Italy
8Chemical Engineering Department, Princeton University, Princeton, NJ 08544, U.S.A.
9Institut f¨ur Experimentalphysik, Universit¨at Hamburg, 22761 Hamburg, Germany
10INFN Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy
11Physics Department, Princeton University, Princeton, NJ 08544, U.S.A.
12Dipartimento di Fisica, Universit`a degli Studi e INFN, 16146 Genova, Italy
13Physics Department, Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061, U.S.A.
14Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics,
119234 Moscow, Russia
15Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, U.S.A.
16St. Petersburg Nuclear Physics Institute NRC Kurchatov Institute, 188350 Gatchina, Russia
17Gran Sasso Science Institute, 67100 L’Aquila, Italy
18Joint Institute for Nuclear Research, 141980 Dubna, Russia
19AstroParticule et Cosmologie, Universit´e Paris Diderot, CNRS/IN2P3, CEA/IRFU,
Observatoire de Paris, Sorbonne Paris Cit´e, 75205 Paris Cedex 13, France
20Kepler Center for Astro and Particle Physics, Universit¨at T¨ubingen, 72076 T¨ubingen, Germany
21Department of Physics, University of Houston, Houston, TX 77204, U.S.A.
22M. Smoluchowski Institute of Physics, Jagiellonian University, 30348 Krakow, Poland
23RWTH Aachen University, 52062 Aachen, Germany
24Institute for Nuclear Research of NAS Ukraine, 03028 Kiev, Ukraine
25National Research Nuclear University MEPhI (Moscow Engineering Physics Institute),
115409 Moscow, Russia
26Institute of Physics and Excellence Cluster PRISMA+, Johannes Gutenberg-Universit¨at Mainz,
55099 Mainz, Germany
27Department of Physics, Technische Universit¨at Dresden, 01062 Dresden, Germany
28Dipartimento di Chimica, Biologia e Biotecnologie, Universit`a degli Studi e INFN,
06123 Perugia, Italy
29Amherst Center for Fundamental Interactions and Physics Department,
University of Massachusetts, Amherst, MA 01003, U.S.A.
30CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, P.R. China
31Department of Physics, Brown University, Providence, RI 02912 U.S.A.
E-mail: spokesperson-borex@lngs.infn.it

JHEP02(2020)038
Abstract: The Borexino detector measures solar neutrino fluxes via neutrino-electron
elastic scattering. Observed spectra are determined by the solar-νesurvival probability
Pee(E), and the chiral couplings of the neutrino and electron. Some theories of physics
beyond the Standard Model postulate the existence of Non-Standard Interactions (NSI’s)
which modify the chiral couplings and Pee(E). In this paper, we search for such NSI’s, in
particular, flavor-diagonal neutral current interactions that modify the νeeand ντecou-
plings using Borexino Phase II data. Standard Solar Model predictions of the solar neutrino
fluxes for both high- and low-metallicity assumptions are considered. No indication of new
physics is found at the level of sensitivity of the detector and constraints on the parameters
of the NSI’s are placed. In addition, with the same dataset the value of sin2θWis obtained
with a precision comparable to that achieved in reactor antineutrino experiments.
Keywords: Neutrino Physics, Beyond Standard Model
ArXiv ePrint: 1905.03512

JHEP02(2020)038
Contents
1 Introduction 1
2νe elastic scattering 2
2.1 Standard Model interactions 2
2.2 Radiative corrections 4
2.3 Non-Standard Interactions (NSI’s) 4
3 Analysis 7
3.1 Overview 7
3.2 Detector model and choice of parameters 9
3.3 Backgrounds 11
3.4 Fit procedure 12
4 Results 13
4.1 Bounds on NSI parameters 13
4.2 Evaluation of sin2θW18
5 Summary and concluding remarks 19
A Derivation of the matter effect potential in the presence of NSI’s 20
1 Introduction
The study of solar neutrinos is relevant not only for probing our understanding of the
Sun but also for investigating neutrino properties. Solar neutrino experiments, primarily
SNO [1] and Super-Kamiokande [2], together with KamLAND [3–5], have resolved the solar
neutrino problem with the large mixing angle (LMA) MSW flavor conversion effect [6–9].
Improved experimental precision may reveal the effects of physics beyond the Standard
Model, such as sterile neutrinos, particle dark matter or non-standard interactions (NSI’s)
of the neutrino [10–13]. In this article, we present the latest sensitivity of Borexino to
study the latter.
The Borexino experiment at the Laboratori Nazionali del Gran Sasso (LNGS) [14]
detects solar neutrinos through the neutrino-electron elastic scattering interaction on a
∼280 ton liquid scintillator target with (3.307 ±0.003) ×1031 electrons per 100 ton of
the mass. During the Phase-I period (May 16, 2007–May 8, 2010) Borexino had 740.7
live days of data taking [15,16]. Following Phase-I, an extensive scintillator purification
campaign was conducted resulting in significant reductions of radioactive contaminants.
Uranium-238 and Thorium-232 levels were reduced to 238U<9.4×10−20 g/g (95% C.L.)
and 232Th <5.7×10−19 g/g (95% C.L.). 85Kr and 210Bi concentrations were reduced by fac-
tors ∼4.6 and ∼2.3, respectively [17]. The Phase-II data, analyzed in this paper, were col-
lected from December 14, 2011 until May 21, 2016, corresponding to 1291.51 days ×71.3 t
– 1 –

JHEP02(2020)038
(252.1 ton·years) of fiducial exposure. Reduction of the background, longer exposure, and
better understanding of the detector response allowed for fits to be performed in a wider
energy range (0.19 MeV < T < 2.93 MeV, where Tis the recoil-electron kinetic energy) to
include pp,7Be, pep, and CNO electron-recoil spectra [18].1Taking advantage of these im-
provements, this paper uses the Phase-II data to investigate the parameters of non-standard
interactions (NSI’s) of the neutrino with increased sensitivity.
Solar neutrinos can be used to probe for physics beyond the SM that affect neutrino
interactions with the charged leptons and quarks. In this paper, we restrict our analysis to
the neutrino-flavor-diagonal NSI’s that affect νeeand ντeinteractions to which Borexino
is particularly sensitive. We do not consider NSI’s that affect the νµeinteraction, which
are strongly constrained by the νµescattering CHARM II experiment [19].
Using Borexino to constrain NSI’s was originally discussed by Berezhiani, Raghavan,
and Rossi in refs. [20,21]. They argued that the monochromatic nature of 7Be solar
neutrinos results in an electron recoil spectrum whose Compton-like shape is more sensitive
to the νe couplings than that from a continuous neutrino energy spectrum. Following
refs. [20,21], a purely phenomenological analysis based on Borexino Phase-I results [22]
was carried out in ref. [23], in which the roles of the main backgrounds were analyzed and
bounds on νeeand ντeNSI’s obtained.
However, the analysis considered the effects of the NSI’s at detection only. High solar
metallicity (HZ) was also assumed as input to the Standard Solar Model (SSM) [24–27] to
predict the 7Be solar neutrino flux.
This paper updates and improves upon the analysis of ref. [23] by using the Phase-II
data set with the full arsenal of improved analysis tools developed by the Borexino collabo-
ration. NSI effects are included in both propagation and detection. At production the NSI’s
affect the solar-neutrino spectrum only below the Borexino threshold of ∼50 keV [18,28],
and are therefore neglected. To account for the effect of solar metallicity, analyses are
performed for both high- (HZ) and low-metallicity (LZ) solar models.
This paper is organized as follows. In section 2, we review the neutrino-electron in-
teractions in the SM and with additional effects due to NSI’s, and introduce the notation.
Section 3provides an outline of the analysis strategy and, in particular, how backgrounds
and uncertainties are handled. Results and their discussion are presented in section 4. A
summary of the main findings is presented in section 5.
2νe elastic scattering
2.1 Standard Model interactions
Within the SM, the elastic scattering of να(α=e, µ, τ ) on electrons proceeds via Z-
exchange (Neutral Current, NC) and, for νe, also via W-exchange (Charged Current, CC).
1The energy spectra of pp and CNO neutrinos are continuous and extend up to 0.42 MeV and 1.74 MeV,
respectively. 7Be (E= 0.384 MeV and 0.862 MeV) and pep (E= 1.44 MeV) neutrinos are monoenergetic.
In ref. [18], a high-energy region of 3.2< T < 16 MeV was also considered to measure 8B neutrinos with
a continuous energy spectrum extending up to about 16.5 MeV.
– 2 –

JHEP02(2020)038
At momentum transfers relevant for Borexino (Q2M2
W, M 2
Z), the CC and NC processes
are well approximated by the point interaction:
−Lνe
CC =GF
√2hνeγµ1−γ5eihe γµ1−γ5νei= 2√2GFhνeL γµνeL iheLγµeLi,(2.1)
−Lνe
NC =GF
√2hναγµ1−γ5ναiheγµgν e
LV −gνe
LAγ5ei
= 2√2GFhναLγµναL ihgν e
LL (eLγµeL) + gνe
LR (eRγµeR)i,(2.2)
where we have used the Fierz transformation [29,30] to rewrite the CC interaction into
NC form, and we follow the notation of the Review of Particle Physics [31] for the NC
coupling constants. The tree-level values of these couplings are
gνe
LV =−1
2+ 2 sin2θW,
gνe
LA =−1
2,
gνe
LL =1
2(gνe
LV +gνe
LA) = −1
2+ sin2θW,
gνe
LR =1
2(gνe
LV −gνe
LA) = sin2θW.(2.3)
Combining (2.1) and (2.2) we have
− Lναe= 2√2GFhνLγµνLihgαL (eLγµeL) + gαR (eRγµeR)i,(2.4)
with
gαL =(gνe
LL + 1 for α=e,
gνe
LL for α=µ, τ ,
gαR =gνe
LR for α=e, µ, τ . (2.5)
For a monochromatic neutrino of energy Eand flavor αscattering off an electron at rest,
the interaction (2.4) predicts the spectrum of the kinetic energy Tof the recoiling electrons
to be [24,32]
dσα(E, T )
dT =2
πG2
Fme"g2
αL +g2
αR 1−T
E2
−gαLgαR
meT
E2#,(2.6)
where neutrino masses have been neglected and Tis constrained as:
0≤T≤Tmax =E
1 + me
2E
.(2.7)
– 3 –

JHEP02(2020)038
2.2 Radiative corrections
The tree-level expression for the cross section given in eq. (2.6) is modified by radiative
corrections [33–38]. In the present analysis, these corrections are accounted for following
the 1995 paper of Bahcall, Kamionkowski, and Sirlin [37] with parameters updated to reflect
the more recently available experimental data, e.g. the Higgs mass, and ˆs2
Z= 0.23129.2
Borexino does not distinguish between muon- and tau-neutrinos, and the difference in
radiative corrections for the two flavors is consequently ignored: the radiative corrections
to ντwere set to be the same as those for the νµ. The sizes of these radiative corrections
are generally small compared to the experimental precision of Borexino with the exception
of the recent 2.7% measurement of the 7Be solar neutrino flux [18]. The effect of radiative
corrections has a comparable magnitude, resulting in a ∼2% reduction of the total cross
section for νe, and a 1.2% increase for νµ/τ [37]. Nevertheless, they have little impact on
the present analysis.
2.3 Non-Standard Interactions (NSI’s)
In addition to the SM interactions presented above, many models of physics beyond the
Standard Model (BSM) predict new interactions of the neutrinos with the other SM
fermions [41–51]. Phenomenologically, such non-standard interactions (NSI’s) of the NC
type are described by the Lagrangian density [52,53]
− LNC-NSI =X
α,β
2√2GFεff0C
αβ ¯ναγµPLνβ¯
fγµPCf0,(2.8)
where α, β =e, µ, τ label the neutrino flavor, fand f0are leptons or quarks of the same
charge but not necessarily the same flavor, Cis the chirality of the ff0current (Lor R),
and εff0C
αβ is a dimensionless coupling parametrizing the strength of the NSI interaction
normalized to GF. Allowing α6=βand f6=f0in (2.8) accounts for possible flavor-changing
NSI’s. Hermiticity of the interaction demands
εff0C
αβ =εf0fC∗
βα ,(2.9)
where the asterisk denotes complex conjugation. In the current analysis, however, we
restrict our attention to the flavor-diagonal case f=f0=eand α=β, and denote
εC
α≡εeeC
αα . Borexino, relying on neutrino-electron elastic scattering, is particularly sensitive
to this type. A discussion on BSM models which may produce such NSI’s can be found in
refs. [52,54–56].3
2ˆs2
Zdenotes the MS value of sin2θWat the Z-mass scale. The value of ˆs2
Z= 0.23129 ±0.00005 is from
the 2016 Review of Particle Physics [39]. It has subsequently been updated to ˆs2
Z= 0.23122 ±0.00003
in the 2018 Review of Particle Physics [31,40], but this difference is too small to be of relevance to the
analysis of this paper.
3Before the confirmation of neutrino oscillations by the KamLAND experiment, NSI’s with massless
neutrinos had also been invoked to address the solar neutrino anomaly. See refs. [57–62].
– 4 –

JHEP02(2020)038
NSI’s can affect neutrino production, detection, and propagation. Inside the Sun, the
flavor diagonal NSI’s under consideration contribute to the production of same-flavor νν
pairs via photo-production (γe →eνν), νν-Bremsstrahlung (the photon leg in γe →eνν is
anchored on an ion or another electron), etc. [28]. However, the energies of the neutrinos
and anti-neutrinos produced by these processes are expected to be in the few keV range,
well below the ∼50 keV detection threshold of Borexino [18].
At detection, εL/R
α(α=e, µ, τ ) shift the coupling constants that appear in the expres-
sion for the differential cross section, eq. (2.6):
gαR →˜gαR =gαR +εR
α,(2.10)
gαL →˜gαL =gαL +εL
α.(2.11)
Strong bounds on εL/R
µhad already been obtained by the νµescattering experiment
CHARM II [19], namely −0.025 < εL
µ<0.03 and −0.027 < εR
µ<0.03 at 90% C.L. [54].4
Therefore, we restrict our attention to the remaining four parameters: εL/R
eand εL/R
τ. We
do not consider the full 4-dimensional space εL/R
α(α=e, τ ): such a detailed description
is not necessary at the current level of sensitivity to NSI’s. Instead, we investigate the
εL/R
eand εL/R
τcases separately, even though — as it will become evident later with (2.13)
and (3.1) — these groups of parameters cannot be decoupled with Borexino.
The description of how NSI’s affect neutrino propagation can be found in refs. [10,56,
63,64]. Let us discuss in some detail what we should expect from their inclusion. Neutrino
propagation in matter is only sensitive to the vectorial combinations εV
α≡εL
α+εR
α. They
modify the matter-effect potential in the flavor basis to
V(x)


1 0 0
0 0 0
0 0 0

→V(x)


1 + εV
e0 0
0 0 0
0 0 εV
τ


,(2.12)
where V(x) = √2GFNe(x), and Ne(x) is the electron density at location x. From a
practical point of view, εV
e=εL
e+εR
eand εV
τ=εL
τ+εR
τcan be introduced as a shift in the
matter-effect potential V(x) in two-flavor oscillation analysis:
V(x)→V0(x) = (1 −ε0)V(x),(2.13)
where ε0=εV
τsin2θ23 −εV
e[63]. The derivation of this effective potential is given in
appendix A, assuming |∆m2
31|  2EV (x), where Eis the neutrino energy. There, it is
also shown that the first oscillation resonance occurs at 2EV 0(x)c2
13 = 2E(1 −ε0)V(x)c2
13 ≈
∆m2
21 cos 2θ12.
4These are one-parameter-at-a-time bounds. One-parameter projections of two-parameter bounds at
90% C.L. are given as −0.033 < εL
µ<0.055 and −0.040 < εR
µ<0.053 in ref. [55].
– 5 –

JHEP02(2020)038
For neutrinos coming from the center of the Sun, where the SSM predicts N
e(r= 0)
≈102NA= 6 ×1025 /cm3[25,26], the resonance energy is
E
res(0) ≈∆m2
21 cos 2θ12
(1 −ε0)2√2GFN
e(0)c2
13 ≈2 MeV
(1 −ε0),(2.14)
where for ∆m2
21 cos 2θ12 and c2
13 = 1 −s2
13 we have used the central values of the global
averages from ref. [65].
As the electron density N
e(r) decreases towards the surface of the Sun, r→R,
the resonance energy E
res(r) will increase. The presence of non-zero ε0will also shift the
resonance energy: positive ε0to higher values and negative ε0to lower values.
The MSW effect [6–9] in the energy range E&E
res(r) ensures a well-defined electron
neutrino survival probability Pee(E). For lower energies, neutrino oscillates in a vacuum
regime, with a smooth Pee (E) change in the transition region between the two regimes
of oscillations. Since the energy ranges of pp,7Be, and pep neutrinos are below the reso-
nance, the influence of matter effect for those components is small compared to that for
8B neutrinos.
The mass density at the center of the Earth according to the Preliminary Reference
Earth Model (PREM) [66] is ρ(r= 0) ≈13 g/cm3, which gives us an estimate of the
electron density there as N⊕
e(r= 0) ≈NAρ(r= 0)/2=4×1024 /cm3. So the resonance
energy of the neutrinos at the Earth’s center is
E⊕
res(0) ≈∆m2
21 cos 2θ12
(1 −ε0)2√2GFN⊕
e(0)c2
13 ≈30 MeV
(1 −ε0),(2.15)
and E⊕
res(r) will grow larger as the electron density decreases toward the surface of the
Earth, r→R⊕. From this, one can expect matter effects due to the Earth to be small
for all solar neutrino components.5Indeed, the day-night asymmetry at Borexino for the
ε0= 0 case has been predicted to be a mere fraction of a percent [73,74], and Borexino
reports A7Be
dn = 0.001 ±0.012(stat) ±0.007(syst) in ref. [75]. A negative value of ε0could,
of course, lower the resonance energy and affect this prediction but due to the difference
in the energy scales of eqs. (2.14) and (2.15), one expects the effect of ε0would appear in
the Sun first.
Figure 1illustrates the effect of LMA-MSW on Pee(E) for several representative values
of ε0. NSI’s with ε0>0 enhance Pee(E). For ε0<0 case, Pee(E) is reduced. According to
eq. (2.13), as ε0→1, the matter effect potential vanishes and the Pee(E) tends to Vacuum-
LMA scenario that assumes all solar neutrinos are oscillating in the vacuum regime. For
the range between ε0=−0.5 and ε0= 0.5, the theoretically predicted shift of Pee(E) is
within the error bars of the experimentally determined values of Borexino. The 90% C.L.
contours obtained in the present analysis are located almost entirely in this range (see
figures 6and 7). Therefore, the effects of NSI’s at propagation are not particularly strong,
and the sensitivity to NSI’s is almost entirely provided at detection.
5For 8B neutrinos, the day-night asymmetry for LMA-MSW has been predicted to be a few
percent [67,68], and this has been confirmed experimentally by Super-Kamiokande [69,70] and SNO [71,72].
The sensitivity of Borexino is insufficient to detect this day-night asymmetry.
– 6 –

JHEP02(2020)038
Neutrino energy [MeV]
1 10
ee
P
0.2
0.3
0.4
0.5
0.6
0.7
0.8
pp
Be
7
pep
B
8
Vacuum-LMA
MSW-LMA
0.5
−
0.5
' = 1.0ε
Figure 1. Electron neutrino survival probability Pee(E) as a function of neutrino energy for LMA-
MSW solution with uncertainties of oscillation parameters taken into account (pink band), and
LMA-MSW + NSI solutions for ε0=−0.5,0.5,1.0 and average values of oscillation parameters.
Vacuum oscillations scenario with LMA parameters is also shown (grey band). To illustrate the
capability of the detector to sense NSI’s at propagation, experimental points for Pee(E) shown for
Borexino under the HZ-SSM assumption are also provided (ref. [18]). 8B and pp data points are
set at the mean energy of neutrinos that produce scattered electrons above the detection threshold.
The error bars include experimental and theoretical uncertainties.
3 Analysis
3.1 Overview
The objective of this analysis is to investigate the sensitivity of Borexino to the NSI pa-
rameters εL/R
eand εL/R
τ. In contrast to the analysis of ref. [18], in which the νe couplings
were fixed to those of the SM and the count rates of pp,7Be, and pep neutrinos were fit
to the data, we allow the couplings to float, assuming the SSM neutrino fluxes with either
the HZ- or LZ-SSM values (table 1).
We have argued in the previous section that εL/R
eand εL/R
τaffect neutrino propagation
and detection: (i) the propagation through a shift in the matter-effect potential, eq. (2.13),
leading to a modification in the expected νesurvival probability Pee(E), and (ii) the detec-
tion through shifts in the effective chiral coupling constants, eqs. (2.10) and (2.11), leading
to modifications in the electron recoil spectra dσα/dT (α=e, τ ), eq. (2.6).
Four solar neutrino components are considered in this analysis: pp,7Be, pep, and
CNO.6The SSM [24–27] predicts the energy spectra and fluxes of these neutrinos, which
we denote as dλν/dE and Φν, where the subscript νlabels the neutrino component.
6In the present analysis, we look for deviations from the SSM + LMA-MSW predictions, so the CNO
neutrino flux, together with the other three component fluxes, are simply fixed to those predicted by either
the HZ- or LZ-SSM.
– 7 –

JHEP02(2020)038
Flux, ΦνB16(GS98)-HZ B16(AGSS09met)-LZ
pp 5.98(1 ±0.006) 6.03(1 ±0.005)
pep 1.44(1 ±0.01) 1.46(1 ±0.009)
7Be 4.93(1 ±0.06) 4.50(1 ±0.06)
CNO 4.88(1 ±0.11) 3.51(1 ±0.10)
Table 1. The fluxes predicted by HZ- and LZ-SSM’s (ref. [27]) and used in this analysis. Units
are: 1010 (pp), 109(7Be), 108(pep, CNO) cm−2s−1.
The monochromatic 7Be-component plays a fundamental role in this analysis. Both
the shape and the normalization of the electron-recoil spectrum is well-constrained in the
fit. Together with the 6%-uncertainty in the theoretical 7Be neutrino flux, it provides the
highest sensitivity to NSI’s among all the neutrino components. We do not use 8B neutrinos
to place bounds on NSI’s. The rate of 8B neutrino events cannot be determined with the
spectral fit used in this analysis, being small and hidden by backgrounds in the energy
region considered. Moreover, the relatively large 12%-uncertainty on the 8B neutrino flux
predicted by the SSM limits its utility for this work.
Taking into account the oscillations of νeinto νµand ντ, the recoil spectrum for each
solar neutrino component is given by
dRν
dT =NeΦνZdE dλν
dE dσe
dT Pee(E) + c2
23
dσµ
dT +s2
23
dστ
dT (1 −Pee(E)).(3.1)
Here, Neis the number of electrons in the fiducial volume of the detector, s2
23 ≡sin2θ23,
and c2
23 ≡cos2θ23. Φνis the expected total flux of solar neutrino component νat the Earth,
and dλν/dE is the corresponding differential neutrino energy spectrum. Pee(E) is the solar-
νesurvival probability to which NSI effects at propagation have been added. The effect
of the NSI’s at detection is included in the differential cross sections dσe/dT and dστ/dT ,
with the εL/R
eand εL/R
τparameters always combined in the recoil spectrum of eq. (3.1).
The dependence of the 7Be electron recoil spectrum dRBe7/dT on the NSI’s for several
values of εR
eand εL
eis illustrated in figure 2. Note that εL
emostly modifies the normalization
of the spectrum, while εR
emodifies its slope. εL
τand εR
τrequire much larger magnitudes to
achieve the same effects due to the smaller contribution of ντto dRBe7/dT .
Integrating eq. (3.1), one obtains a relation between the total experimental event rate
Rν, the solar neutrino flux Φν, and the total cross section hσνi:
Rν=ZdRν
dT dT =NeΦνhσνi.(3.2)
NSI effects at propagation and detection are both included in the total cross section hσνi.
Denoting the total cross section in the absence of NSI’s as hσνiSM, we plot the change in
the ratio hσνi/hσνiSM for the 7Be neutrinos due to the presence of εL
eand εR
ein figure 3.
Again, we see that εL
eaffects the normalization of the cross section, while εR
edoes not.
Thus εL
eis mostly constrained by the normalization of the cross section, while εR
eis mostly
constrained by the shape of the recoil spectrum.
– 8 –

JHEP02(2020)038
Energy [keV]
0 100 200 300 400 500 600 700 800
Enents / (day x 100 tons x 1 keV)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
SI
= 0.1
L
e
ε
0.1− =
L
e
ε
= 0.1
R
e
ε
0.1− =
R
e
ε
Figure 2. The distortion of the electron recoil spectrum, eq. (3.1), for the two monochromatic 7Be
solar neutrino lines (E= 0.384 MeV and 0.862 MeV) due to non-zero values of εL
eand εR
e. The
effect of the finite energy resolution of the detector is not included.
R/L
e
ε
0.2−0.15−0.1−0.05−0 0.05 0.1 0.15 0.2
SM
〉
Be
7
σ 〈 / 〉
Be
7
σ 〈
0.6
0.8
1
1.2
1.4
1.6
1.8
R
e
ε
L
e
ε
R
e
ε
Figure 3. The relative change of the total cross section ratio hσ7Be i/hσ7BeiSM as function of εR/L
e
(left panel) and εR/L
τ(right panel).
3.2 Detector model and choice of parameters
We performed the selection of the events according to ref. [18], using a spherical fidu-
cial volume to which the top and bottom polar regions are cut off: R < 2.8 m, and
−1.8 m < z < 2.2 m. To model the detector response, we use the analytical model of the
Borexino detector discussed in detail in ref. [17]. The model uses the number of triggered
PMT’s, Ndt1
p, within a fixed time interval dt1= 230ns as the estimator of the electron
– 9 –

JHEP02(2020)038
recoil energy T. Various model parameters have been fixed utilizing independent measure-
ments, or tuned using the Borexino Monte Carlo [76] and calibrations [77], while some have
been left free to float in the fit. The floating parameters include (i) the light yield, which
determines the energy scale, (ii) two parameters for energy resolution, (iii) two parameters
for the position and the width of the 210Po-αpeak, and (iv) one parameter for the starting
point of the 11Cβ+-spectrum. The detector response function convoluted with the cross
section dRν/dT provides the functional form to be fit to the data.
Throughout the minimization procedure, the neutrino oscillation parameters are fixed
to the central values of the global fit to all oscillation data given in ref. [65].7Their
uncertainties are directly propagated as the uncertainties of predicted neutrino rates. More
details on how the uncertainties are treated can be found in section 3.4.
For the εL/R
eanalysis, we only need
∆m2
21 =m2
2−m2
1= 7.50+0.19
−0.17 ×10−5(3.3)
sin2θ12 = 0.306+0.012
−0.012 ,(3.4)
sin2θ13 = 0.02166+0.00077
−0.00077 ,(3.5)
which are valid for any choice of neutrino mass hierarchy.
It is worthwhile to mention that the measurements of θ12 and ∆m2
21 from the global
oscillation data may be altered if we consider NSI’s in the fit. The solar neutrino experi-
ments such as Super-Kamiokande and SNO provide crucial information on θ12 and ∆m2
21,
and at the same time they are sensitive to the same NSI’s in propagation and detection
that we consider in this paper. However, the reactor experiment KamLAND is unaffected
by flavor-diagonal neutral current NSI’s involving neutrinos and electrons. Therefore, when
we consider the KamLAND data along with the solar neutrino data mostly coming from
Super-Kamiokande and SNO, the solar oscillation parameters θ12, ∆m2
21 remain robust
even in the presence the NSI’s discussed in this paper. In fact, it was shown in ref. [63]
that Super-Kamiokande and SNO can place competitive constraints on εL
eand εR
ewith the
help of KamLAND data which provides NSI-independent measurement of θ12 and ∆m2
21.
Note also that for the εL/R
eanalysis dσµ/dT =dστ/dT when εL/R
τ= 0, and Borexino is
insensitive to the value of θ23.
For the εL/R
τanalysis, we also need to specify θ23. The 1σranges given in ref. [65] for
Normal and Inverted Hierarchies are
sin2θ23 =(0.441+0.027
−0.021 NH
0.587+0.020
−0.024 IH (3.6)
It is easy to see that sin2θ23 is included linearly in expression (3.1), and the sensitivity to
εL/R
τis proportional to its value. To obtain a conservative limit, we fix sin2θ23 to the NH
value and propagate its uncertainty into systematic error together with other oscillation
parameters.
7Strictly speaking, to use the Borexino data to constrain possible new physics effects we should not be
comparing the data to the global average of ref. [65], which includes both Borexino Phase-I and Phase-II
data in its fit.However, the numerical difference from the global average of ref. [78], which includes neither
Borexino Phase I nor Phase II data, is small and does not affect the present analysis.
– 10 –

JHEP02(2020)038
Figure 4. Example of fit of the Borexino energy spectrum. The fit was performed using the Ndt1
p
energy estimator. The bottom horizontal axis has been converted from Ndt1
pinto units of energy;
Npis a number of photoelectrons in the acquisition time window.
3.3 Backgrounds
Radioactive contaminants lead to backgrounds that must be clearly understood to extract
unambiguous conclusions from the Borexino data. The most recent fit of signal+background
to the observed electron recoil spectrum can be found in ref. [18], where the SM couplings
were assumed and the event rates of three solar neutrino components (pp,7Be, and pep)
were allowed to float. An example fit to the experimental spectrum is shown in figure 4. A
full description of the Borexino spectral components and backgrounds is found in ref. [15].
Here, we focus on the components which are the most relevant for the current analysis:
•At low-energies the β-emitter 14C with Q= 156 keV is the main background for pp
neutrinos (Tmax = 261 keV).
The 14C contribution is constrained in the fit with an independent measurement by
selection of events with low energy threshold. Since the rate of 14C is high compared
to the other components, pile-up events need to be taken into account. The detailed
data selection and analysis procedures are found in ref. [16].
•Decays of 85Kr (β−,Q= 687 keV), 210Bi (β−,Q= 1160 keV), and 210Po (α,
E= 5.3 MeV) are the main backgrounds for the detection of the electron recoil spec-
tra from the two mono-energetic 7Be solar neutrino lines (E= 384 keV and 862 keV).
– 11 –

JHEP02(2020)038
The 210Po α-decay peak (E= 5.3 MeV) appears at ∼400 keV due to ionization
quenching effects in the liquid scintillator. While very intense with respect to the
other spectral components, the shape of the polonium peak is very distinct, well
understood, and easily separable in the fit.
The βspectra of 210Bi and 85Kr overlap with the 7Be electron-recoil spectrum leading
to a modification of its shape. This reduces the sensitivity to the right-handed NSI
parameter εR
α. The background from 85Kr is quite serious since the shape of its
β-spectrum and its end-point are close to the step-like spectrum of 7Be.
•Other backgrounds necessary to the fit of the experimental spectrum are cosmogenic
β+emitter 11C, and γ-rays from 208Tl, 214Bi, and 40 K from components of the
detector external to the scintillator.
3.4 Fit procedure
The fitting procedure consists of the multivariate maximization of the composite likelihood
function L(~
k|ε, ~
θ), specifically developed to be able to detect pep, and CNO neutrinos
hidden by the cosmogenic β+ 11C and external backgrounds:
L(~
k|ε, ~
θ) = LTFC
sub (~
k|ε, ~
θ)· LTFC
tag (~
k|ε, ~
θ)· LP(~
k|~
θ)· LR(~
k|~
θ).(3.7)
Here, εis the NSI parameter we would like to constrain, and the vector ~
θcollectively
represents all the other model parameters of the fit, including the rates of the four solar
neutrino components Rν, the intensities of the backgrounds, detector response parameters,
etc., and ~
kdenotes the set of experimental data.
In order to deal with 11C background, the dataset was divided into two parts by
the so-called three-fold coincidence (TFC) technique (refs. [15,17]). The method tags
events correlated in space and time with a parent muon and one or several neutrons often
produced together with 11C. The division is based on the probability for an event to be
11C and results in 11 C-depleted (TFC-subtracted) and 11C-enriched (TFC-tagged) data
samples. The first and the second factors of eq. (3.7) represent two separate likelihoods for
TFC-subtracted and TFC-tagged experimental spectra, respectively. They are a standard
Poisson likelihood:
LTFC
sub,tag(~
k|ε, ~
θ) =
NE
Y
i=1
λi(ε, ~
θ)kie−λi(ε,~
θ)
ki!(3.8)
where NEis the number of energy bins, λi(ε, ~
θ) is the expected number of events in the
i-th bin for a given set of parameters εand ~
θ, and kiis the measured number of events in
the i-th bin.
The residual events from 11C in the TFC-subtracted spectrum can be discriminated
by the algorithm incorporated into LP(~
k|~
θ). To account for external backgrounds which
penetrate into the fiducial volume, the fit of the spatial radial distribution of events is
incorporated by LR(~
k|~
θ). The more detailed description of the likelihood function and the
fitting procedure can be found in section XXI of ref. [15], and in ref. [17].
– 12 –

JHEP02(2020)038
We add penalty factors to L(~
k|ε, ~
θ) to constrain the four neutrino rates to the SSM
prediction [24–27]:
L(~
k|ε, ~
θ)→ L(~
k|ε, ~
θ)·Y
ν
exp 

−θν−RSSM
ν(ε)2
2δRSSM
ν(ε)2

,(3.9)
where θνrepresents the floating value of Rν.RSSM
ν(ε) is the expected rate calculated
by (3.2) from the prediction of the SSM with either the HZ or LZ assumption and for
a given set of NSI parameters ε, and oscillation parameters fixed to their central values.
δRSSM
ν(ε) is its uncertainty stemming from theoretical uncertainties of the SSM and system-
atic uncertainties on the estimated number of target electrons Ne, on the fiducial volume,
and on the oscillation parameters.
Performing a series of fits for different values of ε, one can obtain a likelihood proba-
bility distribution
p(ε) = L(~
k|ε, ~
θmax(ε))
Rd¯εL(~
k|¯ε, ~
θmax(¯ε)) ,(3.10)
where ~
θmax(ε) is the set of values of ~
θthat maximizes the likelihood for a particular value
of ε. The upper εup and lower εlow bounds for a given confidence level (C.L.) can be
numerically obtained by integrating the tails of the following distribution:
Zεlow
−∞
dε p(ε) = Z∞
εup
dε p(ε) = 1−C.L.
2.(3.11)
For the two dimensional case when two parameters (ε1, ε2) are under investigation, the
confidence region is formed by the isocontour p0= const, defined though the integral over
the excluded region: ZZ
p(ε1,ε2)<p0
dε1dε2p(ε1, ε2)=1−C.L. , (3.12)
where p(ε1, ε2)< p0stands for the region outside of the isocontour p0.
4 Results
4.1 Bounds on NSI parameters
In this section, we present our results. Left panels of figure 5shows the one-dimensional
log-likelihood profiles for εR
e(red curve) and εL
e(blue curve) assuming HZ- (top panel) and
LZ-SSM (bottom panel). Right panels of figure 5portrays the same for εR
τ(red curve) and
εL
τ(blue curve).
Let us first discuss the HZ-SSM case (top panels). One can see that the sensitivity of
Borexino to the NSI parameter εL
eis more pronounced as compared to its sensitivity to εR
e
(see top left panel of figure 5). The main reason behind this is that the normalization of
neutrino events is well determined by the fit, which in turn provides competitive constraints
for εL
e. In contrast, the fit still permits quite a wide range for εR
e, since the possible
– 13 –

JHEP02(2020)038
R/L
e
ε
0.25−0.2−0.15−0.1−0.05−0 0.05 0.1 0.15 0.2 0.25
ln L∆- 2
0
0.5
1
1.5
2
2.5
3
3.5
4
R
e
εL
e
ε
HZ-SSM
R/L
τ
ε
1−0.5−0 0.5 1
ln L∆- 2
0
0.5
1
1.5
2
2.5
3
3.5
4
R
τ
εL
τ
ε
HZ-SSM
R/L
τ
ε
1−0.5−0 0.5 1
ln L∆- 2
0
0.5
1
1.5
2
2.5
3
3.5
4
R
τ
εL
τ
ε
LZ-SSM
Figure 5. Left panels show the log-likelihood profiles for the NSI parameter εR
e(red line) and εL
e
(blue line) assuming HZ (top panel) and LZ (bottom panel) SSM’s. Right panels depict the same
for εR
τ(red line) and εL
τ(blue line). The profiles were obtained considering one NSI parameter
at-a-time, while remaining NSI parameters were fixed to zero.
modification in the shape of the event spectra due to non-zero εR
ecan be easily mimicked
by the principle background components (mainly 85Kr) discussed above. Note that the
minima of the one-dimensional log-likelihood profiles for εR
e(red line in left panel) and εR
τ
(red line in right panel) are slightly deviated from zero, but, needless to mention that these
deviations are statistically insignificant.
The one-dimensional log-likelihood profiles for both εR
τand εL
τlook non-parabolic in
the top right panel of figure 5. In particular, εL
τdemonstrates one extra minimum around
εL
τ≈0.6, which is slightly disfavored at ∆χ2=−2∆lnL ≈1.5 as compared to the global
minimum at εL
τ= 0. This minimum originates due to the approximate ˜gαL ↔ −˜gαL
symmetry that eq. (2.6) possesses, since the first term in eq. (2.6) dominates over the third
– 14 –

JHEP02(2020)038
HZ-SSM LZ-SSM Ref. [23] Ref. [55]
εR
e[−0.15, +0.11 ] [−0.20, +0.03 ] [−0.21, +0.16 ] [0.004, +0.151 ]
εL
e[−0.035, +0.032 ] [−0.013, +0.052 ] [−0.046, +0.053 ] [−0.03, +0.08 ]
εR
τ[−0.83, +0.36 ] [−0.42, +0.43 ] [−0.98, +0.73 ] [−0.3, +0.4 ]
εL
τ[−0.11, +0.67 ] [−0.19, +0.79 ] [−0.23, +0.87 ] [−0.5, +0.2 ]
Table 2. The first column shows the limits on the flavor-diagonal NSI parameters εR
e,εL
e,εR
τ, and
εL
τas obtained in the present work using the Borexino Phase-II data and considering HZ-SSM for
the neutrino fluxes. The second column displays the same considering LZ-SSM. These constraints
are obtained varying only one NSI parameter at-a-time, while the remaining three NSI parameters
are fixed to zero. The third column contains the bounds using Borexino Phase-I results as obtained
in ref. [23] (for HZ-SSM case only). For the sake of comparison, we present the global bounds from
ref. [55] in the forth column. All limits are 90% C.L. (1 d.o.f.).
term [63]. Because of this symmetry, the value of ˜g2
τL = (gτ L +εL
τ)2is the same for εL
τ= 0
and εL
τ=−2gτL ≈0.54, and therefore, one may expect a local minimum in vicinity of the
second point. The presence of the third term in eq. (2.6) shifts the position of this local
minimum slightly upward to εL
τ≈0.64.
The profiles for the LZ-SSM case (figure 5, bottom panels) are clearly shifted from zero
and with respect to the HZ-SSM ones. The main reason for this is that LZ-SSM predicts
smaller Φ7Be compared to HZ-SSM. The smaller flux requires a bigger cross section hσ7Bei
for a given observed experimental rate R7Be (see eq. (3.2)). As figure 3illustrates, the
total cross section linearly depends on εL
e. Therefore, the minimum for LZ-SSM should
be shifted in positive direction of εL
e. For εL
τthe minima go in opposite directions due
to the same reason. The only difference is that the cross section increases when εL
τgoes
in negative direction for the first minimum and when εL
τgoes up for the second one (see
figure 3, right panel). Aforementioned shifts for εL
eand εL
τprofiles induce the shifts for
εR
eand εR
τas well. This will be easy to see later on considering two dimensional profiles
(figures 6and 7).
The 90% C.L. (1 d.o.f.) bounds on the flavor-diagonal NSI parameters obtained using
the Borexino Phase-II data are listed in table 2. The first column shows the constraints
assuming HZ-SSM for the neutrino fluxes. The second column presents the same consid-
ering LZ-SSM. These constraints are obtained varying only one NSI parameter at-a-time,
while the remaining three NSI parameters are fixed to zero.
The third column exhibits the bounds obtained by phenomenological analysis with
Borexino Phase-I data in ref. [23]. All experimental limits from Borexino Phase-II are
better than those previously obtained from the Borexino Phase-I data in ref. [23]. For the
sake of comparison, in the forth column, we present the global bounds from ref. [55], where
the authors analyzed the data from the Large Electron-Positron Collider (LEP) experiment,
LSND and CHARM II accelerator experiments, and Irvine, MUNU, and Rovno reactor
experiments. The bounds found in the present analysis are quite comparable to the global
ones. One may note that the best up-to-date bound for εL
ewas obtained in this work.
– 15 –

JHEP02(2020)038
L
e
ε
0.25−0.2−0.15−0.1−0.05−0 0.05 0.1 0.15
R
e
ε
0.8−
0.6−
0.4−
0.2−
0
0.2
0.4
0.6
'
ε
0.5
0.0
0.5
−
1.0
LSND
TEXONO
BOREXINO
90% C.L. (2 d.o.f.)
LZ-SSM
HZ-SSM
Solar+KamLAND
Figure 6. Allowed region for NSI parameters in εL/R
eplane obtained in the present work. The
parameters εL
τand εR
τare fixed to zero. Both HZ- (filled red) and LZ- (dashed red) SSM’s were
assumed. The bounds from LSND [54,79] and TEXONO [80] are provided for comparison. Besides,
the contour obtained from the global analysis of solar neutrino experiments is presented by dashed
black line (ref. [63], NSI’s are included in detection and propagation). All contours correspond
to 90% C.L. (2 d.o.f.). The dotted gray lines represent the corresponding range of ε0parameter,
relevant for NSI’s at propagation.
We have considered above the sensitivity of the Borexino Phase II data to NSI’s apply-
ing the SSM-constraint on the neutrino fluxes. Remarkably, Borexino detector is sensitive
to the modification of the shape of 7Be electron recoil spectra even if the neutrino fluxes
are not constrained by SSM model. Such analysis provides a limit:
−1.14 < R
e<0.10 (90% C.L..) (4.1)
As one may see the limit is highly asymmetric, with a large extension for the negative
values of εR
e. Such a small sensitivity is induced by backgrounds (mostly 85Kr) which can
easily compensate the modification of electron-recoil spectra.
Now let us consider the two-dimensional case when the allowed region for NSI param-
eters εL/R
eis plotted while εL
τand εR
τare fixed to zero (figure 6). Two contours for HZ-
(filled) and LZ-SSM (dashed) were obtained. Compared with other experiments sensitive
to the same NSI’s, the allowed contours for Borexino in the εL
e-εR
eplane have a distinct
– 16 –

JHEP02(2020)038
Figure 7. Allowed region for NSI parameters in εL/R
τplane obtained in the present work. The
parameters εL
eand εR
eare fixed to zero. Both HZ- (filled dark blue) and LZ- (dashed dark blue)
SSM’s were assumed. The contour from LEP [55] is provided for comparison. Both contours
correspond to 90% C.L. (2 d.o.f.). The dotted gray lines represent the corresponding range of ε0
parameter, relevant for NSI’s at propagation.
orientation, cf. figure 6. The TEXONO experiment [80] is mostly sensitive to εR
e, while
LSND [54,79] is mostly sensitive to εL
e. Borexino’s contour intersects the allowed regions
for both experiments at a certain angle, and the three experiments complement each other.
In principle, the overlap of Borexino with TEXONO results in two allowed regions. To
exclude the second intersection, the incorporation of the LSND result is necessary.
As it was already explained in the analysis of one-dimensional profiles, the contours
for HZ- and LZ-SSM’s are shifted along εL
e-axis. Considering two-dimensional case it is
evident that such a shift in εL
ehas to produce also the displacement for εR
e.
The contour for Borexino is extended in the direction of negative εR
eand εL
edue to
the presence of backgrounds, especially 85Kr. The shift of the contour for LZ-case with
respect to HZ one is due to the change of rate of the backgrounds because of the spectral
correlations.
For both HZ- and LZ-SSM cases, the bounds on the left parameter are stronger than
the result from LSND. TEXONO [80] is a reactor antineutrino experiment and its bounds
– 17 –

JHEP02(2020)038
are obtained from νeescattering. For anti-neutrinos the roles of ˜geL and ˜geR are reversed,
leading to a stronger bound on εR
e. Due to the approximate symmetry ˜gR
e↔ −˜gR
ein the
anti-neutrino scattering cross section, two separate contours form the allowed region of
TEXONO around εR
e= 0 and εR
e=−2geR =−2 sin2θW≈ −0.5.
The contour obtained in ref. [63] is presented by a dashed black line. In this work, the
global analysis of several solar neutrino experiments together with KamLAND result was
conducted. NSI’s were considered in both detection and propagation. The very first results
of Borexino were also included [22,81,82]. Though, as the authors underlined, they did
not contribute much in overall sensitivity to NSI’s. As one may see, the present Borexino
results are quite complementary to this contour.
The result of Borexino in the εL
τ-εR
τplane is shown in figure 7. It is similar to that
of LEP [55] in excluded area, but it occupies a slightly different region, favoring posi-
tive εR
τand negative εL
τ. NSI’s comparable with the SM neutral current interactions are
still allowed.
The result for LZ-SSM is of particular interest. The shift of the minima discussed
above and observed in figure 5(bottom right) transforms the allowed contour (figure 7,
dashed dark blue) into two separate regions, one of which is already almost completely
excluded by LEP data. So, the remaining allowed region, in this case, is relatively small.
The dotted gray lines in figures 6and 7indicate the range for the parameter ε0relevant
for NSI’s at propagation. The contours are almost entirely located between ε0=−0.5 and
ε0= 0.5. As it was previously shown in section 2.3 (see figure 1), NSI’s at propagation are
not very pronounced for these magnitudes of ε0compare to the precision of the measure-
ments. Thus, the sensitivity of the detector is mostly determined by NSI’s at detection.
4.2 Evaluation of sin2θW
In addition to the analysis of NSI’s, we use the same data and analysis approach to constrain
the value of sin2θW. Instead of introducing NSI’s, we simply allow sin2θWin the SM
couplings (2.3) to vary. The sensitivity of the analysis to sin2θWis mostly dominated by
gL
e, while contributions of the other five coupling constants are almost negligible. For the
HZ-SSM case, the analysis of a likelihood profile results in
sin2θW= 0.229 ±0.026 (stat+syst) ,(4.2)
which is consistent with theoretical expectations [31] and comparable in precision with the
value found by the reactor νeescattering experiment TEXONO [80]:
sin2θW= 0.251 ±0.031 (stat) ±0.024 (syst) .(4.3)
The most accurate determination of sin2θWby neutrino-electron scattering is from the νµe
scattering experiment CHARM II [19]:
sin2θW= 0.2324 ±0.0058 (stat) ±0.0059 (syst) .(4.4)
– 18 –

JHEP02(2020)038
5 Summary and concluding remarks
In the present work, we search for Non-Standard Interactions (NSI’s) of the neutrino using
Borexino Phase-II data. The NSI’s considered are those of the flavor-diagonal neutral
current type that modify the νeeand ντecouplings while preserving their chiral and flavor
structures.
Such NSI’s can affect solar neutrinos at production, propagation, and detection. Neu-
trino production in the Sun can be affected via processes such as γe →ν¯νe, but the
expected modification in the neutrino spectrum is at energies well below the detection
threshold of Borexino (∼50 keV), so this effect does not need to be included. The NSI’s
considered also modify the solar neutrino survival probability Pee(E) via the LMA-MSW
effect as the neutrinos propagate through dense solar matter. This effect is strong at 8B
neutrino energies but not particularly large at 7Be neutrino energies, limiting the sensitivity
of Borexino to such deviations. The effect of the NSI’s to which Borexino is most sensitive
is at detection, where the shape of the electron-recoil spectrum is affected by changes in
the νeeand ντecouplings.
The solar neutrino fluxes were constrained to the prediction of the Standard Solar
Model (SSM) with the LMA-MSW oscillation mechanism. SSM’s with both high- (HZ)
and low-metallicity (LZ) were considered. Systematic effects related to the characterization
of the target mass of the detector and the choice of oscillation parameters were taken
into account.
The modifications to the νeeand ντecouplings are quantified by parameters εL/R
e
and εL/R
τ. The bounds to all four parameters were obtained in this analysis, and they all
show marked improvement compared to the Borexino Phase-I analysis [23], regardless of
the choice of metallicity in the SSM, cf. table 2. The bounds are quite comparable to the
global ones. In particular, the best constraint to-date on εL
ewas obtained.
The log-likelihood profiles and corresponding bounds for HZ- and LZ-SSM’s are shifted
with respect to each other due to different expected neutrino detection rates. The minima of
HZ-profiles are less shifted from zero as a result of better agreement between the measured
neutrino rates and HZ-SSM. For LZ-SSM, the deviations of the minima of the profiles
from zero are more pronounced but still statistically insignificant. The allowed contour
of Borexino in the εL/R
e-plane is quite distinct with respect to other νe or νe scattering
experiments, also sensitive to the same NSI’s, such as TEXONO and LSND. Borexino is
sensitive to both εR
eand εL
eparameters while TEXONO and LSND mostly constrain εR
eor
εL
e, respectively. Notably, in the case of εL/R
τtwo local minima are observed. The distance
between the minima is larger for LZ-SSM, resulting in the splitting of the 90% C.L. allowed
contour into two contours in the εL/R
τ-plane.
An important sensitivity-limiting factor is the presence of backgrounds, especially 85Kr,
whose forbidden β-spectrum can mimic the spectral modifications induced by NSI’s.
The smaller, conservative, NH-value for θ23 was chosen for the εL/R
τ-analysis. Should
the neutrino mass hierarchy be identified as inverted in future experiments, the contribution
of the τ-neutrino to the cross section would be larger and the bounds for εL/R
τwould be
slightly improved. The most important factor which determines the sensitivity of this study
– 19 –

JHEP02(2020)038
is the uncertainty on the ν-fluxes predicted by the SSM (currently 6% for Φ7Be). Their
improvement would directly refine the bounds on NSI’s presented here.
The detector is sensitive to εR
e, even without constraining the solar neutrino fluxes to
those of the SSM, purely via the modification to the electron-recoil spectral shape. However,
it was found that background greatly reduce the ideal sensitivity by compensating for the
modification to the spectra, especially for negative εR
e.
The same dataset and approach, but without any NSI’s assumed, was used to con-
strain sin2θW. The resulting value is comparable in precision to that measured in reactor
antineutrino experiments.
Acknowledgments
The Borexino program is made possible by funding from INFN (Italy), NSF (U.S.A.),
BMBF, DFG, HGF and MPG (Germany), RFBR (grants 19-02-0097A, 16-29-13014ofi-m,
17-02-00305A, 16-02-01026), RSF (grant 17-12-01009) (Russia), and NCN (grant number
UMO 2017/26/M/ST 2/00915) (Poland).
We acknowledge also the computing services of the Bologna INFN-CNAF data centre
and LNGS Computing and Network Service (Italy), of J¨ulich Supercomputing Centre at
FZJ (Germany), of ACK Cyfronet AGH Cracow (Poland), and of HybriLIT (Russia). We
acknowledge the hospitality and support of the Laboratori Nazionali del Gran Sasso (Italy).
We are thankful to Zurab Berezhiani for the discussion at the initial stage of the
research. S.K.A. would like to thank A. Smirnov and A. De Gouvea for useful dis-
cussions. S.K.A. acknowledges the support from DST/INSPIRE Research Grant [IFA-
PH-12], Department of Science and Technology, India and the Young Scientist Project
[INSA/SP/YSP/144/2017/1578] from the Indian National Science Academy. A.F. acknowl-
edges the support provided by the University of Hamburg. T.T. is supported in part by
NSF Grant 1413031 and DOE Grant DE-SC0020262. C.S. is supported in part by the
International Postdoctoral Fellowship funded by China Postdoctoral Science Foundation,
and NASA grant 80NSSC18K1010.
A Derivation of the matter effect potential in the presence of NSI’s
The Hamiltonian which governs the propagation of neutrinos in matter in the presence of
the NSI’s εV
e=εL
e+εR
eand εV
τ=εL
τ+εR
τis given by
H=1
2EU


0 0 0
0 ∆m2
21 0
00∆m2
31


U†+V(x)


1 + εV
e0 0
0 0 0
0 0 εV
τ


,(A.1)
where V(x) = √2GFNe(x), and Ne(x) is the electron density at location x. This expression
is in the flavor basis in which the rows and columns are labelled by neutrino-flavor in the
– 20 –

JHEP02(2020)038
order (e, µ, τ ). The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix Uis given by
U=


1 0 0
0c23 s23
0−s23 c23



| {z }
R23



c13 0s13e−iδ
0 1 0
−s13eiδ 0c13



| {z }
R13



c12 s12 0
−s12 c12 0
0 0 1 


| {z }
R12
.(A.2)
Performing the R23 and R13 rotations on both sides of eq. (A.1), we find
H0=R†
13R†
23H R23 R13
=1
2ER12 


0 0 0
0 ∆m2
21 0
00∆m2
31


R†
12 +V(x)R†
13R†
23 


1+εV
e0 0
0 0 0
0 0 εV
τ


R23R13
=1
2E


∆m2
21s2
12 ∆m2
21s12 c12 0
∆m2
21s12 c12 ∆m2
21c2
12 0
0 0 ∆m2
31



+V(x)


(1−ε0)c2
13 +εV
τ(c2
23 −s2
23)s2
13 εV
τs23c23 s13e−iδ (1+εV
e)−V
τc2
23s13 c13e−iδ
εV
τs23c23 s13eiδ 0−εV
τs23c23 c13
(1+εV
e)−V
τc2
23s13 c13eiδ −εV
τs23c23 c13 εV
τ(c2
23 −s2
23)c2
13 +(1−ε0)s2
13



+V(x)εV
τs2
23 ×(unit matrix),(A.3)
where we have set
ε0=εV
τs2
23 −εV
e.(A.4)
In the energy range where |∆m2
31|  2EV (x), the off-diagonal terms in the third row
and third column can be neglected and we can treat H0as already partially diagonalized.
Concentrating on the 2 ×2 upper-left block, we drop the third row and third column
and obtain
H0→1
2E"∆m2
21s2
12 ∆m2
21s12 c12
∆m2
21s12 c12 ∆m2
21c2
12 #
+V(x)"(1 −ε0)c2
13 +εV
τ(c2
23 −s2
23)s2
13 εV
τs23c23 s13e−iδ
εV
τs23c23 s13eiδ 0#
≈1
2E"∆m2
21s2
12 ∆m2
21s12 c12
∆m2
21s12 c12 ∆m2
21c2
12 #+V(x)"(1 −ε0)c2
13 εV
τs23c23 s13e−iδ
εV
τs23c23 s13eiδ 0#,(A.5)
where we have used s2
23 ≈c2
23 and s2
13 1 to simplify the expression for the (1,1) element.
The resonance condition is achieved when the (1,1) and (2,2) elements of this matrix are
equal:
∆m2
21s2
12 + 2EV 0(x)c2
13 = ∆m2
21c2
12 →2EV 0(x)c2
13 = ∆m2
21 cos 2θ12 ,(A.6)
where
V0(x) = V(x) (1 −ε0).(A.7)
See, e.g., refs. [83,84] and references therein.
– 21 –

JHEP02(2020)038
Open Access. This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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