aainstitutetext: Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117
Heidelberg, Germanybbinstitutetext: Preussen Elektra GmbH, Kernkraftwerk
Brokdorf, Osterende, 25576 Brokdorf, Germany

<EMAIL_ADDRESS>
# Novel constraints on neutrino physics beyond the standard model from the
CONUS experiment

H. Bonet a A. Bonhomme a C. Buck b K. Fülber a J. Hakenmüller a G. Heusser a
T. Hugle a M. Lindner a W. Maneschg a T. Rink a H. Strecker b and R. Wink

###### Abstract

The measurements of coherent elastic neutrino-nucleus scattering (CE$\nu$NS)
experiments have opened up the possibility to constrain neutrino physics
beyond the standard model of elementary particle physics. Furthermore, by
considering neutrino-electron scattering in the keV-energy region, it is
possible to set additional limits on new physics processes. Here, we present
constraints that are derived from Conus germanium data on beyond the standard
model (BSM) processes like tensor and vector non-standard interactions (NSIs)
in the neutrino-quark sector, as well as light vector and scalar mediators.
Thanks to the realized low background levels in the Conus experiment at
ionization energies below $1\,\mathrm{keV}$, we are able to set the world’s
best limits on tensor NSIs from CE$\nu$NS and constrain the scale of
corresponding new physics to lie above $360\,\mathrm{GeV}$. For vector NSIs,
the derived limits strongly depend on the assumed ionization quenching factor
within the detector material, since small quenching factors largely suppress
potential signals for both, the expected standard model CE$\nu$NS process and
the vector NSIs. Furthermore, competitive limits on scalar and vector
mediators are obtained from the CE$\nu$NS channel at reactor-site which allow
to probe coupling constants as low as $5\cdot 10^{-5}$ of low mediator masses,
assuming the currently favored quenching factor regime. The consideration of
neutrino-electron scatterings allows to set even stronger constraints for
mediator masses below $\sim 1\,\mathrm{MeV}$ and $\sim 10\,\mathrm{MeV}$ for
scalar and vector mediators, respectively.

##  1 Introduction

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a standard model
(SM) process of elementary particle physics that was predicted shortly after
the discovery of the $Z$-boson Freedman:1973yd ; Tubbs:1975jx ; Drukier:1983gj
. After over forty years, first observations of this process were reported by
the Coherent Collaboration, using a pion-decay-at-rest ($\pi$DAR) source in
combination with scintillation and liquid noble gas detectors COHERENT:2017ipa
; COHERENT:2020iec . The Conus experiment pursues detecting this interaction
channel with reactor electron antineutrinos and recently published first
limits CONUS:2020skt . The underlying data were acquired with low background
germanium detectors located at 17.1 m distance from the reactor core center of
the 3.9 GW (thermal power) nuclear power plant in Brokdorf, Germany.

So far, no deviations from the SM prediction have been observed in the
operational experiments. However, new possibilities to search for physics
beyond the standard model (BSM) have already triggered various
phenomenological investigations Kosmas:2017tsq ; Billard:2018jnl ;
Khan:2019cvi ; Papoulias:2019txv . Together with their expected SM
interactions, any new interaction of neutrinos can play an important role in a
wide range of physics branches: from cosmology to the smallest scales of
nuclear and particle physics. In an astronomical context, they play a key role
in the evolution of stellar collapses Freedman:1977xn ; Amanik:2006ad  and
might influence stellar nucleosynthesis Balasi:2015dba . In addition, with
neutrino detection via CE$\nu$NS at hand, flavor-independent astronomy with
supernova neutrinos becomes feasible Amaya:2011sn ; Brdar:2018zds ;
Agnes:2020pbw  and thus allows to investigate the interior of dense objects as
well as stellar evolution in detail. The next-generation direct detection dark
matter experiments will face an irreducible background, the so-called
neutrino-floor, which is caused by atmospheric, solar and supernova remnant
neutrinos that coherently scatter in such detectors Monroe:2007xp ;
Gutlein:2010tq . From the perspective of neutrino physics, this opens up new
possibilities as new neutrino interactions might manifest themselves in this
“background” as well Cerdeno:2016sfi ; Bertuzzo:2017tuf ; Link:2019pbm ;
Boehm:2018sux .

In a nuclear and particle physics context, even without any new physics
contributions, CE$\nu$NS can allow for a determination of the neutron density
distribution of a target nucleus Patton:2012jr ; Coloma:2020nhf ;
VanDessel:2020epd  as well as the weak mixing angle in the unexplored MeV
regime Lee:2015yht ; Canas:2018rng ; Fernandez-Moroni:2020yyl .

For BSM searches, CE$\nu$NS detectors can be used to search for non-standard
neutrino-quark interactions (NSIs) Barranco:2005yy ; Barranco:2007tz ;
Barranco:2011wx ; Lindner:2016wff ; Bischer:2018zbd ; Dev:2019anc  and to
investigate potential electromagnetic properties of the neutrino Vogel:1989iv
; Giunti:2014ixa ; Cadeddu:2018dux ; Miranda:2019wdy , e.g. finite magnetic
moments or a millicharge. Being at lower energy scales than typical collider
experiments, CE$\nu$NS experiments complement their BSM searches and might
result in either competitive or even stronger bounds for light mediators
deNiverville:2015mwa ; Dent:2016wcr . In particular, investigations of light
scalars and/or axion-like particles Farzan:2018gtr ; Dent:2019ueq ;
AristizabalSierra:2020rom , and light vectors Dutta:2019eml ; Aguilar-
Arevalo:2019zme ; Cadeddu:2020nbr ; Miranda:2020zji , e.g. dark photons, take
advantage of this new channel. Even searches for new fermions seem possible
within the context of CE$\nu$NS measurements Brdar:2018qqj .

More generally, a high statistics CE$\nu$NS measurement can be used to
determine the flux of a neutrino source precisely. Regarding the flux
anomalies reported from several short-baseline experiments and the possible
eV-mass sterile neutrino solution Aguilar:2001ty ; Mention:2011rk ;
Boser:2019rta , CE$\nu$NS might contribute further knowledge, especially since
it provides flavor-blind and energy-threshold-free information about the
source’s (anti)neutrino spectrum Formaggio:2011jt ; Dutta:2015nlo ;
Canas:2017umu ; Blanco:2019vyp ; Miranda:2020syh . Particularly at nuclear
reactors, small (and therefore simpler to integrate) CE$\nu$NS sensitive
devices could help in monitoring their power and flux and, in the future, even
determine a reactor’s antineutrino spectrum below $1.8\,\mathrm{MeV}$, which
is usually limited by the threshold energy of the used detection channel, i.e.
inverse beta-decay (IBD). In this way, neutrino physics might help in reactor
safeguarding and contribute to nuclear non-proliferation Hagmann:2004uv ;
Bernstein:2019hix ; Bowen:2020unj .

All the above mentioned SM and BSM possibilities in combination with
improvements in detector and background suppression techniques have made
CE$\nu$NS measurements a feasible and promising endeavor both at neutrino
$\pi$DAR sources and nuclear reactors. While the Coherent Collaboration is
preparing the operation of further detector systems with different target
elements at a $\pi$DAR neutrino source, there are many more experimental
attempts to measure CE$\nu$NS with electron antineutrinos emitted from nuclear
reactors: Connie Aguilar-Arevalo:2016khx , Miner Agnolet:2016zir , Ncc-1701 at
Dresden-II Colaresi:2021kus , Neon Choi:2020gkm , $\nu$-cleus Strauss:2017cuu
, $\nu$Gen Belov:2015ufh , Red-100 Akimov:2019ogx , Ricochet Billard:2016giu
and Texono Wong:2004ru . In these reactor experiments, different detection
technologies are used, e.g. charged-coupled devices (CCDs)
FernandezMoroni:2014qlq , cryogenic calorimeters Strauss:2017cam , high-purity
germanium (HPGe) crystals Bonet:2020ntx , liquid noble gas detectors
Chepel:2012sj  as well as scintillating crystals Choi:2020qcj . In this way,
the field of CE$\nu$NS is going to be probed with the full range of recent
detector technologies and different target nuclei – each with its own
particular advantages and complementarities – allowing to expect interesting
results from SM as well as BSM investigations.

As a part of the experimental efforts in this direction, we present here the
first BSM results derived from the Conus Run-1 data. We use a very similar
analysis procedure to the one employed for the experiment’s first CE$\nu$NS
limit determination CONUS:2020skt  and apply it to common BSM models that have
already been investigated in the context of other CE$\nu$NS measurements. In
particular, we show bounds on tensor and vector NSIs as well as simplified
light vector and scalar mediator models. For the latter two, we deduce bounds
from neutrino scattering off electrons and off nuclei.

This paper is structured as follows: In Section 2 we describe the analysis
method that is used for the BSM models in the course of this paper. Next to a
general introduction of the Conus set-up, we give an overview of the analysis
procedure as well as systematic uncertainties that underlie this
investigation. We further introduce two datasets that are chosen for the two
scattering channels under study, i.e. neutrino-nucleus and neutrino-electron
scattering. Subsequently, we show the results of the performed investigations
in Section 3. Limits on tensor and vector NSIs are presented and in the
context of light vector and scalar mediator searches, we derive bounds from
electron scattering in the ionization energy region between $2$ and
$8\,\mathrm{keV}_{ee}$.111 The notations “eVee” and “eVnr”, will be used in
the following as a shorthand notation to distinguish ionization energy,
denoted as $ee$ (as a reference to “electron equivalents”), and nuclear recoil
energy, denoted as $nr$. Finally, in Section 4 we conclude and give an outlook
on the various BSM investigations that will become feasible with Conus and the
next generation of CE$\nu$NS experiments.

##  2 Datasets, experimental framework and analysis method

For the analysis presented here, we use the Conus Run-1 data and employ a
binned likelihood analysis to derive limits on parameters of the considered
BSM models. In addition to the Run-1 dataset used for the CE$\nu$NS analysis
described in Ref. CONUS:2020skt , we work with a second Run-1 dataset at
energies between $2$ and $8\,\mathrm{keV}_{ee}$, which exhibits longer data
collection periods for the BSM channels that are sensitive to neutrino-
electron scattering. The details of both datasets as well as the likelihood
analysis are laid out in the following subsections.

###  2.1 Datasets and the experimental framework of the CONUS experiment

The datasets used in this BSM analysis were gathered during Run-1 (Apr 01 -
Oct 29, 2018) of the Conus experiment which is operated at the commercial
nuclear power plant in Brokdorf, Germany. At the center of the nuclear power
plant is a single-unit pressurized water reactor that is operated at a maximal
thermal power of 3.9 GW and serves as an intense electron antineutrino source
at the 17m-distant experimental site. The expected antineutrino spectrum is a
typical reactor spectrum, dominated by the contribution of the four isotopes
235U, 238U, 239Pu and 241Pu Hayes:2016qnu , with all of the neutrinos having
energies of less than $\sim\\!10\,\mathrm{MeV}$. To describe the antineutrino
emission spectrum from the reactor, we start from the predicted antineutrino
spectra by Huber and Müller Huber:2011wv ; Mueller:2011nm  and correct for the
$5\,\mathrm{MeV}$-bump observed in experimental data An:2016srz . The relative
contribution of the different isotopes can be accounted for by weighting the
different isotopes according to their time-dependent fission fractions, which
are provided to us by the reactor operating company Preussen Elektra GmbH, cf.
Table 1.

Detector |  235U [%] |  238U [%] |  239Pu [%] |  241Pu [%] |  $\bar{P}_{\mathrm{th}}$ [%]
---|---|---|---|---|---
C1 | 60.3; 56.8 | 7.1; 7.2 | 27.0; 29.9 | 5.4; 6.1 | 92.33; 89.80
C2 | 63.8; 56.9 | 7.1; 7.2 | 24.2; 29.8 | 4.9; 6.1 | 92.70; 90.12
C3 | 57.2; 56.8 | 7.2; 7.2 | 29.7; 29.9 | 6.0; 6.1 | 88.79; 90.10
Table 1: Average fission fractions of the most relevant isotopes in the
reactor antineutrino spectrum and average reactor powers
$\bar{P}_{\mathrm{th}}$ in terms of the reactor’s maximal thermal power of
$3.9$ GW for standard/extended datasets of Conus Run-1. Individual values are
attributed to each detector due to their specific data collection periods.

This reactor spectrum above the $1.8\,\mathrm{MeV}$ threshold of IBD
experiments determines the neutrino spectrum for all processes associated with
nucleus scattering. For the electron scattering channels that we analyze, also
the low-energy part (below $1.8\,\mathrm{MeV}$) of the spectrum becomes
relevant for which we use the simulation data provided by Ref. Kopeikin:2003gu
. These simulations for the different isotopes can be weighted by the fission
fractions and normalized to the total number of neutrinos emitted over the
whole spectrum, of which there are on average $\sim\\!7.2$ per fission, cf.
Ref. Beda:2007hf . To determine the total flux of antineutrinos that can
interact with the Conus detectors, we can use the total number of fissions per
second derived from the reactor thermal power, as every fission releases about
$200\,\mathrm{MeV}$ of energy (cf. Ref. Ma:2012bm  for details and exact
isotope specific values). This leads to a total antineutrino flux at the
experimental site of $2.3\cdot 10^{13}$ s-1 cm-2. The influence of the shape
uncertainties, i.e. the covariance matrix of the neutrino spectrum as provided
by Ref. An:2016srz , was investigated in the context of the Conus CE$\nu$NS
analysis CONUS:2020skt  and turned out to be negligible in our case.
Therefore, we do not include them in the present analysis.

Figure 1:  Position of the Conus detector set-up within the building of the
nuclear power plant at Brokdorf, Germany. It is located under the spent fuel
storage pool at 17.1 m distance to the 3.9 GW (thermal power) reactor core.
The vertical position of the set-up coincides approximately with the reactor
core’s center. The enlarged image shows the set-up at its experimental site.
Within the shown stainless steel cage, layers of lead as well as pure and
borated polyethylen serve as passive shield around the embedded four HPGe
detectors against external radiation and other background sources. Further, it
includes plastic scintillator plates equipped with photomultiplier tubes which
are used as muon veto.

Besides the immense reactor flux and the corresponding spectral distribution
of antineutrinos, the achieved background level with the deployed shield is
another cornerstone of the whole experimental framework. The shield is
extremely compact, with a volume of only 1.65 m3 and a mass of 11 tonnes, and
exhibits an onion-like structure. It consists of lead bricks, borated and non-
borated polyethylene plates, and plastic scintillator plates equipped with
photomultiplier tubes serving as an active muon anticoincidence system (muon
veto). Around the layers, a protective stainless steel cage helps fulfilling
the safety requirements. The shield design is based on the long-time
experience with low background techniques at MPIK (e.g. Refs. Heusser:1995wd ;
Heusser:2015ifa ), while being optimized to the experimental site at shallow
depth next to a reactor core. The location of the CONUS detector and the
dimension of the whole set-up within the nuclear power plant are illustrated
in Figure 1.

The influence of possible reactor-correlated background types was confirmed to
be negligible via dedicated neutron and $\gamma$-ray measurement campaigns.
These were supported by validated background Monte Carlo (MC) simulations that
incorporated a large fraction of the reactor geometry surrounding the
experimental site Hakenmuller:2019ecb . Thus, the background to the BSM
analyses is uncorrelated to the reactor thermal power. It is described like in
the CE$\nu$NS investigation by MC simulations. For the BSM analyses of both
scattering channels, the background model is almost identical to the one used
in the CE$\nu$NS publication, cf. Ref. CONUS:2020skt . Only small adjustments
to the background model have been made for the extended datasets, which are
used for the electron scattering channels. In that context due to the extended
region of interest (ROI) to higher energies, systematic uncertainties on the
spectral shape of the background model was considered in order to account for
uncertainties regarding the production rate of cosmogenic induced isotopes as
well as surface contamination on the Ge diodes. Details of the applied
background model and its uncertainties can be found in a dedicated background
description of the Conus experiment, cf. Ref. CONUSbackground . In the energy
window of $500$ to $1000\,\mathrm{eV}_{ee}$, just above the ROI for CE$\nu$NS
studies, the Conus detectors achieve background levels of a few
$10\,\mathrm{\,counts\,kg^{-1}\,d^{-1}\,keV}_{ee}^{-1}$, while having an
effective overburden of 24 m of water-equivalent (m w.e.) only.

To detect the antineutrinos that cross the shield, Conus uses four 1 kg-sized
point-contact HPGe spectrometers with sub-keVee energy thresholds. A full
description can be found in Ref. Bonet:2020ntx . The four detectors have a
total active mass of $(3.73\,\pm\,0.02)\,$kg and provide they necessary
characteristics for a CE$\nu$NS measurement at a commercial reactor site:
ultra-low noise levels and thus very low energy thresholds, i.e. $\lesssim
300\,\mathrm{eV}_{ee}$, low concentrations of radioactive contamination as
well as electrically powered cryocoolers. Within a CE$\nu$NS process, the
induced nuclear recoil releases heat and ionization electrons that might be
collected by an appropriate detector for signal formation. However, in the
present case, only the ionization energy part is registered by the HPGe
detectors, resulting in an energy that is suppressed by $75-85\%$ compared to
the original recoil energy. This phenomenon is commonly referred to as
‘quenching’. Consequently, this makes detecting CE$\nu$NS signals even more
difficult. To take the effect of quenching into account, we apply the widely
used Lindhard model Lindhard:1961zz , modified with an adiabatic correction
Scholz:2016qos . Its associated parameter $k$ roughly corresponds to the
quenching factor at nuclear recoils of $\sim 1\,\mathrm{keV}_{nr}$. One recent
measurement indicates that quenching deviates from this description especially
at ionization energies of $\sim\\!250\,\mathrm{eV}_{ee}$ and below, cf. Ref.
Collar:2021fcl . Thus, an accurate determination of the quenching factor
cannot only support CE$\nu$NS measurements, but also affects BSM studies
Liao:2021yog  as it appears in any process that involves scattering off a
nucleus. So far, there is a variety of measurements for the quenching factor
in germanium with larger systematic uncertainties that still leave enough room
to constitute the dominating source of uncertainty for our BSM analyses here.
To account for this uncertainty, we always present the results for different
quenching factors which cover the range of currently available experimental
data.

Generally, the Conus data acquisition is divided into reactor On and reactor
Off periods as well as periods reserved for commissioning and optimization.
Each dataset then has been defined individually according to the stability of
environmental parameters like air temperature. For the details of this data
selection procedure we refer to Ref. Bonet:2020ntx . In the present analysis,
we use data of the first acquisition period which we refer to as Run-1
dataset. For this dataset, the Conus-4 (C4) detector is excluded due to a
temporarily appearing artifact, cf. Ref. CONUS:2020skt . Besides neutrino-
nucleus scattering, where only the region below $1\,\mathrm{keV}_{ee}$ is
important, we also analyze neutrino-electron scattering at energies between
$2$ and $8\,\mathrm{keV}_{ee}$. We limit our analysis to this energy interval
because of two reasons: First, we are looking at signals that emerge as
broader spectral contribution above the continuum of the spectrum. The
selected region is line-free and naturally confined by x-ray peaks around
$\sim 1\,\mathrm{keV}$ and $\sim 10\,\mathrm{keV}$, which are due to K- and
L-shell transitions in decays of Ge-related isotopes. These isotopes were/are
produced by cosmic activation above ground and partially in-situ at the
experimental site, as well as via sporadically deployed artificial neutron
calibration sources. Second, the new ROI is not affected at all by potential
noise, that is correlated with the air temperature, cf. Ref. Bonet:2020ntx ,
and which caused an exclusion of parts of the data from our first CE$\nu$NS
analysis in the sub-keV regime. Thereby, we can increase the total lifetime of
the extended dataset, compared to the CE$\nu$NS dataset, by a factor of 3.1
for On and a factor of 2.5 for Off periods. The specifications of all final
datasets after data selection and cuts, used for the BSM analysis in this
paper, are depicted in Table 2.

Scattering channel | Detector |  On [d] |  Off [d] | ROI [eVee]
---|---|---|---|---
| C1 | 96.7 | 13.8 | 276 - 741
$\bar{\nu}_{e}+A(Z,N)$ | C2 | 14.6 | 13.4 | 281 - 999
| C3 | 97.5 | 10.4 | 333 - 991
| C1 | 215.4 | 29.6 | 2013 - 7968
$\bar{\nu}_{e}+e$ | C2 | 184.6 | 32.2 | 2006 - 7990
| C3 | 248.5 | 31.7 | 2035 - 7989
Table 2: Lifetimes for reactor On and Off periods together with the regions of
interest (ROIs) for the different detectors in both scattering channels during
Run-1, specifying the datasets that are investigated for BSM signatures in
this work.

###  2.2 Standard model expectation, likelihood function and systematic
uncertainties

The following investigation relies on a similar analysis chain as the
CE$\nu$NS investigation in Ref. CONUS:2020skt . In this way, we are able to
determine realistic bounds on the individual model parameters, while including
all relevant experimental uncertainties. Here we briefly introduce the SM
expectations, the performed likelihood procedure and give an overview of the
included systematic uncertainties.

The main ingredient of our analysis is a binned likelihood ratio test, cf.
Refs. Wilks:1938dza ; Cowan:2010js ; Lista:2016chp . We fix the individual BSM
parameters and compare their likelihood value to the one of the null
hypothesis, which includes the SM signal of neutrino-nucleus as well as
neutrino-electron scattering. Hence, CE$\nu$NS and neutrino-electron
scattering are either modified through interference with new BSM physics or,
in the case they are independent, simply appear as an additional background
component in the BSM analysis. From a simulation of the corresponding test
statistic (toy MC) we extract limits on these model parameters at 90 %
confidence level (C.L.).

The differential cross section of the SM predicted CE$\nu$NS process is given
by, cf. Ref. Freedman:1973yd ,

$\displaystyle\frac{\mathrm{d}\sigma}{\mathrm{d}T_{A}}(T_{A},E_{\nu})=\frac{G_{F}^{2}}{\pi}\mathcal{Q}^{2}_{W}m_{A}\left(1-\frac{m_{A}T_{A}}{2E^{2}_{\nu}}\right)F^{2}(T_{A})\,,$
(1)

with the nuclear recoil energy $T_{A}$, Fermi’s constant $G_{F}$, the nuclear
mass $m_{A}$ and the neutrino energy $E_{\nu}$. We use the nuclear
charge222Sometimes, the weak nuclear charge is defined as
$\mathcal{Q}_{W}=(1-4\sin^{2}\theta_{W})Z-N$ such that the prefactor of Eq.
(1) includes an additional factor of $\frac{1}{4}$.

$\displaystyle\mathcal{Q}_{W}=g^{p}_{V}Z+g^{n}_{V}N=\left(\frac{1}{2}-2\sin^{2}\theta_{W}\right)Z-\frac{1}{2}N\,,$
(2)

with the Weinberg angle $\theta_{W}$, the number of protons $Z$ and the number
of neutrons $N$ in the target nucleus, respectively. Further, the nuclear form
factor $F(T_{A})$ describes the degree of deviation from scattering off a
point-like object.It is approximated with unity for the rest of this analysis
which is justified by the small momentum transfer of reactor antineutrinos.
Thus, at a reactor-site the interaction of antineutrinos with the target
nuclei can be seen as a process in the fully coherent regime. At higher
energies, i.e. at $\pi$DAR sources, the loss of coherent enhancement is
usually described via the form factor parameterization by Helm Helm:1956zz  or
by Klein and Nystrand Klein:1999qj .

Though the (anti)neutrino-electron scattering process
$\bar{\nu}_{e}e^{-}\rightarrow\bar{\nu}_{e}e^{-}$ contributes only as a small
background to the CE$\nu$NS ROI, it is relevant for our analysis of the light
mediator electron channels at higher energies. The corresponding SM cross
section is found to be, cf. Ref. Giunti:2007ry ,

$\displaystyle\frac{\mathrm{d}\sigma}{\mathrm{d}T_{e}}(T_{e},E_{\nu})=\frac{G_{F}^{2}m_{e}}{2\pi}\Big{[}\left(g_{V}+g_{A}\right)^{2}+\left(g_{V}-g_{A}\right)^{2}\left(1-\frac{T_{e}}{E_{\nu}}\right)+\left(g_{A}^{2}-g_{V}^{2}\right)\frac{m_{e}T_{e}}{E_{\nu}^{2}}\Big{]}\,.$
(3)

Herein, $T_{e}$ stands for the electron recoil, and
$g_{V}=\frac{1}{2}+2\sin^{2}\theta_{W}$ and $g_{A}=-\frac{1}{2}$ for the
effective vector and axial-vector couplings, respectively.333Generally, the
vector and axial-vector couplings to the Z boson are defined as
$g_{V}^{f}=I_{3}^{f}-2q^{f}\sin^{2}\theta_{W}$ and $g_{A}=I_{3}^{f}$,
respectively. For example, in the case of a muon one obtains
$g_{V}^{\mu}=-\frac{1}{2}+2\sin^{2}\theta_{W}$ and $g_{A}^{\mu}=-\frac{1}{2}$
which reflects a pure neutral current interaction. In case of an electron,
there is an additional W boson exchange that enhances the couplings, i.e.
$g_{V,A}\rightarrow g_{V,A}+1$. For antineutrinos, the charged current is
mediated via a s-channel diagram (instead of a t-channel), which further leads
to $g_{A}\rightarrow-g_{A}$. In the case of neutrino-electron scattering,
atomic binding effects for recoil energies comparable to atomic binding
energies have to be taken into account. We follow the procedure proposed in
Ref. Mikaelyan:2002nv  and apply electron binding energies of germanium taken
from Ref. Perkins:1991 .

Both interaction channels exhibit a maximum recoil energy obtained from pure
forward scattering,

$\displaystyle
T^{\mathrm{max}}_{x}=\frac{2E_{\nu}^{2}}{m_{x}+2E_{\nu}}\,\quad\text{for
}x=\\{e,A\\}\,.$ (4)

Note that electron recoils are, contrary to CE$\nu$NS, not affected by
quenching, and, thus, the maximal detectable energy, i.e. recoil energy
subtracted by the electron’s binding energy, lies far above the analyzed ROIs.
For antineutrinos emitted from a reactor core, i.e. $E_{\nu}\sim
10\,\mathrm{MeV}$, we obtain maximal recoil energies of $\sim
9.9\,\mathrm{MeV}$ and $\sim 3.0\,\mathrm{keV}$ for electrons and germanium
nuclei, respectively. As a result, SM neutrino-electron scattering features a
flat contribution in our ROI whereas the CE$\nu$NS signal rises towards lower
energies with a shift in energy according to the underlying quenching factor.

Both cross sections have to be convoluted with the reactor antineutrino
spectrum $\frac{\mathrm{d}N}{\mathrm{d}E_{\nu}}$, such that the final number
of events is given by

$\displaystyle N^{\rm SM}_{x}=t\cdot\Phi^{*}\cdot
N_{x}^{\mathrm{Ge}}\sum_{i}^{N_{\mathrm{bins}}}\int_{T_{i}-0.5\Delta
T}^{T_{i}+0.5\Delta
T}\mathrm{d}T\int_{E_{\mathrm{min}}}^{E_{\mathrm{max}}}\mathrm{d}E_{\nu}\frac{\mathrm{d}N}{\mathrm{d}E_{\nu}}(E_{\nu})\left(\frac{\mathrm{d}\sigma}{\mathrm{d}T}\right)_{x}\\!(T,E_{\nu})$
(5)

with the experimental lifetime $t$, $N_{x}^{\mathrm{Ge}}$ for $x=\\{e,A\\}$ as
the number of target electrons and nuclei respectively, $N_{\mathrm{bins}}$
the number of spectral bins and $T_{i}$ the energy at the bin center with the
bin width $\Delta T$. The ‘reduced’ reactor flux incorporates all reactor-
related quantities and is given by

$\displaystyle\Phi^{*}=\frac{P_{\mathrm{th}}}{4\pi d^{2}\bar{E}}\,,$ (6)

with the thermal reactor power $P_{\mathrm{th}}$, the detector’s distance to
the reactor $d$ and the average energy release per fission $\bar{E}$, cf.
Section 2.1. The integral over the applied reactor model yields the number of
neutrinos emitted per fission and, multiplied with $\Phi^{*}$, gives the
expected neutrino flux in units of cm-2 s-1 at the experimental site. Special
care has to be taken for the conversion of nuclear recoil energy into
detectable signal (ionization energy), which depends on dissipation processes
in the chosen detector technology and target material. To describe this
quenching process in germanium, cf. Section 2.1, we select three
representative $k$-parameter values $k=\\{0.12,0.16,0.20\\}$, i.e. spanning
the available measured range in the keVee regime Jones:1971ya ; Jones:1975zze
; Messous:1995dn ; Barbeau:2007qi ; Barker:2012ek ; Scholz:2016qos ;
Collar:2021fcl . Thereby we make a substantial uncertainty appearing in our
analysis explicit. Finally, the signal expectation has to be convolved with
the individual detector response, i.e. the energy resolution and the
electronic detection efficiency. For details of the HPGe detectors used within
Conus, we refer to our detector publication Bonet:2020ntx .

In our likelihood procedure, On and Off spectra are fitted simultaneously and
additional knowledge on parameters is represented by Gaussian pull terms,

$\displaystyle-2\log\,\mathcal{L}=-2\log\,\mathcal{L}_{\rm
ON}-2\log\,\mathcal{L}_{\rm
OFF}+2\sum_{i}\frac{(\Theta_{i}-\Theta_{i}^{*})^{2}}{2\sigma_{i}^{2}}\,.$ (7)

Herein, the parameters $\Theta_{i}$ of the pull terms have central values
$\Theta_{i}^{*}$ and uncertainties $\sigma_{i}$. The individual detector’s
noise edge is fitted with an exponential shape parameterized by two free
parameters, $\Theta_{\rm thr_{1}}$ and $\Theta_{\rm thr_{2}}$. For the noise
edge description, we refined the exponential function used in Ref.
CONUS:2020skt  and extended the fit range slightly to lower energy thresholds.
The MC background model, which will be discussed in detail in a separate
publication, cf. Ref. CONUSbackground , represents the physical background
components and appears in the likelihood together with a factor
$\Theta_{b_{0}}$ that allows for an overall rescaling as well as two
additional uncertainties $\Theta_{b_{1,2}}$ allowing for small variations in
the shape of the background model. These additional degrees of freedom are
necessary to incorporate the uncertainties on the production rates of
cosmogenic induced isotopes as well as on detector surface effects, i.e. from
the thickness of the passivation layer. The latter especially influences the
spectral shape of the background contributions resulting from decays of
contaminants on the diode surface such as 210Pb. The corresponding
uncertainties do not exceed 5% and the energy spectrum of the background model
is allowed to vary within this range via a second order polynomial distorsion.
Overall, pull terms are assigned to each detector’s active volume, its
electronic detection efficiency $c_{\rm eff}$, its energy scale calibration
uncertainty $\Delta E$ and the reduced flux $\Phi^{*}$. The uncertainty of the
reduced neutrino flux $\Delta\Phi^{*}$ is found to be $\sim\\!3\,\%$,
depending on the detector and run, and is dominated by the uncertainty on the
reactor thermal power ($\Delta P=2.3\,\%$) Hakenmuller:2019ecb , the energy
released per fission and isotope (cf. Ref. Ma:2012bm ), as well as the
detector’s distance to the reactor core ($17.1\pm 0.1$) m and correlations
among fission fractions (cf. Ref. An:2016srz ). Summarizing the parameters
related to the reactor model as $\Theta_{\rm reactor}$ and the ones related to
the detector as $\Theta_{\rm det}$, we can write schematically:

$\displaystyle-2\log$ $\displaystyle\mathcal{L}_{\rm ON}(\Theta_{\rm
b_{0,1,2}},\Theta_{\rm thr_{1,2}},\Theta_{\rm reactor},\Theta_{\rm det},\Delta
E)\,,$ (8) $\displaystyle-2\log$ $\displaystyle\mathcal{L}_{\rm
OFF}(\Theta_{\rm b_{0,1,2}},\Theta_{\rm thr_{1,2}},\Theta_{\rm det},\Delta
E)\,.$

In Table 3, we provide an overview of the uncertainties that enter our
likelihood procedure and their approximate size.

Quantity |  Uncertainty or related parameter
---|---
background MC |  $\Theta_{b_{0}}$ (free), $\Theta_{b_{1},b_{2}}$ ($\leq 5\,\%$, uncertainty from background model)
noise threshold |  $\Theta_{\rm thr_{1}}$, $\Theta_{\rm thr_{2}}$ (free, uncertainty calculated via toy MC)
reduced neutrino flux $\Delta\Phi^{*}$ |  $\sim\\!3\,\%$
neutrino spectrum |  subdominant uncertainty (compared to quenching)
reactor On and Off duration |  negligible uncertainty
active mass |  $<1\,\%$
electronic detection efficiency $c_{\mathrm{eff}}$ |  $\leq 5\,\%$
energy calibration uncertainty $\Delta E$ |  $15\,\mathrm{eV}_{ee}$
quenching |  k (explicitly included)
Table 3: Overview of the quantities entering the likelihood and their
corresponding uncertainties. For details and further information see main
text.

Note that the quenching factor is not quoted with an uncertainty as it is the
overall dominating systematics and thus is explicitly taken into account by
deriving the limits for different $k$-values.

The signal hypotheses, which the likelihood compares to the experimental data,
are defined by the BSM models described in Section 3. They are implemented
through their corresponding cross sections. For the minimization of the
likelihood we use the iminuit package iminuit2020 ; minuit1975 , while the
whole analysis is set up within the SciPy framework ScientificComputing2007 ;
ScientificComputing2011 ; Scipy2020 ; Matplotlib2007 ; Ipython2007 ; Numpy2020
; Pandas2010 ; JupyterLab . The extensive cluster computations are done with
the help of the software package MPI for Python MPI4Py2005 ; MPI4Py2008 .

##  3 Constraints on beyond the standard model neutrino physics

Now, we have everything at hand to investigate the Conus Run-1 dataset with
respect to BSM signatures and compare our results to limits obtained from
other CE$\nu$NS experiments. In particular, we are going to deduce constraints
for tensor and vector NSIs as well as simplified light vector and scalar
mediators. For the latter cases, we can additionally analyze the electron
channels of these models with an extended dataset at energies between 2 and
$8\,\mathrm{keV}_{ee}$.

###  3.1 Non-standard interactions

A rather model-independent probe of various BSM neutrino physics scenarios are
so-called NSIs in the neutrino-quark sector, which are an extension of the
neutral current with effective four-fermion operators, generally assuming new
mediators that are much heavier than the SM gauge bosons Dev:2019anc . Since
the heavy mediators are conventionally integrated out, the new couplings are
defined in terms of Fermi’s constant $G_{F}$ analogously to weak interactions
at low energy. In general, these new couplings can be flavor-preserving
$\epsilon_{\alpha\alpha}$ and/or flavor-violating $\epsilon_{\alpha\beta}$
with $\alpha\neq\beta$ and $\alpha,\beta=\\{e,\mu,\tau\\}$ being the lepton
flavor indices. Searches of these new neutrino interactions are relevant since
they may affect neutrino oscillations Farzan:2017xzy  and even other physics
branches like cosmology Du:2021idh  or astrophysics Amanik:2006ad ;
Stapleford:2016jgz . NSIs in their original definition can be studied since
they enter the SM CE$\nu$NS cross section via a modified or an additional weak
nuclear charge Barranco:2005yy ; Barranco:2007tz ; Lindner:2016wff . More
recently, they have been investigated on more general grounds, i.e. in the
context of so-called general neutrino interactions (GNIs)
AristizabalSierra:2018eqm ; Bischer:2019ttk . As Conus operates in the fully
coherent regime, the subtleties that can arise for the form factor in BSM
models, cf. Ref. Hoferichter:2020osn , are not of relevance to our analysis
here.

####  3.1.1 Tensor-type interaction

Figure 2: Top: Expected tensor NSI signals of detector C1 for a quenching
parameter of $k=0.16$ and different coupling values from all quadrants in
comparison to the standard CE$\nu$NS signal. Due to a different chiral
structure, additional tensor NSIs can only enhance the expected signal.
Bottom: Allowed regions (at 90% C.L.) of tensor NSI couplings
$\epsilon^{u\mathrm{T}}_{ee}$ and $\epsilon^{d\mathrm{T}}_{ee}$ deduced from
the Run-1 Conus dataset. The exemplary points of the upper plot are marked
with crosses, where bold crosses indicate couplings that are (almost)
excluded, i.e. the solid lines from above. Normal crosses refer to coupling
combinations that cannot be excluded with the current dataset, i.e. the dashed
lines. In addition, constraints (90% C.L.) obtained from Coherent data are
plotted for comparison, cf. Ref. Kosmas:2017tsq .

Non-standard neutrino-quark interactions of tensor-type can arise in
generalizations of the conventional vector NSI approach Barranco:2011wx  and
naturally occur in the context of GNIs AristizabalSierra:2018eqm ;
Bischer:2019ttk . Furthermore, they might also be associated with
electromagnetic properties of neutrinos Healey:2013vka ; Papoulias:2015iga .
Here, we assume the existence of new tensor-type interactions between
neutrinos and quarks which are induced by an operator of the form

$\displaystyle\mathcal{O}^{q\mathrm{T}}_{\alpha\beta}=\left(\bar{\nu}_{\alpha}\sigma^{\mu\nu}\nu_{\beta}\right)\left(\bar{q}\sigma_{\mu\nu}q\right)+\text{h.c.}\,,$
(9)

with $q$ denoting the first generation of quarks $q=\\{u,d\\}$ and
$\alpha,\beta=\\{e,\mu,\tau\\}$ being the lepton flavor indices. Due to a
different chiral structure, there is no possibility of destructive
interference with the SM channel. The corresponding couplings to quarks can be
combined into a new nuclear charge in equivalence to the SM weak charge
appearing in the CE$\nu$NS cross section of Eq. (1). Thus, in our case we have

$\displaystyle\mathcal{Q}_{\rm
NSI}^{\mathrm{T}}=\left(2\epsilon^{u\mathrm{T}}_{\alpha\beta}+\epsilon^{d\mathrm{T}}_{\alpha\beta}\right)Z+\left(\epsilon^{u\mathrm{T}}_{\alpha\beta}+2\epsilon^{d\mathrm{T}}_{\alpha\beta}\right)N\,,$
(10)

with the lepton flavor indices $\alpha,\beta$ as well as $Z$ and $N$
representing the respective number of protons and neutrons in the target
nucleus. Note that in contrast to the SM case, cf. Eq. (1) and Eq. (2), here,
as well as in the other BSM models, the proton number does not get weighted
with a small prefactor. Thus, the cross section does not necessarily scale
with the characteristic dependence on the squared neutron number. Although
flavor-changing tensor-type interactions can in principal appear and are for
example tested at $\pi$DAR sources Kosmas:2017tsq , at reactor site we are
only able to probe couplings related to the electron flavor. Therefore, in
this analysis, we focus on flavor-diagonal couplings, i.e.
$\epsilon^{u\mathrm{T}}_{ee}$ and $\epsilon^{d\mathrm{T}}_{ee}$.

The new tensor-type interaction simply adds to the conventional CE$\nu$NS
cross section, resulting in, cf. Ref. Papoulias:2015iga ,

$\displaystyle\left(\frac{d\sigma}{dT_{A}}\right)=\left(\frac{d\sigma}{dT_{A}}\right)_{\rm
CE\nu NS}+\frac{4G^{2}_{F}}{\pi}{Q^{\mathrm{T}}_{\rm
NSI}}^{2}\,m_{N}\left(1-\frac{m_{A}T_{A}}{4E^{2}_{\nu}}\right)\,.$ (11)

Note the different kinematic factors between the CE$\nu$NS cross section in
Eq. (1) and Eq. (11) which allow the tensor NSI signal to extend to higher
energies. The upper plot of Figure 2 illustrates the modified signal
expectation in detector C1 due to additional tensor NSIs in comparison to the
SM case. It shows when up- and down-quark couplings have different signs, the
amplitude of the BSM signal is significantly smaller than in the case of same
signs.

The obtained limits at 90% C.L. for tensor NSIs from the analysis of the Conus
Run-1 data can are shown in the lower plot of Figure 2, where they are
compared with similar bounds deduced from CsI(Na) data of the Coherent
experiment.444For the extraction of limits shown throughout this paper, we
used the tool WebPlotDigitizer Rohatgi2020 . For illustrative purposes, the
parameter points of the example BSM signal rates, shown in the upper plot of
Figure 2, are marked with crosses. Although Conus has not observed a CE$\nu$NS
signal yet, we place competitive bounds on the tensor NSI couplings
$\epsilon^{u\mathrm{T}}_{ee}$ and $\epsilon^{d\mathrm{T}}_{ee}$.555 Note that
the indices here, referring to the electrons (anti)neutrinos involved in the
new scattering process, are not to be confused with the indices of eVee,
referring to the ionization energy. This is due to the signal’s higher extent
(compared to SM CE$\nu$NS) and the low background levels obtained below
$1\,\mathrm{keV}_{ee}$. Here, the quenching factor’s impact is of minor
importance since, for the values considered, the tensor NSI signal lies way
above the Conus energy threshold allowing for bounds that are mainly dominated
by the experimental conditions like background and exposure. Figure 2
furthermore illustrates how the degeneracy between the two NSI couplings,
$\epsilon^{u\mathrm{T}}_{ee}$ and $\epsilon^{d\mathrm{T}}_{ee}$, can be
broken. The different slopes of the limit bands that are visible for Conus and
Coherent are due to the different detector isotopes used in the experiments.
In general, they allow for breaking the degeneracy of the couplings. However,
with data obtained so far the difference between detector materials CsI and Ge
(in terms of $N$ and $Z$) is not sufficient to have a substantial impact on
the combined allowed regions.

Since NSIs are by definition induced by a new heavy mediator that has been
integrated out, we can translate the bounds we found for the tensor NSIs into
a scale at which this effective description is expected to break down. This
scale, where new physics gets probed, is given by $\Lambda\approx g_{x}/g\cdot
M_{W}/\sqrt{\epsilon}\sim M_{W}/\sqrt{\epsilon}$, cf. Ref. Lindner:2017nmb ,
and, in the case of our determined limits, turns out to be higher than $\sim
360\,\mathrm{GeV}$. Hence, with increasing sensitivity low energy experiments
like Conus might probe physics at energy scales comparable to the Lhc (TeV
scale).

####  3.1.2 Vector-type interaction

Figure 3: Top: Expected vector NSI signals in detector C1, assuming a
quenching parameter of $k=0.16$ and different coupling values from all
quadrants in comparison to the standard CE$\nu$NS signal. Note that, depending
on the explicit couplings, destructive interference between the vector NSIs
and the SM signals is possible and the expected number of events can be
reduced (with respect to the pure SM case). Bottom: Allowed regions (at 90%
C.L.) of vector NSI couplings $\epsilon^{u\mathrm{V}}_{ee}$ and
$\epsilon^{d\mathrm{V}}_{ee}$ deduced from the Run-1 Conus dataset. As in
Figure 2, the example points of the upper plot are marked with crosses, where
bold crosses indicate signals stronger than the SM expectation and normal
crosses point to the parameter space of destructive interference between the
SM and BSM channels. For comparison, constraints (90% C.L.) obtained from
Coherent data Papoulias:2019txv  are shown. Further existing limits, e.g. from
Charm (90% C.L.) Dorenbosch:1986tb  and Lhc monojet searches (95% C.L.)
Friedland:2011za  are indicated with grey elliptic regions.

Using the same notation as for the tensor-type NSIs, the vector-type NSIs
represent a four-fermion interaction described by the operator

$\displaystyle\mathcal{O}^{q\mathrm{V}}_{\rm
NSI}=\left(\bar{\nu}_{\alpha}\gamma^{\mu}L\nu_{\beta}\right)\left(\bar{q}\gamma_{\mu}Pq\right)+\text{h.c.}\,,$
(12)

with left- and right-handed projection operators $P=\\{L,R\\}$. Since this new
vector-type interaction exhibits a structure similar to the conventional SM
CE$\nu$NS, the related couplings to quarks can be directly absorbed in the
weak charge, cf. Eq. (1):
$\mathcal{Q}_{W}^{\mathrm{V}}\rightarrow\mathcal{Q}_{\rm NSI}^{\mathrm{V}}$.
Furthermore, the operator in Eq. (12) can trigger a flavor change among the
involved neutrinos and, thus, the neutrino-nucleus scattering might become
flavor-dependent. In its most general version, the modified weak charge now
reads, cf. Ref. Barranco:2005yy ,

$\displaystyle\mathcal{Q}_{\rm NSI}^{\mathrm{V}}=$
$\displaystyle\left(g_{V}^{p}+2\epsilon^{u\mathrm{V}}_{\alpha\alpha}+\epsilon^{d\mathrm{V}}_{\alpha\alpha}\right)Z+\left(g_{V}^{n}+\epsilon^{u\mathrm{V}}_{\alpha\alpha}+2\epsilon^{d\mathrm{V}}_{\alpha\alpha}\right)N$
(13)
$\displaystyle+\sum_{\alpha,\beta}\left[\left(2\epsilon^{u\mathrm{V}}_{\alpha\beta}+\epsilon^{d\mathrm{V}}_{\alpha\beta}\right)Z+\left(\epsilon^{u\mathrm{V}}_{\alpha\beta}+2\epsilon^{d\mathrm{V}}_{\alpha\beta}\right)N\right]\,,$

where the first line represents the flavor-preserving interactions (including
SM CE$\nu$NS) and the second line the flavor-changing interactions. As for
tensor NSIs, with reactor antineutrinos it is only possible to probe effective
couplings of electron-type, i.e. $\epsilon^{u\mathrm{V}}_{ee}$ and
$\epsilon^{d\mathrm{V}}_{ee}$. In contrast, with $\pi$-DAR beams it is
possible to investigate several types of couplings since they contain muon
(anti)neutrinos as well. Investigations of the Coherent data have already led
to bounds on such couplings, either assuming one to be non-vanishing at a
time, e.g. Ref. Khan:2019cvi ; Papoulias:2019txv , or in a combined approach
with oscillation data that takes into account flavor-changing couplings as
well, cf. Ref. Coloma:2019mbs .

The expectation of potential vector NSI signals within the detector C1 are
shown in the upper plot of Figure 3 together with the corresponding SM
CE$\nu$NS signal. Both signals share the same kinematic cut-off and due to the
same chiral structure, destructive interference is possible in some regions of
the parameter space. Thus, (CE$\nu$NS + vector NSI) signal rates smaller than
the expected CE$\nu$NS rate alone are possible in the context of vector NSIs
as indicated by the dashed lines in the upper plot of Figure 3.

In contrast to tensor NSIs, the vector NSI case does not benefit from an
extent to higher energies. As a consequence, we cannot hope to obtain equally
strong bounds as Coherent. This effect is visible in the lower plot of Figure
3, which shows the deduced limits on vector NSIs from the Conus Run-1 dataset
in comparison to the existing Coherent limits. It is apparent that the
strength of the limits for vector NSIs strongly depends on the quenching
factor, which is due to the fact that the quenching factor significantly
influences the expected number of events in the ROI. Comparing the derived
Conus limits on vector NSIs for the currently favored quenching value of
$k=0.16$ to bounds from other experiments, we find that they are currently
subdominant. Furthermore, resolving the region of destructive interference is
beyond the current experimental reach. However, further experimental
improvements that could lead to a future detection of CE$\nu$NS would also
significantly improve the sensitivity to vector NSIs and could even allow to
probe the parameter region of strong destructive interference.

###  3.2 Simplified mediator models

Another class of models that can be constrained with Conus data are so-called
‘simplified models’ that have been intensively studied, e.g. in the dark
matter searches at the Lhc Abdallah:2015ter ; Abercrombie:2015wmb ;
Boveia:2016mrp . Although such kind of models have to be taken with care
Kahlhoefer:2015bea ; Ellis:2017tkh ; Morgante:2018tiq , they experience great
popularity since they do not need to be fully specified at high energy.
Besides dark matter and neutrino physics, this simple framework is applied in
various contexts, such as in searches for two Higgs doublet models at the Lhc
Arcadi:2020gge  or for leptoquark investigations of B-mesons anomalies
Vignaroli:2019lkg . For neutrino-electron scattering or neutrino-nucleus
scattering measurements, such models are interesting since the mediators can
have an impact on the recorded recoil spectra, most pronounced for mediator
masses that are smaller than the maximal momentum transfer. Thus, experiments
using reactor antineutrinos can, especially in the mediator mass region below
$\sim\\!10\,\mathrm{MeV}$, be even more sensitive than experiments using
$\pi$-DAR sources. In the following, we investigate signatures of new scalar
and vector mediators that might scatter off nuclei or electrons by using the
Conus Run-1 datasets as defined in Table 2.

####  3.2.1 Light vector bosons

Figure 4: Top: Expected light vector signals of detector C1 in the low energy
region below $500\,\mathrm{eV}_{ee}$ for a quenching parameter of $k=0.16$
(left) and in the higher energy region between $2$ and $8\,\mathrm{keV}_{ee}$
(right) for different couplings and masses in comparison to the SM signals of
CE$\nu$NS and elastic neutrino-electron scattering, respectively. Bottom:
Limits (90% C.L.) on the light vector mediator parameters
$(m_{Z^{\prime}},g_{Z^{\prime}})$ deduced from CE$\nu$NS and neutrino-electron
scattering with the Run-1 Conus datasets. The exemplary parameter points of
the upper signal spectra are shown as well. Bold crosses indicate parameter
points that can already be excluded while regular crosses refer to points that
are still allowed. For comparison, limits obtained from Coherent (CsI and Ar)
data (90% C.L.) Cadeddu:2020nbr  and Connie (95% C.L.) Aguilar-Arevalo:2019zme
are shown. The ‘island of non-exclusion’ in the Coherent limits is due to
destructive interference and does not appear in the Connie and Conus limits as
these experiments have not yet reached the necessary sensitivity.

New $Z$-like vector bosons arise in simple $U(1)$ extensions of the SM and
have been studied in various scenarios such as gauged $B-L$, sequential SM and
multiple others, cf. e.g. Refs. Bauer:2018onh ; Arcadi:2017hfi . Setting the
model-building aside, we can work with an effective Lagrangian including
vector-type interactions of neutrinos, quarks and electrons, of the form

$\displaystyle\mathcal{L}_{Z^{\prime}}=Z^{\prime}_{\mu}\left(g^{\nu\mathrm{V}}_{Z^{\prime}}\bar{\nu}_{L}\gamma^{\mu}\nu_{L}+g^{e\mathrm{V}}_{Z^{\prime}}\bar{e}\gamma^{\mu}e+g^{q\mathrm{V}}_{Z^{\prime}}\bar{q}\gamma^{\mu}q\right)+\frac{1}{2}m^{2}_{Z^{\prime}}Z^{\prime}_{\mu}Z^{\prime\mu}\,,$
(14)

with vector-type couplings $g^{x\mathrm{V}}_{Z^{\prime}}$
($x=\\{\nu,\,e,\,q\\}$ and $q=\\{u,\,d\\}$) and mass of the new vector boson
$m_{Z^{\prime}}$. Within this simplified model, we only include interactions
of SM neutrinos, i.e. left-handed neutrinos and right-handed antineutrinos,
and do not take into account characteristic features like kinetic or mass
mixing. In the following, we investigate two reaction channels that arise from
Eq. (14): neutrino-nucleus as well as neutrino-electron scattering. In both
cases, the light vector boson adds a new reaction channel that can interfere
with the SM one, since both share the same final state. For our investigation,
we assume universal couplings, i.e. $g_{Z^{\prime}}\equiv
g^{\nu\mathrm{V}}_{Z^{\prime}}=g^{e\mathrm{V}}_{Z^{\prime}}=g^{u\mathrm{V}}_{Z^{\prime}}=g^{d\mathrm{V}}_{Z^{\prime}}$,
allowing us to reduce the parameter space to only two parameters:
$(m_{Z^{\prime}},\,g_{Z^{\prime}})$.

The cross section of neutrino-nucleus scattering including a light vector
contribution can be expressed as Kosmas:2017tsq

$\displaystyle\left(\frac{d\sigma}{dT_{A}}\right)_{\rm CE\nu
NS\,+\,Z^{\prime}}=\mathcal{G}_{Z^{\prime}}^{2}(T_{A})\left(\frac{d\sigma}{dT_{A}}\right)_{\rm
CE\nu NS}\,,$ (15)

with the SM cross section as given in Eq. (1) and the prefactor
$\mathcal{G}_{Z^{\prime}}$ defined as666In literature, other definitions of
$\mathcal{G}_{Z^{\prime}}$ can be found which differ by a factor of
$\frac{1}{2}$. As mentioned before, these differences are due to different
definitions of $\mathcal{Q}^{\mathrm{V}}_{W}$.

$\displaystyle\mathcal{G}_{Z^{\prime}}(T_{A})=1-\frac{g^{\nu\mathrm{V}}_{Z^{\prime}}}{\sqrt{2}G_{F}}\frac{\mathcal{Q}_{Z^{\prime}}}{\mathcal{Q}^{\mathrm{V}}_{W}}\frac{1}{2m_{A}T_{A}+m^{2}_{Z^{\prime}}}\,.$
(16)

The nuclear charge associated to the light vector mediator is given by
Bertuzzo:2017tuf

$\displaystyle\mathcal{Q}_{Z^{\prime}}=\left(2g^{u\mathrm{V}}_{Z^{\prime}}+g^{d\mathrm{V}}_{Z^{\prime}}\right)Z+\left(g^{u\mathrm{V}}_{Z^{\prime}}+2g^{d\mathrm{V}}_{Z^{\prime}}\right)N\rightarrow
3\,g_{Z^{\prime}}\left(Z+N\right)\,,$ (17)

where the last step is due to our assumption of universal couplings to leptons
and quarks. As a result, the light vector part of Eq. (16) scales as
$g_{Z^{\prime}}^{2}$, leading to a proportionality of up to
$g_{Z^{\prime}}^{4}$ in the cross section of Eq. (15). A second effect that
becomes visible in Eq. (16) is the possibility of destructive interference,
showing up as a negative sign between the two terms and which can, depending
on the sensitivity of the experiment, lead to ‘islands of non-exclusion’ in
the exclusion plot, cf. Coherent limits in Figure 4. In this case the
prefactor $\mathcal{G}_{Z^{\prime}}$ turns from the SM value $1$ into $-1$ due
to the $Z^{\prime}$ contribution, leaving the resulting cross section
invariant, cf. Eq. (15). However, both Conus and Connie do not have the
sensitivity to see this effect yet, cf. Figure 4.

It is worth to mention that there is in principal a connection between the
vector mediators discussed here and the previously discussed vector NSIs.
Integrating out the vector mediator allows for a mapping between the
$Z^{\prime}$ couplings and mass and the $\epsilon$-parameters of vector NSIs
Denton:2018xmq

$\displaystyle\epsilon^{q\mathrm{V}}_{\alpha\beta}=\frac{\left(g_{Z^{\prime}}^{\nu\mathrm{V}}\right)_{\alpha\beta}g^{q\mathrm{V}}}{2\sqrt{2}G_{F}M^{2}_{Z^{\prime}}}\,,$
(18)

where the couplings $\left(g_{Z^{\prime}}^{\nu V}\right)_{\alpha\beta}$ can in
general be flavor-dependent. However, integrating out the mediating particle
is only possible when the mediator is significantly heavier than the momentum
transfer in the scattering process. Since this condition is violated for light
mediators, we discuss the two models separately.

In addition to neutrino-nucleus scattering, we also look at the influence of a
new vector mediator on neutrino-electron scattering. The corresponding cross
section is given by Cerdeno:2016sfi

$\displaystyle\left(\frac{d\sigma}{dT_{e}}\right)_{\nu
e+Z^{\prime}}=\left(\frac{d\sigma}{dT_{e}}\right)_{\nu
e}+\frac{\sqrt{2}G_{F}m_{e}g_{V}g_{Z^{\prime}}^{\nu\mathrm{V}}g_{Z^{\prime}}^{e\mathrm{V}}}{\pi(2m_{e}T_{e}+m_{Z^{\prime}}^{2})}+\frac{m_{e}(g_{Z^{\prime}}^{\nu\mathrm{V}}g_{Z^{\prime}}^{e\mathrm{V}})^{2}}{2\pi(2m_{e}T_{e}+m_{Z^{\prime}}^{2})^{2}}\,,$
(19)

with the electron vector coupling to Z bosons
$g_{V}=-\frac{1}{2}+2\sin^{2}\theta_{W}$. By comparing the last term of Eq.
(19) to Eq. (15), we can see how neutrino-electron scattering can enable us to
set stronger limits for small $Z^{\prime}$ masses. For $m_{Z^{\prime}}^{2}\ll
2m_{e}T_{e}$, the electron mass $m_{e}$ in the numerator cancels out and we
end up with $4m_{e}T_{e}^{2}$ in the denominator. Comparing this to the
denominator $4m_{N}T_{N}^{2}$ in Eq. (15) (together with Eq. (1)), we note
that the smaller electron mass enhances our cross section and thus leads to a
stronger limit for universal couplings in this region of our parameter space.

Exemplary event spectra for neutrino-nucleus and neutrino-electron scattering
for detector C1 are shown in the upper plots of Figure 4 for two different
masses of the $Z^{\prime}$ and two different couplings for each mass. The
conventional SM channels are illustrated for comparison. Especially, note the
change in shape for elastic neutrino-electron scatterings of the shown
parameter points in the upper right plot of Figure 4 which illustrates the
different behavior for the denominator in Eq. (19) mentioned above. In the
lower plot of Figure 4, the resulting limits of our analysis are depicted in
the ($m_{Z^{\prime}}$, $g_{Z^{\prime}}$)-plane together with bounds from
Coherent Dutta:2019eml ; Cadeddu:2020nbr ; Miranda:2020zji ; Kosmas:2017tsq
and Connie Aguilar-Arevalo:2019zme . For $Z^{\prime}$ masses above
$10\,\mathrm{MeV}$, the strongest bounds can be set by $\pi$DAR experiments
because of their higher neutrino energies, while for smaller masses reactor
experiments like Conus and Connie can set competitive or stronger bounds.
Furthermore, the limits we can set from neutrino-electron scattering are
stronger than the ones from neutrino-nucleus scattering for
$m_{Z^{\prime}}\lesssim 10\,\mathrm{MeV}$ as explained before. With the
current dataset and the most favored quenching value $k=0.16$, the lowest
coupling value that can be probed with CE$\nu$NS is $\sim 4\cdot 10^{-5}$. In
the case of elastic neutrino-electron scattering the coupling can be
constrained down to $\sim 6\cdot 10^{-7}$ for lowest mediator masses.

Besides the bounds from CE$\nu$NS experiments shown in Figure 4, there exists
a plethora of bounds on vector mediators from various other types of
experiments, especially in the context of a gauged $U(1)_{B-L}$ symmetry. This
includes searches for dielectron resonances at Atlas Aaboud:2016cth , beam
dump investigations Batell:2009di ; Bjorken:2009mm , bounds from neutrino-
electron scattering Bilmis:2015lja ; Lindner:2018kjo  as well as dark photon
searches at BaBar Lees:2014xha ; Lees:2017lec  and LHCb Aaij:2017rft .
Numerous collections of bounds can be found e.g. in Refs. Ilten:2018crw ;
Bauer:2018onh  for general models and Ref. Harnik:2012ni  for B-L extensions.
While focusing on the strengths of the limits derived in this work in context
of CE$\nu$NS experiments, we mention the broader scope of bounds for the
inclined reader.

####  3.2.2 Light scalar bosons

Figure 5: Top: Expected light scalar signals of detector C1 in the low energy
region below $500\,\mathrm{eV}_{ee}$ for a quenching parameter of $k=0.16$
(left) and in the higher energy region between $2$ and $8\,\mathrm{keV}_{ee}$
(right) for different couplings and masses in comparison to the SM signals of
CE$\nu$NS and elastic neutrino-electron scattering, respectively. Note that
the wiggles at $\sim 2\,\mathrm{keV}$ are not artifacts but result from the
applied reactor model. Bottom: Limits (90% C.L.) on the light scalar mediator
parameters $(m_{\phi},g_{\phi})$ deduced from CE$\nu$NS and neutrino-electron
scattering with the Run-1 Conus datasets. As before, we point out the
exemplary parameter points of the signal spectra above. Bold crosses indicate
parameter points that can already be excluded while regular crosses refer to
points that are still in agreement with the data. For comparison, limits
obtained from Coherent data (90% C.L.) Papoulias:2019txv  and Connie (95%
C.L.) Aguilar-Arevalo:2019zme  are shown.

Finally, we investigate elastic neutrino-nucleus and neutrino-electron
scattering induced by a light scalar mediator $\phi$. We select a simple
benchmark model, i.e. a CP-even massive real scalar boson with pure scalar-
type couplings to the first generation of leptons and quark. The Lagrangian of
this simplified model is given by Cerdeno:2016sfi

$\displaystyle\mathcal{L}_{\phi}=\phi\left(g^{q\mathrm{S}}_{\phi}\bar{q}q+g^{e\mathrm{S}}_{\phi}\bar{e}e+g^{\nu\mathrm{S}}_{\phi}\bar{\nu}_{R}\nu_{L}+\text{h.c.}\right)-\frac{1}{2}m^{2}_{\phi}\phi^{2}\,,$
(20)

with the individual scalar coupling $g^{x\mathrm{S}}_{\phi}$
($x=\\{\nu,\,e,\,q\\}$ and $q=\\{u,\,d\\}$). As for the vector mediator case,
we put model-building aspects aside and work with this simplified model even
though a realistic low-energy model needs to be more complex to become
consistent with the SM symmetries Bell:2016ekl . Along the line of Refs.
Kosmas:2017tsq ; Billard:2018jnl , we also ignore resulting consequences for
neutrino phenomenology in this analysis.

The associated neutrino-nucleus scattering cross section takes the form
Kosmas:2017tsq ; Cerdeno:2016sfi

$\displaystyle\left(\frac{d\sigma}{dT_{A}}\right)_{\rm CE\nu
NS+\phi}=\left(\frac{d\sigma}{dT_{A}}\right)_{\rm CE\nu
NS}+\frac{(g^{\nu\mathrm{S}}_{\phi}Q_{\phi})^{2}m_{A}^{2}T_{A}}{4\pi
E_{\nu}^{2}(2m_{A}T_{A}+m_{\phi}^{2})^{2}}\,,$ (21)

with the nuclear charge associated to the light scalar mediator being
DelNobile:2013sia

$\displaystyle
Q_{\phi}=\sum_{N,q}g^{q\mathrm{S}}_{\phi}\frac{m_{N}}{m_{q}}f^{(N)}_{T,q}\rightarrow
g_{\phi}(14N+15.1Z)\,.$ (22)

The last step is obtained by assuming a universal coupling to leptons and
quarks, and summing up all nucleon form factors $f_{T,q}^{(N)}$, which
incorporate the effective low-energy couplings of the scalar $\phi$ to the
nucleons $N=\\{p,n\\}$, cf. Ref. DelNobile:2013sia . Thus, with the assumption
of a universal coupling, the corresponding part of the cross section in Eq.
(21) scales with $g_{\phi}^{4}$ and the model’s parameter space is now spanned
by only two parameters, the scalar mass $m_{\phi}$ and its couplings to
fermions $g_{\phi}$. Since the scalar-neutrino interaction flips chirality (in
contrast to the chirality-conserving SM case), there is no interference and
the scalar cross section is simply added to the SM CE$\nu$NS signal. Another
interesting aspect that appears in Eq. (21) is the scaling with the recoil
energy $T_{N}$ in comparison to the vector case, cf. Eq. (15). For the scalar
mediator, the corresponding part of the cross section scales with $1/T_{N}$,
whereas in the vector case it scales with $1/T_{N}^{2}$, leading to a less
steep signal.

The Lagrangian in Eq. (20) also induces an additional interaction between
neutrinos and electrons. Thus, there is an contribution to the cross section
for neutrino-electron scattering, leading in total to Cerdeno:2016sfi

$\displaystyle\left(\frac{d\sigma}{dT_{e}}\right)_{\nu
e+\phi}=\left(\frac{d\sigma}{dT}\right)_{\nu
e}+\frac{(g_{\phi}^{\nu\mathrm{S}}g^{e\mathrm{S}}_{\phi})^{2}\,m_{e}^{2}T_{e}}{4\pi
E_{\nu}^{2}(2m_{e}T_{e}+m_{\phi}^{2})^{2}}\,.$ (23)

Under the assumption of universal scalar couplings, this shrinks down to the
same quadratic dependence as for neutrino-nucleus scattering, i.e.
$(g_{\phi}^{\nu\mathrm{S}}g^{e\mathrm{S}}_{\phi})^{2}\rightarrow
g_{\phi}^{4}$. As for the case of a light vector mediator, the denominator in
Eq. (23) can be separated into two different cases, i.e. $2m_{e}T_{e}\ll
m_{\phi}^{2}$ and $2m_{e}T_{e}\gg m_{\phi}^{2}$, which correspond to the
different behaviors of the obtained limit curves.

The expected event rates and the signal shape of elastic neutrino-nucleus and
neutrino-electron scattering mediated by a light scalar mediator are depicted
in the upper left and right plots of Figure 5, respectively. For comparison to
the different signal expectations (two coupling values for each of the two
scalar mediator masses), we also indicated the SM signal channels. By
comparing the upper left plots of Figure 4 and Figure 5, one notes the
previously mentioned difference in steepness or scaling with $T_{N}$ between
the scalar and the vector mediator. Further, this different scaling yields a
different behavior for electron scatterings at higher energies, cf. upper
right plots of Figure 4 and Figure 5. Here, the electron scattering exhibits a
linear dependence on the recoil energy. In the end, this difference leads to
stronger limits for the scalar mediator, which are displayed in the lower plot
of Figure 5. For comparison, we also show the limits obtained from Coherent
CsI data and marked the parameter points of the upper plots with crosses.
Again, we highlighted both cases, points that are already excluded as well as
points that still agree with the used dataset. The lowest coupling value that
can be probed with CE$\nu$NS is $\sim 10^{-5}$ for the currently most favoured
quenching value of $k=0.16$, while elastic neutrino electron scattering allows
us to constrain the coupling down to $\sim 2\cdot 10^{-6}$ for lowest mediator
masses. As before, competitive CE$\nu$NS bounds can be gained for especially
low mediator masses, i.e. below $\sim 1\,\mathrm{MeV}$, which is attributed to
the low neutrino energy provided by the reactor antineutrinos.

##  4 Conclusions

The Conus experiment aims at the detection of CE$\nu$NS with four HPGe
detectors in a sophisticated shield at 17.1 m-distance to the 3.9 GWth core of
the nuclear power plant in Brokdorf, Germany. After a first spectral analysis
devoted to the CE$\nu$NS search in Conus data, cf. Ref. CONUS:2020skt , we
used here Run-1 data to constrain several BSM models. In particular, we
searched for modifications of CE$\nu$NS due to NSIs of both tensor and vector
type as well as light vector and scalar mediators. The latter two have been
tested as so-called simplified models on their impact on CE$\nu$NS and
neutrino-electron scattering. We make use of a similar analysis procedure that
has already been used in the first CE$\nu$NS investigation, including all
systematic uncertainties therein. Small modifications have been applied due to
the inclusion of uncertainties on the used background MC simulation in the
higher energy spectrum, cf. Section 2, and the background-related publication,
cf. Ref. CONUSbackground . Further, a refined noise edge parameterization was
applied, leading to energy thresholds of the ROIs that are slightly lower
compared to the analysis in Ref. CONUS:2020skt .

During our analysis, the likelihood function, cf. Eq. (7), was varied with the
cross sections of the individual models. Limits were derived from data of
three detectors in the experiment’s first data collection period Run-1. For
the investigation of neutrino-electron scatterings above
$2\,\mathrm{keV}_{ee}$, a dataset with extended exposure is used to increase
the experimental sensitivity, cf. Table 2 for an overview of all datasets used
throughout this work. For Conus, quenching, i.e. the fraction of nuclear
recoil energy available as ionization for signal formation, is the least known
input parameter and thus the dominating uncertainty. In combination with
neutrino energies below 10 MeV, this renders CE$\nu$NS measurements at a
reactor site especially demanding. Thus, we derive our BSM constraints for
three different quenching parameters which span the range of currently favored
values: $k=\\{0.12,0.16,0.20\\}$, where $k$ represents the quenching factor at
recoil energies around $1\,\mathrm{keV}_{ee}$, cf. Section 2. The obtained
bounds, except in the case of vector NSIs, are at least in some regions of the
parameter space competitive with existing bounds from other CE$\nu$NS
experiments, cf. Section 3. For tensor NSIs, we present limits that represent
the world’s best limits on electron-type couplings to up- and down-type quarks
from CE$\nu$NS. The scale of associated BSM physics can be constrained to lie
above $\sim 360\,\mathrm{GeV}$, cf. Figure 2. Corresponding bounds in the case
of vector-type NSI are highly dependent on the quenching parameter $k$ and at
the moment not competitive to existing bounds due to the limited sensitivity
of Conus on the CE$\nu$NS signal itself, cf. Figure 3. Since reactor
antineutrinos are emitted at lower energies than neutrinos from a $\pi$-DAR
source, our bounds on light scalar or vector mediators are stronger at lower
mediator masses. For higher masses, neutrinos from a $\pi$-DAR source yield
currently the strongest CE$\nu$NS limits, cf. Figure 4 and Figure 5. Moreover,
limits obtained from electron scatterings are stronger than the ones obtained
from CE$\nu$NS for masses below $\sim 10\,\mathrm{MeV}$ and $\sim
1\,\mathrm{MeV}$ for vector and scalar mediators, respectively. However, we
note that the shown parameter space region can only be excluded for models
that incorporate electron and quark interactions with universal couplings. For
more concrete frameworks, i.e. nucleophilic/leptophilic mediators or non-
universal couplings, the obtained contours have to be viewed individually
and/or with appropriate corrections.

After a series of experimental improvements, i.e. an advanced data acquisition
system and more stable environmental conditions, Conus continues data
collection. Thus, for the future we expect our bounds to strengthen with more
exposure. After the reactor shutdown at the end of 2021, additional OFF data
are expected to increase the experimental sensitivity. Further, the CONUS
Collaboration developed a program to pin-down the dominating uncertainty
related to the not well known quenching factor in germanium. Our recently
conducted measurement is indicating a quenching factor value that agrees with
the currently favored one and that follows the Lindhard theory down to nuclear
recoils of a few keV, cf. Ref. CONUSquenching . With a future CE$\nu$NS
detection via the Conus set-up, we expect stronger bounds, especially in the
case of vector NSI. Then, investigation of further BSM topics like neutrino
electromagnetic properties, sterile neutrino and dark matter will lead to
further constraints. An investigation of neutrino magnetic moments via
neutrino-electron scattering at energies above 2 keVee is already in
preparation.

While first BSM constraints of Coherent, Connie, Conus and Ncc-1701 at
Dresden-II Colaresi:2021kus  already revealed the huge potential of CE$\nu$NS
measurements, which can be viewed as a proof of principle by itself, more
experiments are going to contribute further knowledge by using different
target elements and detection technologies. There are various endeavors close
to nuclear reactors and first sensitivity studies for the European Spallation
Source (Ess) already exist, cf. Refs. Blennow:2019bvl ; Baxter:2019mcx .
Taking advantage of these different neutrino sources, in terms of
complementary measurements between reactor and neutrino beam experiments,
allows for further interesting physics investigations Dent:2017mpr ;
Lindner:2017nmb . Therefore, the next generation of CE$\nu$NS experiments
promises an active field with new approaches and interesting possibilities
Bellenghi:2019vtc ; Cadeddu:2019qmv ; Abdullah:2020iiv ;
AristizabalSierra:2021uob ; Fernandez-Moroni:2020yyl ; Tomalak:2020zfh  and
represents another step towards the era of precision neutrino physics.

###### Acknowledgements.

We thank the technical and administrative staff who helped building the
experiment, in particular the MPIK workshops and Mirion Technologies
(Canberra) in Lingolsheim. We express our gratitude to the Preussen Elektra
GmbH for enduring and prolific support and for hosting the Conus experiment.
Moreover, we thank Dr. S. Schoppmann (MPIK) for assistance on the analysis and
Dr. M. Seidl (Preussen Elektra GmbH) for providing simulation data on the
fission rate evolution over a reactor cycle. Further thanks are directed to K.
Zink and the MPIK IT department for their support concerning the institute’s
cluster infrastructure. The Conus experiment is supported financially by the
Max Planck Society (MPG) and T. Rink by the IMPRS-PTFS as well as by the
German Research Foundation (DFG) through the research training group GRK 1940.

## References

  * (1) D. Z. Freedman, _Coherent effects of a weak neutral current_ , _Physical Review D_ 9 (1974) 1389.
  * (2) D. L. Tubbs and D. N. Schramm, _Neutrino Opacities at High Temperatures and Densities_ , _The Astrophysical Journal_ 201 (1975) 467.
  * (3) A. Drukier and L. Stodolsky, _Principles and Applications of a Neutral Current Detector for Neutrino Physics and Astronomy_ , _Phys.Rev.D_ 30 (1984) 2295.
  * (4) COHERENT collaboration, D. Akimov et al., _Observation of Coherent Elastic Neutrino-Nucleus Scattering_ , _Science_ 357 (2017) 1123 [1708.01294].
  * (5) COHERENT collaboration, D. Akimov et al., _First Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Argon_ , _Phys. Rev. Lett._ 126 (2021) 012002 [2003.10630].
  * (6) CONUS collaboration, H. Bonet et al., _Constraints on Elastic Neutrino Nucleus Scattering in the Fully Coherent Regime from the CONUS Experiment_ , _Phys. Rev. Lett._ 126 (2021) 041804 [2011.00210].
  * (7) D. K. Papoulias and T. S. Kosmas, _COHERENT constraints to conventional and exotic neutrino physics_ , _Phys.Rev.D_ 97 (2018)  [1711.09773].
  * (8) J. Billard, J. Johnston and B. J. Kavanagh, _Prospects for exploring New Physics in Coherent Elastic Neutrino-Nucleus Scattering_ , _JCAP_ 11 (2018) 016 [1805.01798].
  * (9) A. N. Khan and W. Rodejohann, _New physics from COHERENT data with an improved quenching factor_ , _Phys.Rev.D_ 100 (2019)  [1907.12444].
  * (10) D. K. Papoulias, _COHERENT constraints after the COHERENT-2020 quenching factor measurement_ , _Phys.Rev.D_ 102 (2020)  [1907.11644].
  * (11) D. Z. Freedman, D. N. Schramm and D. L. Tubbs, _The Weak Neutral Current and its Effects in Stellar Collapse_ , _Annual Review of Nuclear Science_ 27 (1977) 167.
  * (12) P. S. Amanik and G. M. Fuller, _Stellar Collapse Dynamics With Neutrino Flavor Changing Neutral Currents_ , _Phys.Rev.D_ 75 (2007)  [astro-ph/0606607].
  * (13) K. G. Balasi, K. Langanke and G. Martínez-Pinedo, _Neutrino–nucleus reactions and their role for supernova dynamics and nucleosynthesis_ , _Prog.Part.Nucl.Phys._ 85 (2015) 33 [1503.08095].
  * (14) M. Biassoni and C. Martinez, _Study of supernova $\nu$ -nucleus coherent scattering interactions_, _Astropart.Phys._ 36 (2012) 151 [1110.3536].
  * (15) V. Brdar, M. Lindner and X.-J. Xu, _Neutrino astronomy with supernova neutrinos_ , _JCAP_ 04 (2018) 025 [1802.02577].
  * (16) DarkSide 20k collaboration, P. Agnes et al., _Sensitivity of future liquid argon dark matter search experiments to core-collapse supernova neutrinos_ , _JCAP_ 03 (2021) 043 [2011.07819].
  * (17) J. Monroe and P. Fisher, _Neutrino Backgrounds to Dark Matter Searches_ , _Phys.Rev.D_ 76 (2007)  [0706.3019].
  * (18) A. Gutlein, C. Ciemniak, F. von Feilitzsch, N. Haag, M. Hofmann, C. Isaila et al., _Solar and atmospheric neutrinos: Background sources for the direct dark matter search_ , _Astropart.Phys._ 34 (2010) 90 [1003.5530].
  * (19) D. G. Cerdeño, M. Fairbairn, T. Jubb, P. A. N. Machado, A. C. Vincent and C. Bœhm, _Physics from solar neutrinos in dark matter direct detection experiments_ , _JHEP_ 05 (2016) 118 [1604.01025].
  * (20) E. Bertuzzo, F. F. Deppisch, S. Kulkarni, Y. F. Perez Gonzalez and R. Zukanovich Funchal, _Dark Matter and Exotic Neutrino Interactions in Direct Detection Searches_ , _JHEP_ 04 (2017) 073 [1701.07443].
  * (21) J. M. Link and X.-J. Xu, _Searching for BSM neutrino interactions in dark matter detectors_ , _JHEP_ 08 (2019) 004 [1903.09891].
  * (22) C. Bœhm, D. G. Cerdeño, P. a. N. Machado, A. Olivares-Del Campo, E. Perdomo and E. Reid, _How high is the neutrino floor?_ , _JCAP_ 01 (2019) 043 [1809.06385].
  * (23) K. Patton, J. Engel, G. C. McLaughlin and N. Schunck, _Neutrino-nucleus coherent scattering as a probe of neutron density distributions_ , _Phys.Rev.C_ 86 (2012)  [1207.0693].
  * (24) P. Coloma, I. Esteban, M. C. Gonzalez-Garcia and J. Menendez, _Determining the nuclear neutron distribution from Coherent Elastic neutrino-Nucleus Scattering: Current results and future prospects_ , _JHEP_ 08 (2020) 030 [2006.08624].
  * (25) N. Van Dessel, V. Pandey, H. Ray and N. Jachowicz, _Nuclear Structure Physics in Coherent Elastic Neutrino-Nucleus Scattering_ , 2007.03658.
  * (26) H.-S. Lee, _sin ${}^{2}\theta_{W}$ theory and new physics_, _J. Univ. Sci. Tech. China_ 46 (2016) 470 [1511.03783].
  * (27) B. C. Cañas, E. A. Garcés, O. G. Miranda and A. Parada, _Future perspectives for a weak mixing angle measurement in coherent elastic neutrino nucleus scattering experiments_ , _Phys.Lett.B_ 784 (2018) 159 [1806.01310].
  * (28) G. Fernandez-Moroni, P. A. N. Machado, I. Martinez-Soler, Y. F. Perez-Gonzalez, D. Rodrigues and S. Rosauro-Alcaraz, _The physics potential of a reactor neutrino experiment with Skipper CCDs: Measuring the weak mixing angle_ , _JHEP_ 03 (2021) 186 [2009.10741].
  * (29) J. Barranco, O. G. Miranda and T. I. Rashba, _Probing new physics with coherent neutrino scattering off nuclei_ , _JHEP_ 12 (2005) 021 [hep-ph/0508299].
  * (30) J. Barranco, O. G. Miranda and T. I. Rashba, _Low energy neutrino experiments sensitivity to physics beyond the Standard Model_ , _Phys.Rev.D_ 76 (2007)  [hep-ph/0702175].
  * (31) J. Barranco, A. Bolanos, E. A. Garces, O. G. Miranda and T. I. Rashba, _Tensorial NSI and Unparticle physics in neutrino scattering_ , _Int.J.Mod.Phys.A_ 27 (2012)  [1108.1220].
  * (32) M. Lindner, W. Rodejohann and X.-J. Xu, _Coherent Neutrino-Nucleus Scattering and new Neutrino Interactions_ , _JHEP_ 03 (2017) 097 [1612.04150].
  * (33) I. Bischer, W. Rodejohann and X.-J. Xu, _Loop-induced Neutrino Non-Standard Interactions_ , _JHEP_ 10 (2018) 096 [1807.08102].
  * (34) P. S. Bhupal Dev, K. S. Babu, P. B. Denton, P. A. N. Machado, C. A. Argüelles, J. L. Barrow et al., _Neutrino Non-Standard Interactions: A Status Report_ , _SciPost Phys.Proc._ 2 (2019) 001 [1907.00991].
  * (35) P. Vogel and J. Engel, _Neutrino Electromagnetic Form-Factors_ , _Phys.Rev.D_ 39 (1989) 3378.
  * (36) C. Giunti and A. Studenikin, _Neutrino electromagnetic interactions: A window to new physics_ , _Rev.Mod.Phys._ 87 (2015) 531 [1403.6344].
  * (37) M. Cadeddu, C. Giunti, K. A. Kouzakov, Y. F. Li, A. I. Studenikin and Y. Y. Zhang, _Neutrino Charge Radii from COHERENT Elastic Neutrino-Nucleus Scattering_ , _Phys. Rev. D_ 98 (2018) 113010 [1810.05606].
  * (38) O. G. Miranda, D. K. Papoulias, M. Tórtola and J. W. F. Valle, _Probing neutrino transition magnetic moments with coherent elastic neutrino-nucleus scattering_ , _JHEP_ 07 (2019) 103 [1905.03750].
  * (39) P. deNiverville, M. Pospelov and A. Ritz, _Light new physics in coherent neutrino-nucleus scattering experiments_ , _Phys.Rev.D_ 92 (2015)  [1505.07805].
  * (40) J. B. Dent, B. Dutta, S. Liao, J. L. Newstead, L. E. Strigari and J. W. Walker, _Probing light mediators at ultralow threshold energies with coherent elastic neutrino-nucleus scattering_ , _Phys.Rev.D_ 96 (2017)  [1612.06350].
  * (41) Y. Farzan, M. Lindner, W. Rodejohann and X.-J. Xu, _Probing neutrino coupling to a light scalar with coherent neutrino scattering_ , _JHEP_ 05 (2018) 066 [1802.05171].
  * (42) J. B. Dent, B. Dutta, D. Kim, S. Liao, R. Mahapatra, K. Sinha et al., _New Directions for Axion Searches via Scattering at Reactor Neutrino Experiments_ , _Phys.Rev.Lett._ 124 (2020)  [1912.05733].
  * (43) D. Aristizabal Sierra, V. De Romeri, L. J. Flores and D. K. Papoulias, _Axionlike particles searches in reactor experiments_ , _JHEP_ 03 (2021) 294 [2010.15712].
  * (44) B. Dutta, S. Liao, S. Sinha and L. E. Strigari, _Searching for Beyond the Standard Model Physics with COHERENT Energy and Timing Data_ , _Phys.Rev.Lett._ 123 (2019)  [1903.10666].
  * (45) CONNIE collaboration, A. Aguilar-Arevalo et al., _Search for light mediators in the low-energy data of the CONNIE reactor neutrino experiment_ , _JHEP_ 04 (2020) 054 [1910.04951].
  * (46) M. Cadeddu, N. Cargioli, F. Dordei, C. Giunti, Y. F. Li, E. Picciau et al., _Constraints on light vector mediators through coherent elastic neutrino nucleus scattering data from COHERENT_ , _JHEP_ 01 (2021) 116 [2008.05022].
  * (47) O. G. Miranda, D. K. Papoulias, M. Tórtola and J. W. F. Valle, _Probing new neutral gauge bosons with $CE\nu NS$ and neutrino-electron scattering_, _Phys. Rev. D_ 101 (2020) 073005 [2002.01482].
  * (48) V. Brdar, W. Rodejohann and X.-J. Xu, _Producing a new Fermion in Coherent Elastic Neutrino-Nucleus Scattering: From Neutrino Mass to Dark Matter_ , _JHEP_ 12 (2018) 024 [1810.03626].
  * (49) LSND collaboration, A. Aguilar-Arevalo et al., _Evidence for neutrino oscillations from the observation of $\bar{\nu}_{e}$ appearance in a $\bar{\nu}_{\mu}$ beam_, _Phys. Rev. D_ 64 (2001) 112007 [hep-ex/0104049].
  * (50) G. Mention, M. Fechner, T. Lasserre, T. A. Mueller, D. Lhuillier, M. Cribier et al., _The Reactor Antineutrino Anomaly_ , _Phys.Rev.D_ 83 (2011)  [1101.2755].
  * (51) S. Böser, C. Buck, C. Giunti, J. Lesgourgues, L. Ludhova, S. Mertens et al., _Status of Light Sterile Neutrino Searches_ , _Prog.Part.Nucl.Phys._ 111 (2020)  [1906.01739].
  * (52) J. A. Formaggio, E. Figueroa-Feliciano and A. J. Anderson, _Sterile Neutrinos, Coherent Scattering and Oscillometry Measurements with Low-temperature Bolometers_ , _Phys.Rev.D_ 85 (2012)  [1107.3512].
  * (53) B. Dutta, Y. Gao, R. Mahapatra, N. Mirabolfathi, L. E. Strigari and J. W. Walker, _Sensitivity to oscillation with a sterile fourth generation neutrino from ultra-low threshold neutrino-nucleus coherent scattering_ , _Phys.Rev.D_ 94 (2016)  [1511.02834].
  * (54) B. C. Cañas, E. A. Garcés, O. G. Miranda and A. Parada, _The reactor antineutrino anomaly and low energy threshold neutrino experiments_ , _Phys.Lett.B_ 776 (2018) 451 [1708.09518].
  * (55) C. Blanco, D. Hooper and P. Machado, _Constraining Sterile Neutrino Interpretations of the LSND and MiniBooNE Anomalies with Coherent Neutrino Scattering Experiments_ , _Phys.Rev.D_ 101 (2020)  [1901.08094].
  * (56) O. G. Miranda, D. K. Papoulias, O. Sanders, M. Tórtola and J. W. F. Valle, _Future CEvNS experiments as probes of lepton unitarity and light-sterile neutrinos_ , _Phys.Rev.D_ 102 (2020)  [2008.02759].
  * (57) C. Hagmann and A. Bernstein, _Two-phase emission detector for measuring coherent neutrino-nucleus scattering_ , _IEEE Trans.Nucl.Sci._ 51 (2004) 2151 [nucl-ex/0411004].
  * (58) A. Bernstein, N. Bowden, B. L. Goldblum, P. Huber, I. Jovanovic and J. Mattingly, _Colloquium: Neutrino detectors as tools for nuclear security_ , _Rev.Mod.Phys._ 92 (2020)  [1908.07113].
  * (59) M. Bowen and P. Huber, _Reactor neutrino applications and coherent elastic neutrino nucleus scattering_ , _Phys.Rev.D_ 102 (2020)  [2005.10907].
  * (60) CONNIE collaboration, A. Aguilar-Arevalo et al., _The CONNIE experiment_ , _J. Phys. Conf. Ser._ 761 (2016) 012057 [1608.01565].
  * (61) MINER collaboration, G. Agnolet et al., _Background Studies for the MINER Coherent Neutrino Scattering Reactor Experiment_ , _Nucl. Instrum. Meth. A_ 853 (2017) 53 [1609.02066].
  * (62) J. Colaresi, J. I. Collar, T. W. Hossbach, A. R. L. Kavner, C. M. Lewis, A. E. Robinson et al., _First results from a search for coherent elastic neutrino-nucleus scattering (CE $\nu$NS) at a reactor site_, 2108.02880.
  * (63) J. J. Choi, _Neutrino Elastic-scattering Observation with NaI[Tl](NEON)_ , _PoS_ NuFact2019 (2020) 047.
  * (64) $\nu$-cleus collaboration, R. Strauss et al., _The $\nu$-cleus experiment: A gram-scale fiducial-volume cryogenic detector for the first detection of coherent neutrino-nucleus scattering_, _Eur. Phys. J. C_ 77 (2017) 506 [1704.04320].
  * (65) $\nu$GeN collaboration, V. Belov et al., _The $\nu$GeN experiment at the Kalinin Nuclear Power Plant_, _JINST_ 10 (2015) P12011.
  * (66) RED-100 collaboration, D. Y. Akimov et al., _First ground-level laboratory test of the two-phase xenon emission detector RED-100_ , _JINST_ 15 (2020) P02020 [1910.06190].
  * (67) Ricochet collaboration, J. Billard et al., _Coherent Neutrino Scattering with Low Temperature Bolometers at Chooz Reactor Complex_ , _J. Phys. G_ 44 (2017) 105101 [1612.09035].
  * (68) TEXONO collaboration, H. T. Wong, _The TEXONO research program on neutrino and astroparticle physics_ , _Mod. Phys. Lett. A_ 19 (2004) 1207.
  * (69) G. Fernandez Moroni, J. Estrada, E. E. Paolini, G. Cancelo, J. Tiffenberg and J. Molina, _Charge Coupled Devices for detection of coherent neutrino-nucleus scattering_ , _Phys. Rev. D_ 91 (2015) 072001 [1405.5761].
  * (70) $\nu$-cleus collaboration, R. Strauss et al., _Gram-scale cryogenic calorimeters for rare-event searches_ , _Phys. Rev. D_ 96 (2017) 022009 [1704.04317].
  * (71) CONUS collaboration, H. Bonet et al., _Large-size sub-keV sensitive germanium detectors for the CONUS experiment_ , _Eur. Phys. J. C_ 81 (2021) 267 [2010.11241].
  * (72) V. Chepel and H. Araujo, _Liquid noble gas detectors for low energy particle physics_ , _JINST_ 8 (2013)  [1207.2292].
  * (73) J. J. Choi, B. J. Park, C. Ha, K. W. Kim, S. K. Kim, Y. D. Kim et al., _Improving the light collection using a new NaI(Tl) crystal encapsulation_ , _Nucl. Instrum. Meth. A_ 981 (2020) 164556 [2006.02573].
  * (74) A. C. Hayes and P. Vogel, _Reactor Neutrino Spectra_ , _Ann.Rev.Nucl.Part.Sci._ 66 (2016) 219 [1605.02047].
  * (75) P. Huber, _On the determination of anti-neutrino spectra from nuclear reactors_ , _Phys. Rev. C_ 84 (2011) 024617 [1106.0687].
  * (76) T. A. Mueller, D. Lhuillier, M. Fallot, A. Letourneau, S. Cormon, M. Fechner et al., _Improved Predictions of Reactor Antineutrino Spectra_ , _Phys.Rev.C_ 83 (2011)  [1101.2663].
  * (77) Daya Bay collaboration, F. P. An et al., _Improved Measurement of the Reactor Antineutrino Flux and Spectrum at Daya Bay_ , _Chin. Phys. C_ 41 (2017) 013002 [1607.05378].
  * (78) V. Kopeikin, L. Mikaelyan and V. Sinev, _Components of anti-neutrino emission in nuclear reactor_ , _Phys.Atom.Nucl._ 67 (2004) 1963 [hep-ph/0308186].
  * (79) GEMMA collaboration, A. G. Beda, V. B. Brudanin, E. V. Demidova, V. G. Egorov, M. G. Gavrilov, M. V. Shirchenko et al., _First Result for Neutrino Magnetic Moment from Measurements with the GEMMA Spectrometer_ , _Phys. Atom. Nucl._ 70 (2007) 1873 [0705.4576].
  * (80) X. B. Ma, W. L. Zhong, L. Z. Wang, Y. X. Chen and J. Cao, _Improved calculation of the energy release in neutron-induced fission_ , _Phys.Rev.C_ 88 (2013)  [1212.6625].
  * (81) G. Heusser, _Low-radioactivity background techniques_ , _Ann.Rev.Nucl.Part.Sci._ 45 (1995) 543.
  * (82) G. Heusser, M. Weber, J. Hakenmüller, M. Laubenstein, M. Lindner, W. Maneschg et al., _GIOVE - A new detector setup for high sensitivity germanium spectroscopy at shallow depth_ , _Eur.Phys.J.C_ 75 (2015) 531 [1507.03319].
  * (83) CONUS collaboration, J. Hakenmüller et al., _Neutron-induced background in the CONUS experiment_ , _Eur. Phys. J. C_ 79 (2019) 699 [1903.09269].
  * (84) CONUS collaboration, H. Bonet et al., “Full background decomposition of the CONUS experiment.” (In preparation).
  * (85) J. Lindhard and M. Scharff, _Energy Dissipation by Ions in the kev Region_ , _Phys.Rev._ 124 (1961) 128.
  * (86) B. J. Scholz, A. E. Chavarria, J. I. Collar, P. Privitera and A. E. Robinson, _Measurement of the low-energy quenching factor in germanium using an 88Y/Be photoneutron source_, _Phys. Rev. D_ 94 (2016) 122003 [1608.03588].
  * (87) J. I. Collar, A. R. L. Kavner and C. M. Lewis, _Germanium response to sub-keV nuclear recoils: a multipronged experimental characterization_ , _Phys. Rev. D_ 103 (2021) 122003 [2102.10089].
  * (88) J. Liao, H. Liu and D. Marfatia, _Coherent neutrino scattering and the Migdal effect on the quenching factor_ , _Phys. Rev. D_ 104 (2021) 015005 [2104.01811].
  * (89) S. S. Wilks, _The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses_ , _Annals Math.Statist._ 9 (1938) 60.
  * (90) G. Cowan, K. Cranmer, E. Gross and O. Vitells, _Asymptotic formulae for likelihood-based tests of new physics_ , _Eur.Phys.J.C_ 71 (2011) 1554 [1007.1727].
  * (91) L. Lista, _Practical Statistics for Particle Physicists_ , in _2016 European School of High-Energy Physics_ , pp. 213–258, 2017, 1609.04150, DOI.
  * (92) R. H. Helm, _Inelastic and Elastic Scattering of 187-MeV Electrons from Selected Even-Even Nuclei_ , _Phys. Rev._ 104 (1956) 1466.
  * (93) S. Klein and J. Nystrand, _Exclusive vector meson production in relativistic heavy ion collisions_ , _Phys.Rev.C_ 60 (1999)  [hep-ph/9902259].
  * (94) C. Giunti and C. W. Kim, _Fundamentals of Neutrino Physics and Astrophysics_. Oxford Univ., 2007.
  * (95) L. A. Mikaelyan, _Investigation of neutrino properties in experiments at nuclear reactors: Present status and prospects_ , _Phys.Atom.Nucl._ 65 (2002) 1173 [hep-ph/0210047].
  * (96) S. Perkins, _Tables and Graphs of Atomic Subshell and Relaxation Data Derived from the LLNL Evaluated Atomic Data Library (EADL), Z_. Lawrence Livermore National Laboratory, 1991.
  * (97) K. W. Jones and H. W. Kraner, _Stopping of 1- to 1.8-keV Ge-73 Atoms in Germanium_ , _Phys. Rev. C_ 4 (1971) 125.
  * (98) K. W. Jones and H. W. Kraner, _Energy lost to ionization by 254-eV Ge-73 atoms stopping in Ge_ , _Phys. Rev. A_ 11 (1975) 1347.
  * (99) Y. Messous, _Calibration of a Ge crystal with nuclear recoils for the development of a dark matter detector_ , _Astropart. Phys._ 3 (1995) 361.
  * (100) P. S. Barbeau, J. I. Collar and O. Tench, _Large-Mass Ultra-Low Noise Germanium Detectors: Performance and Applications in Neutrino and Astroparticle Physics_ , _JCAP_ 09 (2007) 009 [nucl-ex/0701012].
  * (101) D. Barker and D. M. Mei, _Germanium Detector Response to Nuclear Recoils in Searching for Dark Matter_ , _Astropart. Phys._ 38 (2012) 1 [1203.4620].
  * (102) H. Dembinski, P. Ongmongkolkul, C. Deil, D. M. Hurtado, H. Schreiner, M. Feickert et al., _scikit-hep/iminuit: v2.0.0_ , Dec., 2020.  10.5281/zenodo.4310361.
  * (103) F. James and M. Roos, _Minuit - a system for function minimization and analysis of the parameter errors and correlations_ , _Computer Physics Communications_ 10 (1975) 343.
  * (104) T. E. Oliphant, _Python for scientific computing_ , _Computing in Science Engineering_ 9 (2007) 10.
  * (105) K. J. Millman and M. Aivazis, _Python for scientists and engineers_ , _Computing in Science Engineering_ 13 (2011) 9.
  * (106) P. Virtanen et al., _SciPy 1.0: Fundamental algorithms for scientific computing in Python_ , _Nature Methods_ 17 (2020) 261.
  * (107) J. D. Hunter, _Matplotlib: A 2d graphics environment_ , _Computing in Science Engineering_ 9 (2007) 90.
  * (108) F. Perez and B. E. Granger, _Ipython: A system for interactive scientific computing_ , _Computing in Science Engineering_ 9 (2007) 21.
  * (109) C. R. Harris et al., _Array programming with NumPy_ , _Nature_ 585 (2020) 357.
  * (110) W. McKinney, _Data Structures for Statistical Computing in Python_ , _Proceedings of the 9th Python in Science Conference_ (2010) 56.
  * (111) “JupyterLab Documentation — JupyterLab 3.0.15 documentation.”
  * (112) L. Dalcín, R. Paz and M. Storti, _MPI for Python_ , _Journal of Parallel and Distributed Computing_ 65 (2005) 1108.
  * (113) L. Dalcín, R. Paz, M. Storti and J. D’Elía, _MPI for Python: Performance improvements and MPI-2 extensions_ , _Journal of Parallel and Distributed Computing_ 68 (2008) 655.
  * (114) Y. Farzan and M. Tortola, _Neutrino oscillations and Non-Standard Interactions_ , _Front.in Phys._ 6 (2018) 10 [1710.09360].
  * (115) Y. Du and J.-H. Yu, _Neutrino non-standard interactions meet precision measurements of N eff_, _JHEP_ 05 (2021) 058 [2101.10475].
  * (116) C. J. Stapleford, D. J. Väänänen, J. P. Kneller, G. C. McLaughlin and B. T. Shapiro, _Nonstandard Neutrino Interactions in Supernovae_ , _Phys.Rev.D_ 94 (2016)  [1605.04903].
  * (117) D. Aristizabal Sierra, V. De Romeri and N. Rojas, _COHERENT analysis of neutrino generalized interactions_ , _Phys.Rev.D_ 98 (2018)  [1806.07424].
  * (118) I. Bischer and W. Rodejohann, _General neutrino interactions from an effective field theory perspective_ , _Nucl.Phys.B_ 947 (2019)  [1905.08699].
  * (119) M. Hoferichter, J. Menéndez and A. Schwenk, _Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses_ , _Phys.Rev.D_ 102 (2020)  [2007.08529].
  * (120) K. J. Healey, A. A. Petrov and D. Zhuridov, _Nonstandard neutrino interactions and transition magnetic moments_ , _Phys. Rev. D_ 87 (2013) 117301 [1305.0584].
  * (121) D. K. Papoulias and T. S. Kosmas, _Neutrino transition magnetic moments within the non-standard neutrino–nucleus interactions_ , _Phys.Lett.B_ 747 (2015) 454 [1506.05406].
  * (122) A. Rohatgi, _Webplotdigitizer: Version 4.5_ , 2021.
  * (123) M. Lindner, W. Rodejohann and X.-J. Xu, _Neutrino Parameters from Reactor and Accelerator Neutrino Experiments_ , _Phys.Rev.D_ 97 (2018)  [1709.10252].
  * (124) CHARM collaboration, J. Dorenbosch et al., _Experimental Verification of the Universality of $\nu_{e}$ and $\nu_{\mu}$ Coupling to the Neutral Weak Current_, _Phys. Lett. B_ 180 (1986) 303.
  * (125) A. Friedland, M. L. Graesser, I. M. Shoemaker and L. Vecchi, _Probing Nonstandard Standard Model Backgrounds with LHC Monojets_ , _Phys. Lett. B_ 714 (2012) 267 [1111.5331].
  * (126) P. Coloma, I. Esteban, M. C. Gonzalez-Garcia and M. Maltoni, _Improved global fit to Non-Standard neutrino Interactions using COHERENT energy and timing data_ , _JHEP_ 02 (2020) 023 [1911.09109].
  * (127) J. Abdallah, H. Araujo, A. Arbey, A. Ashkenazi, A. Belyaev, J. Berger et al., _Simplified Models for Dark Matter Searches at the LHC_ , _Phys.Dark Univ._ 9-10 (2015) 8 [1506.03116].
  * (128) D. Abercrombie, N. Akchurin, E. Akilli, J. Alcaraz Maestre, B. Allen, B. Alvarez Gonzalez et al., _Dark Matter Benchmark Models for Early LHC Run-2 Searches: Report of the ATLAS/CMS Dark Matter Forum_ , _Phys.Dark Univ._ 27 (2020)  [1507.00966].
  * (129) A. Boveia et al., _Recommendations on presenting LHC searches for missing transverse energy signals using simplified $s$-channel models of dark matter_, _Phys. Dark Univ._ 27 (2020) 100365 [1603.04156].
  * (130) F. Kahlhoefer, K. Schmidt-Hoberg, T. Schwetz and S. Vogl, _Implications of unitarity and gauge invariance for simplified dark matter models_ , _JHEP_ 02 (2016) 016 [1510.02110].
  * (131) J. Ellis, M. Fairbairn and P. Tunney, _Anomaly-Free Dark Matter Models are not so Simple_ , _JHEP_ 08 (2017) 053 [1704.03850].
  * (132) E. Morgante, _Simplified Dark Matter Models_ , _Adv.High Energy Phys._ 2018 (2018)  [1804.01245].
  * (133) G. Arcadi, G. Busoni, T. Hugle and V. T. Tenorth, _Comparing 2HDM $+$ Scalar and Pseudoscalar Simplified Models at LHC_, _JHEP_ 06 (2020) 098 [2001.10540].
  * (134) N. Vignaroli, _Leptoquarks in $B$-meson anomalies: simplified models and HL-LHC discovery prospects_, _Nuovo Cim. C_ 43 (2020) 53 [1912.00899].
  * (135) M. Bauer, P. Foldenauer and J. Jaeckel, _Hunting All the Hidden Photons_ , _JHEP_ 07 (2018) 094 [1803.05466].
  * (136) G. Arcadi, M. D. Campos, M. Lindner, A. Masiero and F. S. Queiroz, _Dark sequential Z’ portal: Collider and direct detection experiments_ , _Phys. Rev. D_ 97 (2018) 043009 [1708.00890].
  * (137) P. B. Denton, Y. Farzan and I. M. Shoemaker, _Testing large non-standard neutrino interactions with arbitrary mediator mass after COHERENT data_ , _JHEP_ 07 (2018) 037 [1804.03660].
  * (138) ATLAS collaboration, M. Aaboud et al., _Search for high-mass new phenomena in the dilepton final state using proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector_, _Phys. Lett. B_ 761 (2016) 372 [1607.03669].
  * (139) B. Batell, M. Pospelov and A. Ritz, _Exploring Portals to a Hidden Sector Through Fixed Targets_ , _Phys.Rev.D_ 80 (2009)  [0906.5614].
  * (140) J. D. Bjorken, R. Essig, P. Schuster and N. Toro, _New Fixed-Target Experiments to Search for Dark Gauge Forces_ , _Phys.Rev.D_ 80 (2009)  [0906.0580].
  * (141) S. Bilmis, I. Turan, T. M. Aliev, M. Deniz, L. Singh and H. T. Wong, _Constraints on Dark Photon from Neutrino-Electron Scattering Experiments_ , _Phys.Rev.D_ 92 (2015)  [1502.07763].
  * (142) M. Lindner, F. S. Queiroz, W. Rodejohann and X.-J. Xu, _Neutrino-electron scattering: general constraints on Z’ and dark photon models_ , _JHEP_ 05 (2018) 098 [1803.00060].
  * (143) BaBar collaboration, J. P. Lees et al., _Search for a Dark Photon in $e^{+}e^{-}$ Collisions at BaBar_, _Phys. Rev. Lett._ 113 (2014) 201801 [1406.2980].
  * (144) BaBar collaboration, J. P. Lees et al., _Search for Invisible Decays of a Dark Photon Produced in ${e}^{+}{e}^{-}$ Collisions at BaBar_, _Phys. Rev. Lett._ 119 (2017) 131804 [1702.03327].
  * (145) LHCb collaboration, R. Aaij et al., _Search for Dark Photons Produced in 13 TeV $pp$ Collisions_, _Phys. Rev. Lett._ 120 (2018) 061801 [1710.02867].
  * (146) P. Ilten, Y. Soreq, M. Williams and W. Xue, _Serendipity in dark photon searches_ , _JHEP_ 06 (2018) 004 [1801.04847].
  * (147) R. Harnik, J. Kopp and P. A. N. Machado, _Exploring nu Signals in Dark Matter Detectors_ , _JCAP_ 07 (2012) 026 [1202.6073].
  * (148) N. F. Bell, G. Busoni and I. W. Sanderson, _Self-consistent Dark Matter Simplified Models with an s-channel scalar mediator_ , _JCAP_ 03 (2017) 015 [1612.03475].
  * (149) M. Cirelli, E. Del Nobile and P. Panci, _Tools for model-independent bounds in direct dark matter searches_ , _JCAP_ 10 (2013) 019 [1307.5955].
  * (150) A. Bonhomme et al., _Detecting CE $\nu$NS and searching for new physics at reactor site with the CONUS experiment_, _17th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2021) – J. Phys. Conf. Ser. (To be published)_ (2021) .
  * (151) M. Blennow, E. Fernandez-Martinez, T. Ota and S. Rosauro-Alcaraz, _Physics potential of the ESS $\nu$SB_, _Eur. Phys. J. C_ 80 (2020) 190 [1912.04309].
  * (152) D. Baxter, J. I. Collar, P. Coloma, C. E. Dahl, I. Esteban, P. Ferrario et al., _Coherent Elastic Neutrino-Nucleus Scattering at the European Spallation Source_ , _JHEP_ 02 (2020) 123 [1911.00762].
  * (153) J. B. Dent, B. Dutta, S. Liao, J. L. Newstead, L. E. Strigari and J. W. Walker, _Accelerator and reactor complementarity in coherent neutrino-nucleus scattering_ , _Phys.Rev.D_ 97 (2018)  [1711.03521].
  * (154) C. Bellenghi, D. Chiesa, L. Di Noto, M. Pallavicini, E. Previtali and M. Vignati, _Coherent elastic nuclear scattering of 51Cr neutrinos_, _Eur. Phys. J. C_ 79 (2019) 727 [1905.10611].
  * (155) M. Cadeddu, F. Dordei, C. Giunti, K. A. Kouzakov, E. Picciau and A. I. Studenikin, _Potentialities of a low-energy detector based on 4He evaporation to observe atomic effects in coherent neutrino scattering and physics perspectives_, _Phys. Rev. D_ 100 (2019) 073014 [1907.03302].
  * (156) M. Abdullah, D. Aristizabal Sierra, B. Dutta and L. E. Strigari, _Coherent Elastic Neutrino-Nucleus Scattering with directional detectors_ , _Phys.Rev.D_ 102 (2020)  [2003.11510].
  * (157) D. Aristizabal Sierra, B. Dutta, D. Kim, D. Snowden-Ifft and L. E. Strigari, _Coherent elastic neutrino-nucleus scattering with the $\nu$BDX-DRIFT directional detector at next generation neutrino facilities_, _Phys. Rev. D_ 104 (2021) 033004 [2103.10857].
  * (158) O. Tomalak, P. Machado, V. Pandey and R. Plestid, _Flavor-dependent radiative corrections in coherent elastic neutrino-nucleus scattering_ , _JHEP_ 02 (2021) 097 [2011.05960].