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Search for exotic interactions of solar neutrinos in the CDEX-10 experiment
X. P. Geng,1L. T. Yang ,1,* Q. Yue,1,†K. J. Kang,1Y. J. Li,1H. P. An,1,2 Greeshma C.,3,‡J. P. Chang,4Y. H. Chen,5
J. P. Cheng,1,6 W. H. Dai,1Z. Deng,1C. H. Fang,7H. Gong,1Q. J. Guo,8X. Y. Guo,5L. He,4S. M. He,5J. W. Hu,1
H. X. Huang,9T. C. Huang,10 H. T. Jia,7X. Jiang,7S. Karmakar,3,‡H. B. Li,3,‡J. M. Li,1J. Li,1Q. Y. Li,7R. M. J. Li,7
X. Q. Li,11 Y. L. Li,1Y. F. Liang,1B. Liao,6F. K. Lin,3,‡S. T. Lin,7J. X. Liu,1S. K. Liu,7Y. D. Liu,6Y. Liu,7Y. Y. Liu,6
Z. Z. Liu,1H. Ma,1Y. C. Mao,8Q. Y. Nie,1J. H. Ning,5H. Pan,4N. C. Qi,5J. Ren,9X. C. Ruan,9Z. She,1M. K. Singh,3,12,‡
T. X. Sun,6C. J. Tang,7W. Y. Tang,1Y. Tian,1G. F. Wang,6L. Wang,13 Q. Wang,1,2 Y. F. Wang,1Y. X. Wang,8
H. T. Wong,3,‡S. Y. Wu,5Y. C . W u , 1H. Y. Xing,7R. Xu,1Y. X u , 11 T. Xue,1Y. L. Yan,7N. Yi,1C. X. Yu,11 H. J. Yu,4
J. F. Yue,5M. Zeng,1Z. Zeng,1B. T. Zhang,1F. S. Zhang,6L. Zhang,7Z. H. Zhang,1Z. Y. Zhang,1K. K. Zhao,7
M. G. Zhao,11 J. F. Zhou,5Z. Y. Zhou,9J. J. Zhu,7
(CDEX Collaboration) and Y. C. Wu14
1Key Laboratory of Particle and Radiation Imaging (Ministry of Education)
and Department of Engineering Physics, Tsinghua University, Beijing 100084
2Department of Physics, Tsinghua University, Beijing 100084
3Institute of Physics, Academia Sinica, Taipei 11529
4NUCTECH Company, Beijing 100084
5YaLong River Hydropower Development Company, Chengdu 610051
6College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875
7College of Physics, Sichuan University, Chengdu 610065
8School of Physics, Peking University, Beijing 100871
9Department of Nuclear Physics, China Institute of Atomic Energy, Beijing 102413
10Sino-French Institute of Nuclear and Technology, Sun Yat-sen University, Zhuhai 519082
11School of Physics, Nankai University, Tianjin 300071
12Department of Physics, Banaras Hindu University, Varanasi 221005
13Department of Physics, Beijing Normal University, Beijing 100875
14Department of Physics and Institute of Theoretical Physics, Nanjing Normal University,
Nanjing 210023
(Received 21 October 2022; revised 22 November 2022; accepted 17 May 2023; published 1 June 2023)
We investigate exotic neutrino interactions using the 205.4-kg · day dataset from the CDEX-10
experiment at the China Jinping Underground Laboratory. New constraints on the mass and couplings
of new gauge bosons are presented. Two nonstandard neutrino interactions are considered: a Uð1ÞB–L
gauge-boson-induced interaction between an active neutrino and electron/nucleus, and a dark-photon-
induced interaction between a sterile neutrino and electron/nucleus via kinetic mixing with a photon. This
work probes an unexplored parameter space involving sterile neutrino coupling with a dark photon. New
laboratory limits are derived on dark photon masses below 1eV=c2at some benchmark values of Δm2
41 and
g02sin22θ14.
DOI: 10.1103/PhysRevD.107.112002
I. INTRODUCTION
Various cosmological and astrophysical observations at
different scales reveal phenomena beyond the Standard
Model (SM) [1]. The measurement of nonstandard inter-
action (NSI) in the neutrino sector is an attractive approach
to probe beyond-SM physics [2,3]. Current experimental
efforts on neutrino NSI are conducted with different
neutrino sources, such as reactor neutrinos [4–12], accel-
erator neutrinos [13–16], and radioactive sources [17–21].
In addition to these terrestrial sources, NSI can also be
*Corresponding author.
yanglt@mail.tsinghua.edu.cn
†Corresponding author.
yueq@mail.tsinghua.edu.cn
‡Participating as a member of TEXONO Collaboration.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
and DOI. Funded by SCOAP3.
PHYSICAL REVIEW D 107, 112002 (2023)
2470-0010=2023=107(11)=112002(7) 112002-1 Published by the American Physical Society
probed with neutrinos from astrophysical sources, such as
stars [22], supernovae [23,24], terrestrial atmosphere [25],
and others [26]. In this paper, we investigate two attractive
exotic neutrino NSIs, where new gauge boson mediators
(generically denoted as A0) from the hidden sector couple
active or sterile neutrinos with SM particles. Constraints are
placed with data from the CDEX-10 experiment [27–32]
using solar neutrino (ν⊙) as the source.
The first NSI model is based on a gauged Uð1ÞB–L
symmetry [33,34] with the corresponding A0interacting
with SM particles with a nonzero B–L number (baryon
number minus lepton number) at tree level. This global
Uð1Þsymmetry appears in grand unified theory and will
not be violated by chiral and gravitational anomalies. The
symmetry can give rise to neutrino mass when sponta-
neously broken, and the corresponding A0is a dark matter
(DM) candidate. The free parameters are the new gauge
coupling constant (gB–L) and the gauge boson mass (MA0).
This additional Uð1ÞB–Lmediator would lead to a new
interaction between the neutrino and the SM particles
which is measurable by enhanced event rates. The second
NSI model considers the existence of a sterile neutrino (νs)
which couples with A0, called a dark photon, under a new
gauged symmetry Uð1Þ0[33]. The dark photon is a popular
DM candidate and can be a portal between the SM and the
dark sector. Observable interactions between νsand SM
matter are induced by A0. The coupling strength between A0
and νsis parametrized by g0, while that with SM particles
with charge Qis via its kinetic mixing (ε) with the SM
photons. Other interesting NSI models with an extra Uð1Þ
gauge boson [35,36] are beyond the scope of this work.
The p-type point contact germanium (PPCGe) semi-
conductor in ionization mode is ideal for the studies of
exotic processes due to its ultralow-energy threshold of
Oð100 eVeeÞ(“eVee”represents the electron equivalent
energy derived from energy calibration) and low background
level of Oð1count kg−1keVee−1day−1Þ[37,38]. It has been
adopted by the CDEX experiment [27–32,39–44] for
searches of DM and beyond-SM NSI at the China Jinping
Underground Laboratory (CJPL) where the rock overburden
is about 2400 m [45]. The second phase of the CDEX
experiment, CDEX-10, takes data with a 10-kg PPCGe
detector array, consisting of three triple-element PPCGe
detector strings encapsulated in copper vacuum tubes and
immersed in liquid nitrogen which serves both for cooling
and shielding. The CDEX-10 experimental configuration
was described in Refs. [27,32]. Data taking started in
February 2017, and the physics analysis threshold is
160 eVee [27]. Previous scientific results were published
in Refs. [27–31].
II. DATA ANALYSIS
The data analysis of this work is based on a 205.4-kg ·
day dataset from CDEX-10 [28–31] and follows the estab-
lished procedures of previous works [27,28,32,42,43].
The energy calibration was performed with zero energy
(defined by random trigger events) and the internal cosmo-
genic K-shell x-ray peaks: 8.98 keVee of 65Zn and
10.37 keVee of 68;71Ge. The signal events are identified
after pedestal noise cut, physics events selection, and bulk/
surface events discrimination [46,47]. The measured
energy spectrum in the detector (Edet) in keVee units after
physics event selections and efficiency corrections is shown
in Fig. 1. The physics analysis threshold is set to be
160 eVee at which the combined signal efficiency (includ-
ing the trigger efficiency and the efficiency for the pulse
shape discrimination) is 4.5% [32]. The characteristic
K-shell x-ray peaks from internal cosmogenic radionu-
clides like 68Ge, 68Ga, 65Zn, 55Fe, 54Mn, and 49V can be
identified. Their intensities are derived from the best fit of
the spectrum [27]. At the sub-keVee energy range relevant
to this analysis, background events are dominated by
Compton scattering of high-energy gamma rays and
internal radioactivity from long-lived cosmogenic isotopes.
Figure 2shows the residual spectrum in the region of 0.16–
2.16 keVee after subtracting the contributions from L- and
M-shell x-ray peaks which are derived from the corre-
sponding K-shell line intensities [27–31]. This is illustrated
in the inset of Fig. 1. The count rate is several orders of
magnitude larger than the predictions of SM ν⊙interaction.
A minimum-χ2analysis [27,28,31,41] is applied to the
residual spectrum in the range 0.16–2.16 keVee, in which
χ2is defined as
FIG. 1. The measured energy spectrum with error bars includ-
ing both the statistical and systematical uncertainties based on the
205.4-kg · day dataset of the CDEX-10 experiment [28–31]. The
bin width is 100 eVee and the energy range is 0.16–11.76 keVee.
The characteristic K-shell x-ray peaks from internal cosmogenic
radionuclides are marked by the isotope symbols in color. Both
the best fit curve of the measured energy spectrum in 4–11.8 keV,
which is the red line, and the contributions of these radionuclides
derived by the best fit are superimposed. Displayed in the inset
are the contributions of L- and M-shell x-ray peaks derived from
the corresponding K-shell line intensities [48]. The L-shell x-ray
peaks are shown in solid lines. The dashed line represents the
M-shell x-ray peak of 68Ge.
X. P. GENG et al. PHYS. REV. D 107, 112002 (2023)
112002-2
χ2¼X
i
½ni−Si−B2
Δ2
i
;ð1Þ
where niis the measured count at the ith energy bin, and Si
is the expected event rate due to the neutrino NSI model
being probed. Δiis the combination of the statistical and
systematic uncertainties [27], and Bis the flat background
contribution from the Compton scattering of high-energy
gamma rays. The best estimator of the couplings (see
discussion below) at certain mediator mass MA0is evaluated
by minimizing the χ2values. Upper limits at 90% con-
fidence level (CL) are derived by the unified approach [50].
III. FRAMEWORK OF EXOTIC NEUTRINO
INTERACTIONS
Within the SM, neutrinos can interact with Ge and
produce detectable electronic and nuclear recoils via elastic
ν-eand ν-Nelectroweak interactions, respectively. A
popular model for exotic neutrino interactions introduces
a new gauge boson mediator described by
Lint ⊃ge¯
eγμeA0
μþgq¯
qγμqA0
μþgν¯
νγμPL;R νA0
μ;ð2Þ
where A0is the extra mediator with mass MA0from a Uð1Þ
gauge group, νcan be either an active or sterile neutrino,
and ge;q;νare the couplings between the A0with the
corresponding fermions. The neutrino-induced scattering
rate is
dR
dEr
¼NT×Z∞
Emin
ν
dΦ
dEν
dσ
dEr
dEν;ð3Þ
where NTis the number of target nuclei, or electrons, per
unit of mass of the detector material (for ν-Nand ν-e,
respectively), and Emin
νis the minimum neutrino energy
required to generate recoil energy Er.dσ
dEris the differential
cross section, and dΦ
dEνis the differential flux of neutrinos.
The B16-GS98 solar model (also referred to as the high-
metallicity, or HZ model) is adopted, and the values for the
ν⊙fluxes are taken from Ref. [51]. Following Eq. (2), the
enhancements of the ν-eand ν-Nscattering cross section
are given by, respectively,
dσðνe→νeÞ
dEr
¼ðgegνÞ2me
4πp2
νðM2
A0þ2ErmeÞ2
×½2E2
νþE2
r−2ErEν−Erme−m2
ν;ð4Þ
dσðνN→νNÞ
dEr
¼ðgNgνÞ2mNF2ðErÞ
4πp2
νðM2
A0þ2ErmNÞ2
×½2E2
νþE2
r−2ErEν−ErmN−m2
ν;
ð5Þ
where Eris the recoil energy of the target, Eνis the neutrino
energy, me;N;νare the masses of the electron, target nucleus,
and neutrino, MA0is the mass of the extra gauge boson,
gNis the coherent coupling of the gauge boson with the
nucleus gN¼gpZþgnðA−ZÞwith gp¼2guþgdand
gn¼guþ2gd, and F2ðErÞis the nuclear form factor which
describes the loss of coherence due to the internal structure
of the nucleus. The conventional Helm form factor [52,53]
is adopted in this analysis. The observed energy deposition
Edet in ν-eis equal to the actual electron recoil energy Er.
For ν-N, the observed total deposited energy Edet is
different from the actual nuclear recoil energy Erand
should be corrected by Edet ¼QnrEr, where the quenching
10-1 100101
10-6
10-4
10-2
100
102
10-2 10-1 100
10-4
10-2
100
102
104
(a)
(b)
FIG. 2. The measured (black data points with uncertainties) and
expected (colored lines) event rates under the two neutrino NSI
models discussed in the text for (a) ν-eand (b) ν-Nscatterings.
Lines A and B correspond to benchmark parameter choices in
model I, while C and D are for model II. For lines C and D, the
parameter sin 2θ14 has been absorbed into the gegνand gNgν. The
energy resolution of CDEX-10 [27,30–32] was considered in the
evaluation of the expected event rates. The quenching factor in Ge
for ν-Nis calculated with the
TRIM
package [49]. The CDEX-10
data corresponds to the residual spectra with the L- and M-shell
x-ray contributions subtracted in 0.16–2.16 keVee, at a bin width
of 100 eVee [27,30,31].
SEARCH FOR EXOTIC INTERACTIONS OF SOLAR NEUTRINOS …PHYS. REV. D 107, 112002 (2023)
112002-3
factor Qnr in Ge is calculated by the
TRIM
package [49].
The differential event rates in Ge for the ν-eand ν-N
scattering from ν⊙at several benchmark physics parameters
are evaluated and displayed in Figs. 2(a) and 2(b),
respectively.
Within this framework, two neutrino NSI models are
studied and limits are derived with the CDEX-10 data.
A. Model I: Active neutrinos and SM particles
coupled through the Uð1ÞB‐Lgauge boson
The coupling of the A0to SM particles gives rise to
additional contributions to the ν-eand ν-Ndifferential
cross sections. The additional contribution can be classified
into two categories: pure contribution from the Uð1ÞB–L
gauge boson and the interference term between the Uð1ÞB–L
gauge boson and the SM [34]. Contributions of the
interference terms should be considered when the effects
due to new physics are small or comparable relative to the
SM contribution. This is the case applicable to experiments
where the SM cross sections are measured, such as
TEXONO-CsI [54], Borexino [55], XMASS [56], and
CHARM II [57,58]. Otherwise, when the ranges of new
physics effects are large compared to the SM, the inter-
ference term can in general be neglected [34], and
as the event rates measured in the CDEX-10 experiment
[27–31] are much larger than the SM prediction, it is
safe to ignore the interference contribution in this work.
For the pure contribution, the induced NSI is universal
and couples to the B–L number of each particle:
3gq¼−ge¼−gν¼gB–L. The active ν⊙’s are considered,
and the approximation mν≈0is made.
The expected event rates for ν⊙-eand ν⊙-Nscattering
with benchmark parameters (cases A and B) are displayed
in Figs. 2(a) and 2(b), respectively, and compared with the
measured CDEX-10 data. Cross-sections enhancement
between the two cases follows the 1=ðM2
A0þ2Erme=N Þ2
dependence in Eqs. (4) and (5). At light A0region where
MA0≪ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Erme=N
p, the energy spectra scale as ∝E−2
r[33],
contributing to enhanced event rates for low threshold
experiments. Upper limits from both channels at 90% CL
on gB–Las a function of MA0derived with the unified
approach [50] are depicted in Fig. 3, with constraints
from previous laboratory experiments [34,54–60] and
model-dependent astrophysical bounds [61–67] superim-
posed. The ν-escattering gives better sensitivity at
MA0<2MeV, while ν-Nscattering dominates at large
MA0. This is due to kinematics constraints as well as me≪
mNin Eqs. (4) and (5). This work on the CDEX-10 ν⊙
analysis provides limits on Uð1ÞB–Lof model I: gB–L<
1.45 ×10−6at MA0¼1keV by ν-escattering and gB–L<
8.74 ×10−4at MA0¼10 MeV by ν-Nscattering. The ν-e
scattering analysis places the strongest limit for the
Uð1ÞB–Lgauge boson with mass MA0<1keV among
solid-state detector-based experiments that use solar
neutrino as the source, which is competitive with those
of current leading laboratory constraints [34,54–60].
B. Model II: Sterile neutrinos and SM particles
coupled through a dark photon
The dark photon couples νsto SM particles with an extra
gauged Uð1Þ0symmetry via the mixing with the photons.
The νs’s are singlet under the SM gauge group but charged
under the Uð1Þ0symmetry. Following Eq. (2),wehave
gν¼g0and gf¼εeQ for f¼e,q, where Qis the charge
of the corresponding fermion, and g0is the Uð1Þ0gauge
coupling constant.
The expected event rate depends on the νsflux. In this
analysis, light νswith a mass less than Oð100ÞkeV is
considered. A small admixture of νsto the ν⊙flux can be
produced by oscillation on its way to Earth [33]. The
vacuum oscillation probability in a two-flavor approxima-
tion is given by the usual expression [33]
Pðνa→νsÞ¼sin22θ14sin2Δm2
41L
4E;ð6Þ
where θ14 is the effective active-sterile neutrino mixing
angle in vacuum, Δm2
41 ¼m2
4−m2
1is the splitting between
the squared mass of νsmass eigenstate (m4) and the
dominant ν⊙mass eigenstate (m1) in vacuum, Lis the
10-24 10-20 10-15 10-10 10-5 100
10-15
10-10
10-5
10-24 10-6
10-6
FIG. 3. Constraints on a Uð1ÞB−Lgauge boson with coupling
gB−Land mass MA0. The 90% CL limits from CDEX-10 ν⊙
analysis are shown in red, where the solid and dashed lines
represent ν-eand ν-Nscattering, respectively. Other laboratory
constraints from ν-escattering are displayed, with the inset in
expanded scale, showing limits from reactor neutrinos at TEX-
ONO [54] and GEMMA [59], solar neutrinos at Borexino [55]
and XMASS [56], and accelerator neutrino beams at CHARM II
[57,58] and the fixed-target experiment NA64 [60]. Excluded
regions from astrophysics analysis [61–67], typically model
dependent, are depicted in light shade. The other constraints
are from Refs. [34,68–76].
X. P. GENG et al. PHYS. REV. D 107, 112002 (2023)
112002-4
distance traveled by the neutrino, and Eis the neutrino
energy.
The expected event rate under this NSI model follows a
similar pattern to that of model I as illustrated in Figs. 2(a)
and 2(b) (cases C and D). The cross-section enhancement at
low recoil energy (∝E−2
r) discussed above also applies.
We note that the extra dependence on sin 2θ14 is absorbed
into ge;Ngν. The constraints on the εparameter depend on
Δm2
41 and g02sin22θ14. Studies of these interactions with
ν⊙would yield much higher sensitivities to the couplings
thanks to the large Lvalues compared to terrestrial sources.
Using a minimum-χ2analysis as discussed, no signifi-
cant signal of ν-eor ν-Nscattering is observed. The
90% CL bounds from CDEX-10 ν⊙analysis are shown
in Fig. 4, at the selected parameters Δm2
41 ¼ð10 keVÞ2
and g02sin22θ14 ¼10−4following earlier analyses of
Borexino [33,55].
Both the ν-eand ν-Nchannels provide improved
sensitivities to some regions of the parameter space. For
MA0<3MeV, the ν-escattering leads to better constraints
in the couplings, while for large MA0, the more stringent
limits come from ν-Nscattering. The CDEX-10 results
from the ν-escattering improve over the Borexino bounds
[33,55] on the kinetic mixing parameter εin MA0<
50 keV. The upper limits at 90% CL of ε<2.89 ×
10−10 for MA0¼1keV are derived for model II. The
limits represent the most sensitive laboratory constraints
for light dark photons with mass MA0<1eV. Unlike
earlier experiments following conventional dark photon
analysis [28,78–81] where the sensitivities are limited by
the detector threshold, the results from CDEX-10 under the
extended model open a new window for the research of an
extremely low-mass dark photon not covered by other
laboratory, cosmological, and astrophysical bounds. In
particular, the results from our analysis are complementary
to the astrophysical bounds from the Sun/Globular Clusters
which are model specific and can be evaded [33] if the νs’s
are more massive than ∼10 keV or are not produced in
a significant amount in the early Universe, or are chame-
leonlike, while our results will be robust against these
variations.
IV. SUMMARY
In this paper, we report results on the searches of
nonstandard neutrino (both active or sterile) interactions
with the dataset corresponding to 205.4-kg · day exposure
from the CDEX-10 experiment. No significant signal is
observed, and the measured event rates are translated into
upper limits on the couplings of two beyond-SM NSIs
using ν⊙as a probe. One model postulates a Uð1ÞB–L
gauge-boson-induced interaction between active neutrinos
and electron/nucleus and another a kinetically mixed dark-
photon-induced interaction between sterile neutrino and
electron/nucleus. The most stringent constraint among
solid-state detector-based experiments that use solar neu-
trino as a source is placed on the Uð1ÞB–Lgauge boson with
mass MA0<1keV. A new parameter space of εon a dark
photon for MA0<1eV at some benchmark values of Δm2
41
and g02sin22θ14 is probed. Our results extend the reach in
these NSI models in laboratory measurements, and espe-
cially extend the sensitivity reach in the searches of a dark
photon to extremely low mass.
ACKNOWLEDGMENTS
We would like to thank Joachim Kopp and Pedro
A. N. Machado for useful discussions. This work was
supported by the National Key Research and Develop-
ment Program of China (Grants No. 2017YFA0402200
and No. 2022YFA1605000) and the National Natural
Science Foundation of China (Grants No. 12175112,
No. 12005111, and No. 11725522).
10-24 10-20 10-15 10-10 10-5 100
10-15
10-10
10-5
FIG. 4. Constraints on light A0gauge bosons kinetically mixed
with the photon as a function of the A0mass and the kinetic
mixing parameter ε, at the benchmark values of Δm2
41 ¼
ð10 keVÞ2and g02sin22θ14 ¼10−4, which follow earlier phe-
nomenological interpretations of Borexino data [55] by Ref. [33].
The 90% CL limits from CDEX-10 ν⊙analysis are shown in red,
where the solid and dashed lines represent ν-eand ν-N,
respectively. The gray lines (CDEX-10) represent previous
CDEX-10 constraints on ϵusing the same dataset under a
different theoretical framework [28]: The solid and dashed
lines stand for DM and solar dark photon, respectively. The
Sun/Globular Clusters bounds marked (*) are valid only for
νs≤10 keV [33]. Excluded regions from astrophysics analysis
[33,61–67], typically model dependent, are depicted in light shade.
The other laboratory constraints are from Refs. [28,55,77–81].
SEARCH FOR EXOTIC INTERACTIONS OF SOLAR NEUTRINOS …PHYS. REV. D 107, 112002 (2023)
112002-5
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