aainstitutetext: Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de
Madrid,
Calle de Nicolás Cabrera 13–15, Cantoblanco, E-28049 Madrid,
Spainbbinstitutetext: Center for Cosmology and AstroParticle Physics (CCAPP),
Ohio State University,
191 W. Woodruff Ave., Columbus, Ohio 43210, U.S.A.ccinstitutetext: Department
of Physics, Ohio State University,
191 W. Woodruff Ave., Columbus, Ohio 43210, U.S.A.ddinstitutetext: C. N. Yang
Institute for Theoretical Physics, Stony Brook University,
Stony Brook NY 11794-3840, U.S.A.eeinstitutetext: Institució Catalana de
Recerca i Estudis Avançats (ICREA),
Pg. Lluis Companys 23, E-08010 Barcelona, Spainffinstitutetext: Departament de
Fisica Quantica i Astrofisica and Institut de Ciencies del Cosmos,
Universitat de Barcelona, Diagonal 647, E-08028 Barcelona,
Spaingginstitutetext: Donostia International Physics Center (DIPC),
Paseo Manuel Lardizabal, 4, Donostia-San Sebastián, E-20018,
Spainhhinstitutetext: Ikerbasque, Basque Foundation for Science,
Plaza Euskadi 5, E-48013 Bilbao, Spainiiinstitutetext: Instituto de Física
Corpuscular (IFIC), CSIC & Universitat de València,
Parc Científic, C/ Catedrático José Beltrán 2, E-46980 Paterna, Spain

# Bounds on new physics with data of the Dresden-II reactor experiment and
COHERENT

Pilar Coloma<EMAIL_ADDRESS>b,c Ivan Esteban<EMAIL_ADDRESS>d,e,f M.C. Gonzalez-Garcia<EMAIL_ADDRESS>g
Leire Larizgoitia<EMAIL_ADDRESS>g,h Francesc Monrabal
<EMAIL_ADDRESS>i Sergio Palomares-Ruiz<EMAIL_ADDRESS>
###### Abstract

Coherent elastic neutrino-nucleus scattering was first experimentally
established five years ago by the COHERENT experiment using neutrinos from the
spallation neutron source at Oak Ridge National Laboratory. The first evidence
of observation of coherent elastic neutrino-nucleus scattering with reactor
antineutrinos has now been reported by the Dresden-II reactor experiment,
using a germanium detector. In this paper, we present constraints on a variety
of beyond the Standard Model scenarios using the new Dresden-II data. In
particular, we explore the constraints imposed on neutrino non-standard
interactions, neutrino magnetic moments, and several models with light scalar
or light vector mediators. We also quantify the impact of their combination
with COHERENT (CsI and Ar) data. In doing so, we highlight the synergies
between spallation neutron source and nuclear reactor experiments regarding
beyond the Standard Model searches, as well as the advantages of combining
data obtained with different nuclear targets. We also study the possible
signal from beyond the Standard Model scenarios due to elastic scattering off
electrons (which would pass selection cuts of the COHERENT CsI and the
Dresden-II experiments) and find more stringent constraints in certain parts
of the parameter space than those obtained considering coherent elastic
neutrino-nucleus scattering.

###### Keywords:

coherent neutrino-nucleus scattering, non-standard interactions, neutrino
magnetic moment, light mediators

††preprint:
IFT-UAM/CSIC-22-10 YITP-SB-2022-03 IFIC/22-06

##  1 Introduction

Low-energy neutrinos can elastically scatter off atomic nuclei via weak
neutral currents, with the initial and final states of the nucleus being
indistinguishable. For low enough momentum transfers, the interaction takes
place coherently with the whole nucleus, leading to an enhancement of the
cross section approximately proportional to the square of its number of
neutrons. Although the so-called coherent elastic neutrino-nucleus scattering
(CE$\nu$NS) was first theoretically described in Freedman’s seminal paper
almost 50 years ago Freedman:1973yd , its detection has not been possible
until very recently. This is so because the single observable for this process
is a recoiling nucleus which generates a signal in the sub-keV to few keV
energy range, difficult to detect. An additional hindrance to CE$\nu$NS
detection is the limited number of suitable neutrino sources, which must be
sufficiently intense in yield and, at the same time, low enough in neutrino
energy for the coherence condition to be satisfied.

The detection of CE$\nu$NS was experimentally demonstrated by the COHERENT
experiment COHERENT:2017ipa  using the currently most intense spallation
neutron source (SNS), sited at the Oak Ridge National Laboratory, U.S.A. The
original observation was obtained with a CsI[Na] scintillation detector
COHERENT:2017ipa ; COHERENT:2018imc , which was later followed by the
observation of CE$\nu$NS at a liquid Argon detector COHERENT:2020iec ;
COHERENT:2020ybo .

In addition to spallation sources, CE$\nu$NS is also searched for in a variety
of experiments using electron antineutrinos emitted by nuclear reactors, such
as TEXONO Wong:2004ru , $\nu$GeN Belov:2015ufh , CONNIE Aguilar-
Arevalo:2016khx , MINER Agnolet:2016zir , Ricochet Billard:2016giu ,
$\nu$-cleus Strauss:2017cuu , RED-100 Akimov:2019ogx , NEON Choi:2020gkm ,
CONUS CONUS:2020skt  and NCC-1701 at Dresden-II Colaresi:2021kus . At present,
most of these reactor experiments have not yet been successful in the
CE$\nu$NS detection. The exception to this is the NCC-1701 experiment at the
Dresden-II nuclear reactor. In their first published data Colaresi:2021kus ,
the experimental collaboration presented an event spectrum with an excess of
events at low energies, compatible with expectations from a CE$\nu$NS signal
in the Standard Model (SM). Recently, the collaboration has released new
results with an increased exposure. The observation of CE$\nu$NS is reported
with strong to very strong preference (with respect to the only-background
hypothesis) in the Bayesian statistics sense, depending on the quenching
factor considered Colaresi2022suggestive .

A precision measurement of CE$\nu$NS provides a direct probe to both SM and
beyond the standard model (BSM) physics. Paradigmatic examples of the former
are the determination of the weak mixing angle at very low momentum transfer
Canas:2018rng ; Cadeddu:2018izq ; Huang:2019ene ; Cadeddu:2019eta ;
Cadeddu:2020lky ; Cadeddu:2021ijh  and the study of nuclear structure
Cadeddu:2017etk ; Ciuffoli:2018qem ; Papoulias:2019lfi ; Cadeddu:2021ijh ;
Coloma:2020nhf . The program of BSM exploration with CE$\nu$NS is broad (see,
e.g., refs. Barranco:2005yy ; Formaggio:2011jt ; Anderson:2012pn ;
Dutta:2015nlo ; Cerdeno:2016sfi ; Dent:2016wcr ; Coloma:2017egw ;
Kosmas:2017zbh ; Ge:2017mcq ; Shoemaker:2017lzs ; Coloma:2017ncl ;
Liao:2017uzy ; Canas:2017umu ; Dent:2017mpr ; Papoulias:2017qdn ;
Farzan:2018gtr ; Billard:2018jnl ; Coloma:2019mbs ; Chaves:2021pey ;
AristizabalSierra:2018eqm ; Brdar:2018qqj ; Cadeddu:2018dux ; Blanco:2019vyp ;
Dutta:2019eml ; Miranda:2019wdy ; CONNIE:2019swq ; Dutta:2019nbn ;
Papoulias:2019txv ; Khan:2019cvi ; Cadeddu:2019eta ; Giunti:2019xpr ;
Baxter:2019mcx ; Canas:2019fjw ; Miranda:2020zji ; Flores:2020lji ;
Miranda:2020tif ; Hurtado:2020vlj ; Miranda:2020syh ; Cadeddu:2020nbr ;
Shoemaker:2021hvm ; delaVega:2021wpx ; Liao:2021yog ; CONUS:2021dwh ;
Flores:2021kzl ; Li:2022jfl ; AristizabalSierra:2019zmy ; Abdullah:2020iiv ;
Fernandez-Moroni:2021nap ; Bertuzzo:2021opb ; Bonet:2022imz  for an incomplete
list) being most sensitive to a variety of scenarios leading to modified
neutrino interactions with nuclei – in particular at low momentum transfer –
but extending also to the production of new light neutral states, and sterile
neutrino searches, among others.

In this paper, we present the first analysis using the new data of the
Dresden-II reactor experiment in the context of BSM searches. In doing so, we
consider several new physics scenarios commonly studied in the literature:
effective four-fermion interactions, neutrino magnetic moments, and light
mediators. In order to place our results in a broader context, we also combine
the Dresden-II data with a germanium detector with the COHERENT data obtained
for neutrino scattering off CsI and Ar. We highlight and quantify the
synergies between SNS and reactor experiments using CE$\nu$NS, as well as the
advantages of the combination of data sets obtained with multiple nuclear
targets. Furthermore, we also study a potential signal from BSM scenarios due
to elastic electron scattering (ES). Although in the SM this contribution to
the event rates is negligible, it could be significantly enhanced in the
presence of new physics effects. The contribution from scattering off
electrons could pass selection cuts of both COHERENT CsI and Dresden-II
experiments and, as we discuss, its inclusion leads to stronger constraints in
certain parts of the parameter space than those obtained using CE$\nu$NS.

The paper is organized as follows. In section 2 we introduce the theoretical
frameworks we consider. Section 3 discusses the computation of the expected
event rates and the details regarding our fit to the experimental data, while
the results of our analysis are presented in section 4. Finally, we summarize
and conclude in section 5, and provide the binding energies for neutrino
scattering off electrons in appendix A.

##  2 Phenomenological frameworks

| $c_{V}$ |  $c_{A}$
---|---|---
$\nu_{e}$ |  $\frac{1}{2}+2\,\sin^{2}\theta_{W}$ |  $+\frac{1}{2}$
$\nu_{\mu},\nu_{\tau}$ |  $-\frac{1}{2}+2\,\sin^{2}\theta_{W}$ |  $-\frac{1}{2}$
Table 1:  Values of the SM effective couplings in neutrino-electron
scattering. For antineutrinos the vector couplings are the same, while the
axial ones change sign, $c_{A}\to-c_{A}$.

Let us start by introducing the differential cross sections for both CE$\nu$NS
and ES in the SM. The SM differential coherent elastic scattering cross
section, for a neutrino with energy $E_{\nu}$ scattering off a nucleus of mass
$m_{A}$, is given111This strictly applies to $J=1/2$ nuclei Lindner:2016wff .
Note that for $J=0$ nuclei the last term is not present Freedman:1973yd ,
although its contribution is negligible for the energies of interest. by
Freedman:1973yd ; Lindner:2016wff

$\frac{\mathrm{d}\sigma^{\rm CE\nu NS}_{\rm SM}}{\mathrm{d}E_{R}}={\cal
Q}_{W}^{2}\,\frac{G_{F}^{2}\,m_{A}}{2\,\pi}\,\left[2-\frac{m_{A}\,E_{R}}{E_{\nu}^{2}}-\frac{2\,E_{R}}{E_{\nu}}+\left(\frac{E_{R}}{E_{\nu}}\right)^{2}\right]\,\left|F(q)\right|^{2}~{},$
(1)

where $G_{F}$ is the Fermi constant, $E_{R}$ is the nuclear (kinetic) recoil
energy, and the weak hypercharge of the nucleus in the SM is ${\cal
Q}_{W}=\left(N\,g_{V,n}+Z\,g_{V,p}\right)$, where $N$ and $Z$ are its number
of neutrons and protons, respectively. The weak charges of the neutron and the
proton are $g_{V,n}=-1/2$ and $g_{V,p}=1/2-2\sin^{2}\theta_{W}$, with
$\sin^{2}\theta_{W}=0.23868$ at zero momentum transfer Erler:2004in ;
Erler:2017knj . For Ge we use $\\{N,Z\\}=\\{40.71,\,32\\}$ (weighted average
of natural isotopic abundances), while for CsI we use
$\\{N,Z\\}=\\{76,\,54\\}$ and for Ar, $\\{N,Z\\}=\\{22,\,18\\}$.

In eq. (1) above, the nuclear form factor $F(q)$ is assumed to be equal for
protons and neutrons. Some commonly used phenomenological parameterizations
are the Klein-Nystrand Klein:1999qj  or the Helm Helm:1956zz  form factors,
among others. Note that, at the energies of interest for the Dresden-II
experiment, $F(q)\simeq 1$, so the choice of form factor is completely
irrelevant. For COHERENT, we use two different form factors, depending on the
target nucleus. For CsI, we use the theoretical calculation from refs.
Klos:2013rwa  (based on refs. Hoferichter:2018acd ; Hoferichter:2016nvd ),
while for Ar we assume a Helm form factor with $s=0.9~{}\mathrm{fm}$, $\langle
r_{n}^{2}\rangle=-0.1161~{}\mathrm{fm}^{2}$ and $\langle
r_{p}^{2}\rangle=0.70706~{}\mathrm{fm}^{2}$ ParticleDataGroup:2020ssz ,
$R_{\mathrm{ch}}=3.4274~{}\mathrm{fm}$ Angeli:2013epw  and
$R_{n,\mathrm{pt}}=3.405~{}\mathrm{fm}$ Payne:2019wvy  (following the same
notation as in ref. Coloma:2020nhf ).

The differential cross section for ES per atom within the SM can be expressed
as (see, e.g., refs. Vogel:1989iv ; Tomalak:2019ibg )

$\frac{\mathrm{d}\sigma^{\rm ES}_{\rm SM}}{\mathrm{d}T_{e}}=Z_{\rm eff}^{\rm
X}(T_{e})\,\frac{G_{F}^{2}\,m_{e}}{2\,\pi}\left[\left(c_{V}+c_{A}\right)^{2}+\left(c_{V}-c_{A}\right)^{2}\left(1-\frac{T_{e}}{E_{\nu}}\right)+\left(c_{A}^{2}-c_{V}^{2}\right)\frac{m_{e}\,T_{e}}{E_{\nu}^{2}}\right]~{},$
(2)

where $T_{e}$ stands for electron (kinetic) recoil energy. The effective
electron couplings $c_{V}$ and $c_{A}$ contain the contributions from the SM
neutral current (NC), which are equal for all flavors, plus the charged-
current (CC) contribution which only affects $\bar{\nu}_{e}e^{-}$ and
$\nu_{e}e^{-}$ scattering. For convenience, their values are given in table 1.

We assume that scattering off electrons is incoherent, so the total ES cross
section per atom is obtained by multiplying the ES cross section per electron
by an effective charge, $Z_{\rm eff}^{\rm X}(T_{e})$, where
$\textrm{X}\equiv^{A}_{Z}\\!\text{X}$ indicates the target nucleus. This takes
into account that, in this process, atomic binding effects have to be
considered for recoil energies comparable to atomic binding energies. In doing
so, we follow the procedure proposed in refs. Kopeikin:1997; Fayans:2000ns;
Mikaelyan:2002nv  and assume $Z_{\rm eff}^{\rm X}(T_{e})$ to be a step
function of the binding energies of the different atomic levels, as provided
in appendix A.

Finally, both types of interactions (off nuclei and off electrons) are two-
body elastic scattering processes, so the kinematics is the same. Hence, the
minimum neutrino energy to produce a recoil with energy $T$ is $E_{\nu,{\rm
min}}=\left(T+\sqrt{T^{2}+2\,m\,T}\right)/2$ and the maximum recoil energy for
a given neutrino energy is $T_{\rm max}=2\,E_{\nu}^{2}/(2\,E_{\nu}+m)$, where
$T\equiv E_{R}$ and $m\equiv m_{A}$ for nuclei, while $T\equiv T_{e}$ and
$m\equiv m_{e}$ for electrons.

Throughout this work we will consider several phenomenological scenarios
leading to modifications to the interaction cross sections in eqs. (1) and
(2), as explained in more detail below.

###  2.1 Non-standard neutrino interactions

The so-called non-standard neutrino interaction (NSI) framework consists on
the addition of four-fermion effective operators to the SM Lagrangian at low
energies. For example, the effective Lagrangian

$\mathcal{L}_{\text{NSI,
NC}}=-\sum_{f,\alpha,\beta}2\sqrt{2}\,G_{F}\,\varepsilon_{\alpha\beta}^{f,P}\,\left(\bar{\nu}_{\alpha}\gamma_{\mu}P_{L}\nu_{\beta}\right)\,\left(\bar{f}\gamma^{\mu}Pf\right)~{},$
(3)

would lead to new NC interactions with the rest of the SM fermions. Here,
$\alpha,\beta\equiv e,\mu,\tau$ while $f$ refers to SM fermions, and $P$ can
be either a left-handed or a right-handed projection operator ($P_{L}$ or
$P_{R}$, respectively). Such new interactions may induce lepton flavor-
changing processes (if $\alpha\neq\beta$), or may lead to a modified
interaction rate with respect to the SM result (if $\alpha=\beta$).

In presence of NC NSI, the effective charge of the nucleus in eq. (1) gets
modified,
$\mathcal{Q}_{W}^{2}\to\mathcal{Q}^{2}_{\alpha}(\boldsymbol{\varepsilon})$.
For real off-diagonal NSI parameters, it reads Barranco:2005yy

$\displaystyle\mathcal{Q}^{2}_{\alpha}(\boldsymbol{\varepsilon})$
$\displaystyle=$
$\displaystyle\left[Z\big{(}g_{p}^{V}+2\,\varepsilon_{\alpha\alpha}^{u}+\varepsilon_{\alpha\alpha}^{d}\big{)}+N\big{(}g_{n}^{V}+\varepsilon_{\alpha\alpha}^{u}+2\,\varepsilon_{\alpha\alpha}^{d}\big{)}\right]^{2}$
(4)
$\displaystyle+\sum_{\beta\neq\alpha}\left[Z\big{(}2\,\varepsilon_{\alpha\beta}^{u}+\varepsilon_{\alpha\beta}^{d})+N\big{(}\varepsilon_{\alpha\beta}^{u}+2\,\varepsilon_{\alpha\beta}^{d}\big{)}\right]^{2}~{}.$

where, in order to simplify notation, we have renamed
$\varepsilon_{\alpha\beta}\equiv\varepsilon_{\alpha\beta}^{q,V}=\varepsilon_{\alpha\beta}^{q,L}+\varepsilon_{\alpha\beta}^{q,R}$.
The weak charge may be rewritten in a more compact form as

$\displaystyle\mathcal{Q}^{2}_{\alpha}(\boldsymbol{\varepsilon})$
$\displaystyle=$
$\displaystyle\left[\mathcal{Q}_{W}+\varepsilon_{\alpha\alpha}^{\text{X}}\right]^{2}+\sum_{\beta\neq\alpha}\big{(}\varepsilon_{\alpha\beta}^{\text{X}}\big{)}^{2}~{},$
(5)

where we have defined

$\varepsilon_{\alpha\beta}^{\text{X}}\equiv
N\,\varepsilon_{\alpha\beta}^{n}+Z\,\varepsilon_{\alpha\beta}^{p}\,,\qquad\varepsilon_{\alpha\beta}^{n}\equiv\varepsilon_{\alpha\beta}^{u}+2\,\varepsilon_{\alpha\beta}^{d}~{},\qquad\varepsilon_{\alpha\beta}^{p}\equiv
2\,\varepsilon_{\alpha\beta}^{u}+\varepsilon_{\alpha\beta}^{d}~{}.$ (6)

The first consequence we observe of the inclusion of NSI effects is that the
weak charge may now depend on the incident neutrino flavor $\alpha$. As will
be discussed below, it is relevant to note that the COHERENT experiment
observes interactions of both electron and muon neutrinos. However, at first
approximation, it measures the linear combination
$\mathcal{Q}^{2}_{e}+2\,\mathcal{Q}^{2}_{\mu}$ and hence, both charges are
degenerate: a reduction in the value of $\mathcal{Q}^{2}_{e}$ can be
compensated by an increase in $\mathcal{Q}^{2}_{\mu}$ and vice versa. At
COHERENT, though, the addition of timing information partially breaks this
degeneracy for CsI, as discussed in detail in ref. Coloma:2019mbs . Including
reactor data, which is only sensitive to interactions with electron
antineutrinos, brings in additional complementary information in this respect
Dent:2017mpr . It provides an additional constraint on $\mathcal{Q}^{2}_{e}$,
which is independent of $\mathcal{Q}^{2}_{\mu}$.

The second relevant feature we observe from eqs. (4)-(6) is that the impact of
NSI on the weak charge depends on the values of $N$ and $Z$ in a non-trivial
manner. Because of this, the combination of data obtained for different nuclei
offers an additional handle to reduce the size of the allowed confidence
regions of this scenario (for earlier discussions see, e.g., refs.
Scholberg:2005qs ; Barranco:2005yy ; Coloma:2017egw ; Baxter:2019mcx ).

###  2.2 Neutrino magnetic moment

In the presence of a neutrino magnetic moment, $\mu_{\nu}$, the cross sections
for neutrino scattering off nuclei and electrons get additional contributions
which do not interfere with the SM ones. The scattering off protons can be
considered coherent and therefore its cross section is given, up to order
${\cal O}((E_{R}/E_{\nu})^{2},E_{R}/m_{A})$, by Vogel:1989iv

$\frac{\mathrm{d}\sigma^{\rm CE\nu
NS}_{\rm\mu_{\nu}}}{\mathrm{d}E_{R}}=Z^{2}\,\left(\frac{\mu_{\nu}}{\mu_{B}}\right)^{2}\,\frac{\alpha^{2}\,\pi}{m_{e}^{2}}\left[\frac{1}{E_{R}}-\frac{1}{E_{\nu}}\right]\;|F(q)|^{2}~{},$
(7)

where the form factor $F(q)$ is assumed to be the same as in the SM, which is
a reasonable approximation at the transfer momenta of interest
Hoferichter:2020osn .

Conversely, the scattering off electrons is incoherent and therefore, the
cross section in this case, up to order ${\cal O}((T_{e}/E_{\nu})^{2})$, is
Vogel:1989iv

$\frac{\mathrm{d}\sigma^{\rm ES}_{\rm\mu_{\nu}}}{\mathrm{d}T_{e}}=Z_{\rm
eff}^{\rm
X}(T_{e})\,\left(\frac{\mu_{\nu}}{\mu_{B}}\right)^{2}\,\frac{\alpha^{2}\,\pi}{m_{e}^{2}}\left[\frac{1}{T_{e}}-\frac{1}{E_{\nu}}\right]~{}.$
(8)

Notice that, in writing eqs. (7) and (8), we have denoted the neutrino
magnetic moment as $\mu_{\nu}$, without specifying the flavor of the neutrino.
However, neutrino magnetic moments arise in a variety of models of new physics
and, in particular, they do not need to be flavor-universal. Therefore, in
what follows, we will allow different magnetic moments for the different
neutrino flavors, reporting their bounds separately.

###  2.3 Light scalar mediators

The Lagrangian of the simplified model of interaction of a scalar $\phi$ with
the relevant fermions we consider is

${\cal
L}_{\phi}=g_{\phi}\,\phi\,\left(\sum_{q}q_{\phi}^{q}\,\bar{q}q+q_{\phi}^{e}\,\bar{e}e+q_{\phi}^{\nu}\,\bar{\nu}_{R}\nu_{L}+\text{h.c.}\right)-\frac{1}{2}\,M^{2}_{\phi}\,\phi^{2}~{},$
(9)

where $q_{\phi}^{i}$ are the charges of each fermion
($i=\\{\nu,\,e,\,u,\,d,\,s,\,c,\,b,\,t\\}$) under the new interaction. This
new interaction does not interfere with the SM one Rodejohann:2017vup ;
Farzan:2018gtr , and the corresponding neutrino-nucleus elastic scattering
cross section, up to order ${\cal O}((E_{R}/E_{\nu})^{2})$, reads
Cerdeno:2016sfi ; Farzan:2018gtr

$\frac{\mathrm{d}\sigma^{\rm CE\nu
NS}_{\phi}}{\mathrm{d}E_{R}}=\frac{g_{\phi}^{4}\,(q_{\phi}^{\nu})^{2}\,\mathcal{Q}_{\phi}^{2}}{4\,\pi}\,\frac{m_{A}^{2}\,E_{R}}{E_{\nu}^{2}\,(2\,m_{A}\,E_{R}+M_{\phi}^{2})^{2}}\,|F(q)|^{2}~{},$
(10)

where $F(q)$ is the form factor (which, with enough precision at the transfer
momenta of interest, can be assumed to be the same as in the SM
Hoferichter:2020osn ), and $\mathcal{Q}_{\phi}$ is the nuclear charge for the
scalar interaction Shifman:1978zn ; DelNobile:2013sia ; Ellis:2018dmb ,

$\mathcal{Q}_{\phi}=\sum_{N,q}q^{q}_{\phi}\,\frac{m_{N}}{m_{q}}\,f^{(N)}_{T,q}+\frac{2}{27}\,\left(1-\sum_{N,q}f^{(N)}_{T,q}\right)\sum_{N,\tilde{q}}q_{\phi}^{\tilde{q}}\,\frac{m_{N}}{m_{q}}~{}.$
(11)

Here $N=n,p$ stands for the nucleons, the superindex $q=u,d,s$ runs over the
light valence and sea quarks, $\tilde{q}=c,b,t$ runs over the heavy quarks,
and the coefficients $f_{T,q}^{(N)}$ incorporate the effective low-energy
couplings of the scalar to the nucleons Shifman:1978zn . For universal
coupling of the scalar to quarks,
$q_{\phi}^{u}=q_{\phi}^{d}=q_{\phi}^{s}=q_{\phi}^{c}=q_{\phi}^{b}=q_{\phi}^{t}\equiv
q_{\phi}^{q}$, the nuclear scalar charge takes the value
$\mathcal{Q}_{\phi}=q_{\phi}^{q}\,(14\,N+15.1\,Z)$ DelNobile:2013sia .222This
is an approximate expression, which actually does not coincide with any of the
sets of values in ref. DelNobile:2013sia  (for updated values of the
coefficients, see ref. Ellis:2018dmb ). We use it for the sake of comparison
with the results from refs. Cerdeno:2016sfi ; CONUS:2021dwh . Current
uncertainties on the low-energy coefficients and masses lead to variations of
20%-30% in eq. (11); we have numerically checked that this leads to a
$\lesssim 10\%$ effect on our constraints.

Scalar exchange also gives a contribution to the cross section for neutrino-
electron elastic scattering as Cerdeno:2016sfi

$\frac{\mathrm{d}\sigma^{\rm ES}_{\phi}}{\mathrm{d}T_{e}}=Z_{\rm eff}^{\rm
X}(T_{e})\,\frac{g_{\phi}^{4}\,(q^{\nu}_{\phi})^{2}\,(q^{e}_{\phi})^{2}}{4\,\pi}\,\frac{m_{e}^{2}\,T_{e}}{E_{\nu}^{2}\,(2\,m_{e}\,T_{e}+M_{\phi}^{2})^{2}}~{}.$
(12)

In order to quantify the contribution of the scattering off electrons, in
section 4 we study the constraints on two specific models: a first one in
which the scalar couples universally to all relevant fermions (hereafter
referred to as _universal_), and another one in which it only couples to
leptons (dubbed _leptonic scalar_ model). For convenience, table 2 summarizes
the explicit values of charges considered for the different SM fermions.

Model |  $q^{q}$ |  $q^{e}$ |  $q^{\nu_{e}}$ |  $q^{\nu_{\mu}}$
---|---|---|---|---
Universal scalar or vector | 1 | 1 | 1 | 1
Leptonic ($\ell$) scalar | 0 | 1 | 1 | 1
$L_{e}$ vector | 0 | 1 | 1 | 0
$B-L$ vector | $\frac{1}{3}$ | -1 | -1 | -1
Table 2: Charges for the scalar and vector mediator models considered in this
work.

###  2.4 Light vector mediators

The Lagrangian of a simplified model of interaction of a neutral vector
$Z^{\prime}$ with the fermions of the first generation is given by

${\cal
L}_{Z^{\prime}}=g_{Z^{\prime}}\;Z^{\prime}_{\mu}\left(q_{Z^{\prime}}^{u}\,\bar{u}\gamma^{\mu}u+q_{Z^{\prime}}^{d}\,\bar{d}\gamma^{\mu}d+q_{Z^{\prime}}^{e}\,\bar{e}\gamma^{\mu}e+q_{Z^{\prime}}^{\nu}\,\bar{\nu}_{L}\gamma^{\mu}\nu_{L}\right)+\frac{1}{2}M^{2}_{Z^{\prime}}{Z^{\prime}}^{\mu}Z^{\prime}_{\mu}~{},$
(13)

where $q_{Z^{\prime}}^{i}$ indicates the charges of each fermion
($i=\\{\nu,\,e,\,u,\,d\\}$) under the new interaction.

Unlike the magnetic-moment and scalar interactions, a neutral vector
interaction interferes with the SM. The additional contribution to the
neutrino-nucleus scattering cross section reads Cerdeno:2016sfi

$\Delta\frac{\mathrm{d}\sigma^{\rm CE\nu
NS}_{Z^{\prime}}}{\mathrm{d}E_{R}}=\frac{g^{2}_{Z^{\prime}}\,m_{A}}{2\,\pi}\left[\frac{g^{2}_{Z^{\prime}}\,(q_{Z^{\prime}}^{\nu})^{2}\,\mathcal{Q}^{2}_{Z^{\prime}}}{\left(2\,m_{A}\,E_{R}+M_{Z^{\prime}}^{2}\right)^{2}}-\frac{2\,\sqrt{2}\,G_{F}\,q_{Z^{\prime}}^{\nu}\,\mathcal{Q}_{Z^{\prime}}\,\mathcal{Q}_{W}}{\left(2\,m_{A}\,E_{R}+M_{Z^{\prime}}^{2}\right)}\right]\left(1-\frac{m_{A}\,E_{R}}{2\,E^{2}_{\nu}}\right)|F(q)|^{2}~{},$
(14)

where $\mathcal{Q}_{Z^{\prime}}$ is the weak charge of the nucleus for the
light vector interaction. Vector current conservation implies that only
valence quarks contribute by simply summing up their charges, so for universal
couplings ($q_{Z^{\prime}}^{u}=q_{Z^{\prime}}^{d}\equiv q_{Z^{\prime}}^{q}$),
$\mathcal{Q}_{Z^{\prime}}=3\,q_{Z^{\prime}}^{q}\,(Z+N)$ (see, e.g., ref.
DelNobile:2013sia ). As in the case of scalar mediators, we use the same
nuclear form factor as in the SM.

The corresponding contribution to the cross section for ES reads
Cerdeno:2016sfi

$\Delta\frac{\mathrm{d}\sigma^{\rm ES}_{Z^{\prime}}}{\mathrm{d}T_{e}}=Z_{\rm
eff}^{\rm
X}(T_{e})\,\frac{g^{2}_{Z^{\prime}}\,m_{e}}{2\,\pi}\left[\frac{{g^{2}_{Z^{\prime}}}\,(q_{Z^{\prime}}^{\nu})^{2}\,(q^{e}_{Z^{\prime}})^{2}}{\left(2\,m_{e}\,T_{e}+M_{Z^{\prime}}^{2}\right)^{2}}\,+\,\frac{2\,\sqrt{2}\,G_{F}\,q_{Z^{\prime}}^{\nu}\,q_{Z^{\prime}}^{e}\,c_{V}}{\left(2\,m_{e}\,T_{e}+M_{Z^{\prime}}^{2}\right)}\right]~{},$
(15)

where $c_{V}$ is the SM effective vector coupling introduced in eq.(2), which
depends on the flavor of the incident neutrino as given in table 1.

As in the case with light scalar mediators, in section 4 we study the
constraints on three specific models in which the vector couples universally
to all relevant fermions, another in which it only couples to electron flavor
($L_{e}$), and the anomaly-free flavor-universal model with coupling to $B-L$
(see table 2).

##  3 Data analysis

In this section we describe the procedure we follow to perform the data
analysis of the Dresden-II and COHERENT data.

###  3.1 The Dresden-II reactor experiment

We use a sample with 96.4-day exposure of a 2.924 kg ultra-low noise p-type
point contact (PPC) germanium detector (NCC-1701) to the high flux of electron
antineutrinos from the Dresden-II boiling water reactor (BWR). The new data
set spans the period between January 22 and May 8, 2021, when the reactor was
operated at its full nominal power of 2.96 GW. In the data release
Colaresi2022suggestive , which we follow closely, the data points and errors
are provided in the form of rate per day. The errors (per day) represent a
combination of statistical and signal acceptance uncertainties. With the new
information obtained from the reactor operator, the improved center-to-center
effective distance between the PPC crystal and the center point of the BWR
core is 10.39 m. The estimate of the $\bar{\nu}_{e}$ flux from the reactor is
$4.8\times 10^{13}~{}\bar{\nu}_{e}/\textrm{cm}^{2}\textrm{s}$ with a $\sim
2\%$ uncertainty Huber:2011wv ; Mueller:2011nm . We describe the reactor
$\bar{\nu}_{e}$ spectrum using the typical average values of fission fractions
of the four main isotopes (making up more than 99% of all reactor neutrinos),
for commercial power reactor using low-enriched uranium: ${}^{235}\rm{U}$
(58%), ${}^{239}\rm{Pu}$ (29%), ${}^{238}\rm{U}$ (8%) and ${}^{241}\rm{Pu}$
(5%) Qian:2018wid . We use the combination of the tabulated spectra for
$E_{\bar{\nu}_{e}}<2$ MeV from ref. Vogel:1989iv  and for
$2~{}\textrm{MeV}\leq E_{\bar{\nu}_{e}}\leq 8$ MeV from ref. Mueller:2011nm .
We set the flux to zero beyond the maximum energy that is tabulated.

The background model consists of four components Colaresi2022suggestive ,
although only two of them really contribute to the SM signal region. The other
two allow constraining these components. The dominant source in the signal
region is the elastic scattering of epithermal neutrons, which is modeled by a
free exponential plus a free constant term, $R_{\rm epith}+A_{\rm
epith}\,e^{-E_{\rm rec}/E_{\rm epith}}$, where $E_{\rm rec}$ is the
reconstructed ionization energy. The other three components of the background
consist of electron capture (EC) peaks in 71Ge, which are all described as
Gaussian probability density functions (PDF) with three free parameters: the
amplitude $A_{\rm shell}$, the centroid $E_{\rm shell}$, and the standard
deviation $\sigma_{\rm shell}$. The $M$-shell EC peak is constrained by the
$L_{1}$-shell EC peak, with parameters
$\\{A_{L_{1}},\,E_{L_{1}},\,\sigma_{L_{1}}\\}$. Although the $L_{1}$-shell
peak is at a nominal energy of 1.297 keV, it is also allowed to vary freely.
The ratio of the amplitudes of the $L_{1}$-shell and $M$-shell has been
experimentally determined to be $0.16\pm 0.03$ SuperCDMS:2015eex , so
following the data release Colaresi2022suggestive , we model this ratio with a
Gaussian prior of width $\sigma_{M/L_{1}}=0.03$ and centered at
$A_{M}/A_{L_{1}}=0.16$, which we add to the likelihood. The centroid of the
$M$-shell EC contribution is fixed at $E_{M}=0.158$ keV SuperCDMS:2015eex ;
Firestone1996  and the standard deviation is set to be equal to the electronic
noise $\sigma_{M}=\sigma_{n}$, which is 68.5 eV during the 96.4 days of
reactor operation (Rx-ON) and 65.25 eV during the 25 days of reactor refueling
outage (Rx-OFF). Finally, the last contribution comes from the $L_{2}$-shell
EC, with the amplitude fixed by $A_{L_{2}}/A_{L_{1}}=0.008$, the centroid at
$E_{L_{2}}=1.142$ keV and the standard deviation
$\sigma_{L_{2}}=\sigma_{L_{1}}$. Explicitly, the background model, in terms of
the reconstructed ionization energy, $E_{\rm rec}$, is described by a
differential rate

$\frac{\mathrm{d}R_{\rm bkg}(\boldsymbol{\beta})}{\mathrm{d}E_{\rm
rec}}=R_{\rm epith}+A_{\rm epith}\,e^{-E_{\rm rec}/E_{\rm
epith}}+\sum_{i=L_{1},L_{2},M}\frac{A_{i}}{\sqrt{2\,\pi}\,\sigma_{i}}\,e^{-\frac{\left(E_{\rm
rec}-E_{i}\right)^{2}}{2\,\sigma_{i}^{2}}}~{},$ (16)

in the reconstructed energy region of interest (ROI) $E_{\rm
rec}=[0.2,1.5]~{}{\rm keV}$. The number of free background parameters to be
fitted in every analysis is seven, which are represented by the vector
$\boldsymbol{\beta}=\left\\{R_{\rm epith},A_{\rm epith},E_{\rm
epith},A_{L_{1}},E_{L_{1}},\sigma_{L_{1}},\beta_{M/L_{1}}\right\\}$. The
parameter $\beta_{M/L_{1}}$, defined as $A_{M}=\beta_{M/L_{1}}\,A_{L_{1}}$, is
added to the likelihood with a Gaussian prior, as described below.

The CE$\nu$NS signal rate from the reactor $\bar{\nu}_{e}$ flux is given by

$\frac{\mathrm{d}R_{\rm sig}^{\textrm{CE}\nu\textrm{NS}}}{\mathrm{d}E_{\rm
rec}}=N_{\rm T}\,\int_{E_{\nu,{\rm
min}}}^{\infty}\mathrm{d}E_{\bar{\nu}_{e}}\int_{E_{R,\rm min}}^{E_{R,\rm
max}}\mathrm{d}E_{R}\,\frac{\mathrm{d}\Phi_{\bar{\nu}_{e}}}{\mathrm{d}E_{\bar{\nu}_{e}}}\,\frac{\mathrm{d}\sigma^{\rm
CE\nu NS}}{\mathrm{d}E_{R}}\,{\cal R}(E_{\rm
rec},E_{I}=Q\,E_{R};\sigma_{I})~{},$ (17)

where $N_{T}=2.43\times 10^{25}$ is the number of germanium nuclei and
$\mathrm{d}\Phi_{\bar{\nu}_{e}}/\mathrm{d}E_{\bar{\nu}_{e}}$ is the reactor
electron antineutrino spectrum. Here $E_{R,\rm min}$ is the minimum nuclear
recoil energy which corresponds to a minimum average ionization energy,
$E_{I,\rm min}\simeq 2.98$ eV, required to produce a hole-pair in germanium
(at 77 K) Antman1966272  (see ref. Wei:2016xbw  for a compilation of existing
data at other temperatures). The ionization energy is defined as
$E_{I}=Q(E_{R})\,E_{R}$, with $Q(E_{R})$ being the quenching factor, which
describes the reduction in ionization yield of a nuclear recoil when compared
to an electron recoil of same energy. We consider two models from the data
release, which are not in tension with CONUS data CONUS:2020skt , and are
denoted by ‘Fef’ (using iron-filtered monochromatic neutrons) and ‘YBe’ (based
on photoneutron source measurements) Collar:2021fcl . The spread between these
two models approximately represents the uncertainty on this parameter. Note
that the cross sections in eqs. (7) and (8) diverge as the recoil energy goes
to zero. Consequently, the contribution arising from the scattering due to the
neutrino magnetic moment (and similarly for models with very light mediators)
is larger in the lower energy bins, a contribution that can be divergently
large under the assumption that asymptotically low ionization energies could
trigger the detector. This unphysical behavior is cut-off by the physical
requirement of the average energy required to produce an electron-hole pair.
Thus, in what follows, we impose $E_{I,\rm min}=3$ eV when evaluating the
expected rate of events.

The energy resolution function, ${\cal R}(E_{\rm rec},E_{I};\sigma_{I})$, is
described as a truncated Gaussian ($E_{\rm rec}>0$),

${\cal R}(E_{\rm
rec},E_{I};\sigma_{I})=\left(\frac{2}{1+\textrm{Erf}\left(\frac{E_{I}}{\sqrt{2}\,\sigma_{I}}\right)}\right)\,\frac{1}{\sqrt{2\,\pi}\,\sigma_{I}}\,e^{-\frac{\left(E_{\rm
rec}-E_{I}\right)^{2}}{2\,\sigma_{I}^{2}}}~{},$ (18)

with $\sigma_{I}^{2}=\sigma_{n}^{2}+E_{I}\,\eta\,F$, where the electronic
noise is $\sigma_{n}=68.5~{}{\rm eV}$ (Rx-ON) and 65.25 eV (Rx-OFF), $\eta$ is
the average energy of electron-hole formation and $F$ is the Fano factor. For
Ge, $\eta=2.96$ eV and $F=0.11$ Colaresi2022suggestive . The prefactor with
the error function is included to guarantee the resolution function is
normalized to 1 for $E_{I}>0$. Note that, although the reconstructed energy
ROI is $E_{\rm rec}=[0.2,1.5]~{}{\rm keV}$, events with $E_{I}<0.2~{}{\rm
keV}$ are assumed to trigger the detector and be susceptible of filtering into
the ROI.

Moreover, it is important to point out that, as provided, all data points are
already corrected for signal acceptance, so this must not be included in the
calculation of the expected signal rate. Ideally, raw data and signal
acceptance as a function of the true ionization energy, $E_{I}$, must be used.
In this way, the signal acceptance must be included in eq. (17). Nevertheless,
the approach used here, following the data release, has a negligible impact on
signals that grow slowly at small ionization energies, as the SM or NSI cases.
Yet, it could have a non-negligible effect on the event rate in models with a
large neutrino magnetic moment or in the presence of light mediators (in the
case of interactions with nucleons). Furthermore, the impact of using signal
acceptance-corrected data also depends on the minimum ionization energy
capable of triggering the detector. Note that the minimum ionization energy at
which the signal acceptance is currently measured is 0.13 keV
Colaresi2022suggestive .

With all these ingredients, the expected event rate is given by

$\frac{\mathrm{d}R\left(\boldsymbol{\theta};\boldsymbol{\beta}\right)}{\mathrm{d}E_{\rm
rec}}=\frac{\mathrm{d}R_{\rm
bkg}\left(\boldsymbol{\beta}\right)}{\mathrm{d}E_{\rm
rec}}+\frac{\mathrm{d}R_{\rm
sig}^{\textrm{CE}\nu\textrm{NS}}\left(\boldsymbol{\theta}\right)}{\mathrm{d}E_{\rm
rec}}+\frac{\mathrm{d}R_{\rm sig}^{\rm
ES}\left(\boldsymbol{\theta}\right)}{\mathrm{d}E_{\rm rec}}~{},$ (19)

where our notation explicitly indicates that the event rates include both the
signal contribution from CE$\nu$NS and from ES.

In general, when considering different new physics scenarios, the signal rate
depends on a set of (one or two in this work) parameters
$\boldsymbol{\theta}$. We use the following $\chi^{2}$,

$\chi_{\rm
D-II}^{2}\left(\boldsymbol{\theta};\boldsymbol{\beta}\right)=\sum_{i=1}^{130}\frac{\left(P_{i}\left(\boldsymbol{\theta};\boldsymbol{\beta}\right)-D_{i}\right)^{2}}{\sigma_{i}^{2}}+\frac{\left(\beta_{M/L_{1}}-A_{M}/A_{L_{1}}\right)^{2}}{\sigma_{M/L_{1}}^{2}}~{},$
(20)

where $P_{i}$ refers to the prediction and $D_{i}$ to the measured rates (or
number of events in the exposure time) in energy bin $i$ (of width 10 eV and
with the center of the bin indicated in the data release), $\sigma_{i}$ is the
standard deviation of the rate (or of the measured number of events in the
exposure time) in bin $i$, which combines statistical and signal acceptance
uncertainties, and $\beta_{M/L_{1}}$ is the ratio between the amplitudes of
the $M$-shell and $L_{1}$-shell EC contributions to the background, with
central value $A_{M}/A_{L_{1}}=0.16$ and $\sigma_{M/L_{1}}=0.03$. We do not
include additional nuisance parameters. Nevertheless, we have checked that
even adding a 10% uncertainty on the normalization of the signal, the results
are only affected at the percent level. Finally, in order to study the
sensitivity to the new physics parameters, we profile the above likelihood,

$\left(\chi^{2}_{\rm D-II}\right)_{\rm
p}\left(\boldsymbol{\theta}\right)=\chi_{\rm
D-II}^{2}\left(\boldsymbol{\theta};\widehat{\widehat{\boldsymbol{\beta}\,}}(\boldsymbol{\theta})\right)\equiv\textrm{min}_{\boldsymbol{\beta}}\left\\{\chi_{\rm
D-II}^{2}\left(\boldsymbol{\theta};\boldsymbol{\beta}\right)\right\\}~{},$
(21)

where the profiled values of $\boldsymbol{\beta}$ that minimize $\chi^{2}$ for
each $\boldsymbol{\theta}$ are indicated by a double hat.

Figure 1:  Left panel: Spectral rate of signal events from CE$\nu$NS and
$\bar{\nu}_{e}e^{-}$ scattering in the SM and from the electromagnetic
scattering induced by a neutrino magnetic moment
$\mu_{\nu_{e}}=10^{-10}\mu_{B}$. Right panel: Spectral rate of signal events
from CE$\nu$NS and $\bar{\nu}_{e}e^{-}$ scattering in the SM and for the
contribution induced by an interaction mediated by a massless scalar boson
(dashed lines) and by a massless vector boson (dotted lines), assuming
universal couplings (see table 2). For a vector mediator, we show the addition
of both contributions, the purely vector boson contribution and the
interference with the SM (see eq. (14)). In both panels we compare the spectra
to data, after subtracting the best-fit background model assuming only the SM
signal. All results in both panels are depicted for the Fef model of the
quenching factor (for interactions with nuclei) and assuming $E_{I,\rm min}=3$
eV.

In figure 1 we show the predicted event distributions for the SM and for the
models of new physics we consider. Along with these spectra, we also include
the Dresden-II data points, after subtracting the best-fit background model
assuming only the SM signal. In the left panel of figure 1 we show the
predicted event distributions for the SM and the extra contribution from a
non-zero magnetic moment. We see that the $\mu_{\nu_{e}}$-induced
electromagnetic scattering off protons dominates over the corresponding
scattering off electrons for $E_{\rm rec}\lesssim 0.35$ keV. This is so
because the coherent cross section off nuclei is enhanced by the factor
$Z^{2}/Z_{\rm eff}^{\rm Ge}$, which is large enough to compensate the
suppression due to the quenching factor (which makes the characteristic
$1/E_{R}$ of the nucleus smaller than $1/T_{e}$ of the electron, for the same
value of $E_{\rm rec}$). Also, from eqs. (10), (12), (14) and (15) we expect
different spectra of events for interactions mediated by light scalars or by
light vectors, as well as a different scaling with energy for scattering off
electrons and off nucleus. This can be seen from the comparison among the
different curves in the right panel of figure 1, where we have assumed
universal couplings (see table 2). The event spectra for interactions mediated
by a massless scalar are very similar to the $\mu_{\nu_{e}}$-induced ones, as
they are governed by the $1/E_{R}$ or $1/T_{e}$ dependence for CE$\nu$NS or
ES, respectively. In this case, the coherent cross section off nuclei is
enhanced by the factor $\mathcal{Q}_{\phi}^{2}/Z_{\rm eff}^{\rm Ge}$ with
respect to that of scattering off electrons. On the other hand, the event
spectra for ES mediated by a massless vector is much larger than the one for
scattering off nuclei. Unlike the cases of the magnetic moment or the scalar
mediator, the dominant contribution at small energies for CE$\nu$NS is a
factor $\sim m_{e}/m_{A}$ smaller than for ES.

###  3.2 The COHERENT experiment

For the COHERENT CsI analysis, we follow the same procedure as in ref.
Coloma:2019mbs . We use the nuclear form factor from ref. Klos:2013rwa , we
estimate the time dependence of the background directly from anti-coincidence
data, and for concreteness, we use the quenching factor from ref.
Collar:2019ihs . In the present work we also include scattering off electrons.
In this case, there is no quenching factor, the target mass is set to the
electron mass, and we use an effective number of electrons per nucleus,
$Z_{\mathrm{eff}}(T_{e})$, as provided in appendix A (see also section 2). The
rest of the details of the analysis are the same as in ref. Coloma:2019mbs .
Here, the minimum recoil energy considered can be safely set to zero, since
the efficiency vanishes at low energies.

For the analysis of Ar data, we follow the official data release
COHERENT:2020ybo . In this case we do _not_ include scattering off electrons,
as the experiment can discriminate nuclear from electron recoils
COHERENT:2020iec . To obtain the CE$\nu$NS event spectrum, we start by
computing the signal event spectrum in nuclear recoil energy, $E_{R}$, which
is given by

$\frac{\mathrm{d}N}{\mathrm{d}E_{R}}=\mathcal{N}\sum_{\alpha}\int_{E_{\nu,\mathrm{min}}}^{m_{\mu}/2}\frac{\mathrm{d}\sigma(E_{\nu},E_{R})}{\mathrm{d}E_{R}}\,\frac{\mathrm{d}\phi_{\alpha}}{\mathrm{d}E_{\nu}}\,\mathrm{d}E_{\nu}~{},$
(22)

where $E_{\nu}$ is the neutrino energy and the sum extends over the three
components of the neutrino flux $\\{\nu_{e},\nu_{\mu},\bar{\nu}_{\mu}\\}$. The
neutrino spectra $\mathrm{d}\phi_{\alpha}/\mathrm{d}E_{\nu}$ are normalized to
1 (see, e.g., eq. (2.1) in ref. Coloma:2019mbs  for the expressions), and all
normalizations are absorbed into an overall constant $\mathcal{N}$ given by

$\mathcal{N}=\frac{1}{4\pi\ell^{2}}\,N_{\mathrm{PoT}}\,f_{\pi/p}\,N_{\mathrm{Ar}}~{},$
(23)

where $\ell=27.5~{}\mathrm{m}$ is the distance to the detector;
$N_{\mathrm{PoT}}=13.77\times 10^{22}$ is the number of protons on target
(PoT), corresponding to an integrated power of 6.12 GW$\cdot$hr;
$f_{\pi/p}=0.09$ is the number of pions produced per PoT; and
$N_{\mathrm{Ar}}=m_{\mathrm{det}}/m_{\rm Ar}$ is the number of nuclei in the
detector, with $m_{\mathrm{det}}=24.4~{}\mathrm{kg}$ the detector mass and
$m_{\rm Ar}$ the 40Ar mass.

However, the experimental collaboration does not bin their data in nuclear
recoil energy (keVnr), but in electron-equivalent recoil energy instead
(keVee). In addition, we have to account for the detection efficiency,
$\epsilon$, and the energy resolution. Introducing these effects, the expected
event rate in each bin $i$ (of width $\Delta E_{\rm rec}$) is computed as:

$N_{i}=\int_{E_{\rm rec,i}-\Delta E_{\rm rec}/2}^{E_{\rm rec,i}+\Delta E_{\rm
rec}/2}\mathrm{d}E_{\rm rec}\,\,\epsilon(E_{\rm
rec})\int_{E_{R,\mathrm{min}}}^{\infty}\mathrm{d}E_{R}\,\frac{\mathrm{d}N}{\mathrm{d}E_{R}}\,\mathcal{R}(E_{\rm
rec},E_{I};\sigma_{I})~{},$ (24)

where $E_{I}$ stands for the true electron-equivalent recoil energy and
$E_{\rm rec}$ is the reconstructed electron-equivalent recoil energy (that is,
after energy smearing effects). The function $\mathcal{R}$ accounts for the
energy resolution of the detector:

$\mathcal{R}(E_{\rm
rec},E_{I};\sigma_{I})=\frac{1}{\sqrt{2\,\pi}\,\sigma_{I}}\,e^{\frac{-\left(E_{\rm
rec}-E_{I}\right)^{2}}{2\,\sigma_{I}^{2}}}~{},$ (25)

with a width
$\sigma_{I}\equiv\sigma(E_{I})=0.58~{}\mathrm{keV}\,\sqrt{E_{I}/\mathrm{keV}}$,
as prescribed in the data release. As the energies in the ROI are much larger
than the standard deviation, this definition, unlike eq. (18), does not
require the extra factor to guarantee it is correctly normalized to 1. Also,
note that in eq. (24) the detection efficiency $\epsilon$ is obtained post-
triggering and it is a function of the reconstructed energy (and not of the
true energy).333Furthermore, contrary to the indications provided in the data
release, in our analysis we include this efficiency as a function of
reconstructed energy _before binning the event distribution_ , as otherwise we
do not find good agreement with the results of the collaboration.

We set the minimum nuclear recoil energy to $E_{I,\mathrm{min}}=19.5$ eV, the
average energy to produce a scintillation photon in Ar Creus:2013sau . As
indicated above, the relation between $E_{I}$ and $E_{R}$ is given by the
quenching factor, $E_{I}=Q(E_{R})\,E_{R}$, which is described as
$Q(E_{R})=a+b\,E_{R}$, with $a=0.246$ and $b=0.00078$ keV-1, as given in the
data release.

Following the procedure above, we obtain a nominal prediction of $135.3$
signal events. This is slightly higher than the rates predicted by the
collaboration, but well within their reported error bars (their nominal
prediction is $128\pm 17$ events). Our spectrum also shows good agreement with
the official one.

To further reduce backgrounds, the analysis includes information not only on
recoil energy, but also on timing and on the fraction of integrated amplitude
within the first 90 ns (this last variable is called F90 by the
collaboration). Once we compute the distribution in recoil energy as described
above, we can obtain the full 3D PDF. We do so by rescaling the original PDF
provided by the collaboration by the ratio of their projected PDF in $E_{\rm
rec}$ to our $E_{\rm rec}$ event distribution, i.e.,

$N_{i,j,k}=\mathrm{PDF}_{i,j,k}\times\frac{N_{i}}{\sum_{j,k}\mathrm{PDF}_{i,j,k}}~{},$
(26)

where $\mathrm{PDF}_{i,j,k}$ stands for the predicted PDF provided by the
collaboration as a function of recoil energy $i$, F90,j and time $k$. To do
this, we use their nominal prediction in absence of systematics.

Finally, we include systematic uncertainties by adding nuisance parameters as
prescribed in the data release.444We have checked that the impact of the
quenching factor uncertainties is negligible at the level of the uncertainties
quoted in the data release. Therefore, they are not included here. For each
nuisance parameter, we add a pull term to either the signal or background
prediction as

$n_{i,j,k}=\bar{n}_{i,j,k}\,(1+\xi\,\sigma_{i,j,k})~{},$ (27)

where $\bar{n}$ is the predicted signal or background event rates with no
systematic errors, $\xi$ is the nuisance parameter, and $\sigma_{i,j,k}$ is
obtained from the data release. We also add a signal normalization uncertainty
as

$s_{i,j,k}=\bar{s}_{i,j,k}\,(1+\xi_{\mathrm{norm}}\,\sigma_{\mathrm{norm}})~{},$
(28)

where we set $\sigma_{\mathrm{norm}}=0.1$ according to the data release (this
corresponds to the “neutrino flux” uncertainty listed in table 1 in ref.
COHERENT:2020iec ).

We use a Poissonian $\chi^{2}$ for statistical uncertainties,

$\left(\chi^{2}_{\rm
COH}\right)_{\mathrm{stat}}=\sum_{i,j,k}2\left(P_{i,j,k}-D_{i,j,k}+D_{i,j,k}\ln\frac{D_{i,j,k}}{P_{i,j,k}}\right)~{},$
(29)

where $D$ stands for the data and $P$ for the prediction (including the effect
of the nuisance parameters). A pull term is then added for each nuisance
parameter $\xi_{r}$, as well as for the normalization of the background
components,

$\chi_{\rm COH}^{2}\left({\boldsymbol{\xi}}\right)=\left(\chi^{2}_{\rm
COH}\right)_{\mathrm{stat}}+\sum_{r}\xi_{r}^{2}+\left(\frac{n_{\rm
pr}-\bar{n}_{\rm pr}}{\sigma_{\rm pr}}\right)^{2}+\left(\frac{n_{\rm
del}-\bar{n}_{\rm del}}{\sigma_{\rm del}}\right)^{2}+\left(\frac{n_{\rm
ss}-\bar{n}_{\rm ss}}{\sigma_{\rm ss}}\right)^{2}~{},$ (30)

where $\bar{n}$ and $\sigma$ are the central values and the uncertainties at
$1\sigma$ provided in the data release for the different background
components. The final $\left(\chi^{2}_{\rm COH}\right)_{\mathrm{p}}$ is
obtained after minimization over all nuisance parameters and the normalization
of the three background components.

##  4 Results

In this section we present the results of the analysis of the Dresden-II
reactor experiment data and its combination with COHERENT CsI and Ar data, for
the BSM frameworks presented in section 2.

###  4.1 Bounds on non-standard neutrino interactions

As described in section 2.1, in presence of NSI the Dresden-II reactor
experiment is sensitive to a unique combination of the $\varepsilon$
coefficients, $\mathcal{Q}^{\rm Ge}_{e}(\boldsymbol{\varepsilon})$, defined in
eq. (5), where we have introduced an explicit superindex indicating the
nucleus it refers to. We show in the left panel of figure 2 the dependence of
$\Delta\chi^{2}_{\rm D-II}$ on this effective NSI combination. In constructing
this $\Delta\chi^{2}_{\rm D-II}$, we have profiled over the background model
parameters for each value of $\mathcal{Q}^{\rm
Ge}_{e}(\boldsymbol{\varepsilon})^{2}$ and we have neglected small effects of
any additional systematic nuisance parameter. As mentioned above, the signal
acceptance uncertainties are included in the data provided by the experiment.

Figure 2: Left panel: Dependence of the profiled $\Delta\chi^{2}_{\rm D-II}$
on the combination of NSI coefficients relevant to CE$\nu$NS of
$\bar{\nu}_{e}$ scattering off the Ge detector of the Dresden-II experiment.
Right panel: Allowed regions at 90% CL (1 dof, two-sided,
$\Delta\chi^{2}=2.71$) in the $(\varepsilon_{ee}^{u},\varepsilon_{ee}^{d})$
plane. In both panels, the results are shown for two quenching factors,
denoted by Fef (in blue), using iron-filtered monochromatic neutrons, and YBe
(in red), based on photoneutron source measurements Collar:2021fcl . Although
not obvious, note that the allowed regions for the two quenching factors have
one common side, so the Fef constraints are more stringent.

From figure 2, we read the following ranges allowed at 90% confidence level
(CL) (1 dof)

$\left(g_{e}^{\rm Ge}\right)^{2}\equiv\left(\frac{\mathcal{Q}^{\rm
Ge}_{e}(\boldsymbol{\varepsilon})}{\mathcal{Q}^{\rm
Ge}_{e}(0)}\right)^{2}=0.91\pm 0.56\;\;(1.36\pm 0.97)~{},$ (31)

derived with the Fef (YBe) quenching factor for germanium. Notice that
$g_{e}^{\rm Ge}=1$ corresponds to the SM prediction and $g_{e}^{\rm Ge}=0$ to
no signal, so this implies that the absence of CE$\nu$NS in the Dresden-II
data is disfavored at 2.6$\sigma$ (2.3$\sigma$) for the analysis with the Fef
(YBe) quenching factor.

In the right panel of figure 2, we show the corresponding 90% CL allowed
regions for the flavor-diagonal NSI coefficients $\varepsilon_{ee}^{u}$ and
$\varepsilon_{ee}^{d}$ assuming vanishing non-diagonal NSI coefficients. The
shape of these bands can be understood directly from the expression of the
weak charge of the nucleus in eq. (4). They are defined as the two regions
around the points that satisfy

$\left[\mathcal{Q}_{W}+(2\,Z+N)\,\varepsilon_{ee}^{u}+(2\,N+Z)\,\varepsilon_{ee}^{d}\right]^{2}={\rm
constant}~{},$ (32)

which follow lines in the $(\varepsilon_{ee}^{u},\varepsilon_{ee}^{d})$ plane
with the slope given by $-(2Z+N)/(2N+Z)$. As seen in the figure, the analysis
employing the Fef quenching factor results in slightly stronger constraints.
In most scenarios we find that the analysis using the Fef quenching factor
reproduces slightly better the SM predictions and therefore leaves less room
for new physics. Exception, as we will see, is the case for some models with
light vector mediators for which a local non-standard minima appears in the
analysis with the YBe quenching factor, which results in slightly stronger
constraints (see section 4.4).

Figure 3: 90% CL allowed regions on flavor diagonal NSI with up-quarks (for
zero values of all other NSI coefficients) from the analysis of COHERENT CsI
and Ar data, the Dresden-II reactor data – with Fef (YBe) quenching factor in
left (right) panel –, and their combination. Note that, in the two-dimensional
panels, the results for the Dresden-II reactor experiment are obtained for 1
dof ($\Delta\chi^{2}=2.71$), while the rest of the regions are obtained for 2
dof ($\Delta\chi^{2}=4.61$).

CE$\nu$NS at the COHERENT experiment is sensitive to interactions of electron
and muon neutrinos and hence, it provides information on the corresponding
effective combinations $\mathcal{Q}^{\rm CsI}_{e}(\boldsymbol{\varepsilon})$,
$\mathcal{Q}^{\rm CsI}_{\mu}(\boldsymbol{\varepsilon})$, $\mathcal{Q}^{\rm
Ar}_{e}(\boldsymbol{\varepsilon})$, $\mathcal{Q}^{\rm
Ar}_{\mu}(\boldsymbol{\varepsilon})$. Generically, because both $\nu_{e}$ and
$\nu_{\mu}$ are present in the beam, degeneracies between NSI parameters
corresponding to $e$ and $\mu$ flavors appear. This is illustrated in figure
3, where we show the allowed regions obtained from our combined analysis of
CE$\nu$NS at COHERENT with both CsI and Ar targets for flavor-diagonal NSIs
with up-quarks only (the results for NSI with only down-quarks are similar).
The shape of these regions for a given nucleus leads to allowed regions
defined by a band around the points that approximately obey the equation of an
ellipse in the $(\varepsilon_{ee}^{u},\varepsilon_{\mu\mu}^{u})$ plane,

$\left[\mathcal{Q}_{W}+\left(2\,Z+N\right)\,\varepsilon_{ee}^{u}\right]^{2}+2\,\left[\mathcal{Q}_{W}+\left(2\,Z+N\right)\,\varepsilon_{\mu\mu}^{u}\right]^{2}={\rm
constant}~{}.$ (33)

Since $\mathcal{Q}_{W}$ depends on the target nucleus, the ellipse obtained is
different for different detector materials and, therefore, it may be broken by
adding information on different nuclei, provided they have a different ratio
of protons to neutrons (for earlier discussions on this, see, e.g., refs.
Scholberg:2005qs ; Barranco:2005yy ; Coloma:2017egw ; Baxter:2019mcx ). Most
importantly, the use of timing information at COHERENT translates into a
partial discrimination between the weak charges for the different flavors,
thanks to the distinct composition of the prompt ($\nu_{\mu}$) and delayed
($\bar{\nu}_{\mu}$ and $\nu_{e}$) neutrino flux. This leads to a partial
breaking of this degeneracy which, however, is not complete (see, e.g., ref.
Coloma:2019mbs  for a more detailed explanation of this effect). This is what
explains the results shown in figure 3. The regions allowed by COHERENT data
present a double-wedge shape due to the partial breaking of the degeneracy
between those two parameters after the inclusion of the energy and, in
particular, the timing information.555For concreteness, the COHERENT analysis
shown in this plot was performed using the quenching factor from the Chicago
group Collar:2019ihs . See ref. Coloma:2019mbs  for a discussion about the
small variation of the results obtained with other quenching factors. But yet,
a continuous wide range of values of $\varepsilon^{u}_{ee}$ remains allowed.

For the considered flavor-diagonal NSI with up-quarks only, CE$\nu$NS at the
Dresden-II reactor experiment provides information on $\varepsilon^{u}_{ee}$
only, so the allowed regions correspond to the vertical bands in the figure.
Consequently, the combined analysis of COHERENT + Dresden-II results in a
substantial reduction of the allowed values of $\varepsilon^{u}_{ee}$ (and
indirectly, also on $\varepsilon^{u}_{\mu\mu}$) as seen in the figure.

We finish by commenting that the results we show correspond to the case of
diagonal NSI with up-quarks only, but as mentioned above, similar results are
obtained for diagonal NSI with down-quarks only. We also notice that the
inclusion of flavor off-diagonal NSI couplings results in the enlargement of
the regions shown in figure 3. Nevertheless, within the current constraints
from other experiments, in particular from neutrino oscillations
Esteban:2018ppq ; Coloma:2019mbs , similar qualitative conclusions hold. For
NSI couplings to both up and down quarks, the complementarity between COHERENT
and Dresden-II data depends on the specific assumption about the ratio of
diagonal couplings to both quarks. If they are varied freely, meaningful
constraints cannot be obtained, as can be understood from figure 2. Therefore,
current data from these experiments is not enough by itself to impose
meaningful constraints on the complete parameter space of NSI with quarks, if
considered in full generality.

###  4.2 Bounds on neutrino magnetic moments

Figure 4: Left panel: Profiled $\Delta\chi^{2}_{\rm D-II}$ including events
induced by a magnetic moment for $\bar{\nu}_{e}$. We show results including
only $\mu_{\nu_{e}}$-induced scattering off electrons (dashed curves) and for
scattering off electrons and nucleons (solid curves). In both cases the SM
CE$\nu$NS contribution is included. Right panel: 90% CL excluded (one-sided)
regions from the combination of Dresden-II and COHERENT data (in color). We
also indicate (with arrows) the 90% CL (one-sided) allowed regions from
Dresden-II data with the Fef (blue dotted line) and YBe (red dotted line)
quenching factor, and from the combined analysis of COHERENT CsI and Ar data
(black dashed line). Notice that the vertical lines for the Dresden-II reactor
experiment are defined one-sided for 1 dof $(\Delta\chi^{2}=1.64$), while the
rest of the regions are defined for 2 dof ($\Delta\chi^{2}=3.22$).

The results of our analysis of data from the Dresden-II reactor experiment,
including the contribution induced by a neutrino magnetic moment, are shown in
figure 4 where, on the left panel, we plot the one-dimensional
$\Delta\chi^{2}_{\rm D-II}$ as a function $\mu_{\nu_{e}}$ after profiling over
all background parameters ${\boldsymbol{\beta}}$. As previously, we have
neglected small effects of any additional systematic nuisance parameter, while
the signal acceptance uncertainties are included in the data provided by the
experiment. For comparison, in the left panel we also show
$\Delta\chi^{2}_{\rm D-II}$ for the case of scattering off electrons only,
including the SM CE$\nu$NS contribution (dashed lines). As discussed in
section 3.1, the contribution from ES induced by a neutrino magnetic moment is
subdominant to that from CE$\nu$NS. One must notice, however, that a better
bound on $\mu_{\nu_{e}}$ (and similarly for models with light scalar
mediators, see below) could be attainable with a dedicated analysis aimed at
optimizing the sensitivity to the signal from scattering of electrons. The
signal acceptance at the lowest energies in the Dresden-II experiment is quite
small Colaresi2022suggestive , which significantly reduces statistics.
Furthermore, given the much flatter shape of the event spectrum for the
magnetic moment contribution than from the SM, as depicted in figure 1,
extending the ROI to higher energies could enhance the signal-to-noise ratio
(see, e.g., ref. Bonet:2022imz ).

The fit shows no evidence of a non-zero magnetic moment and therefore, the
analysis results in a bound which, at 90% CL (1 dof), reads

$\left|\mu_{\nu_{e}}\right|<\left\\{\begin{array}[]{c}1.9\;(2.9)\times
10^{-10}\;\mu_{B}\quad\textrm{(one-sided~{}limit)}\\\\[6.45831pt]
2.2\;(3.3)\times 10^{-10}\;\mu_{B}\quad\textrm{(two-
sided~{}limit)}\end{array}\right.~{},$ (34)

for the Fef (YBe) quenching factor for germanium. This is an order of
magnitude weaker than the current best limit from reactor antineutrinos
Beda:2012zz ; Beda:2013mta . Notice that here we report two different limits
according to different statistical criteria to derive constraints. The reason
is that the experiment is in fact sensitive to $|\mu_{\nu_{e}}|^{2}$, which
can only take non-negative values. Therefore, accounting for the physical
boundary, it is possible to report the limit on $|\mu_{\nu_{e}}|$ as a one-
sided limit, which at 90% CL for 1 dof (2 dof) corresponds to
$\Delta\chi^{2}=1.64\;(3.22)$. Conversely, if this restriction is not imposed,
the result obtained is what is denoted as a two-sided limit, which at 90%CL
for 1 dof (2 dof) corresponds to $\Delta\chi^{2}=2.71\;(4.61)$ and results
into less tight constraints. For the sake of comparison with different results
in the literature, we indicate in eq. (34) bounds obtained with both criteria.
As seen in eq. (34), the difference is at the level of 10%.

As mentioned in section 3.1 the $\mu_{\nu}$-induced cross sections in eqs. (7)
and (8) diverge as the recoil energy goes to zero and this unphysical behavior
is cut-off by the physical requirement of the average energy required to
produce an electron-hole pair, $E_{I,\rm min}=3$ eV. This raises the issue of
the possible dependence of the bounds on the exact value of this minimum
energy that could trigger the detector. The dependence on the cut energy,
however, is approximately logarithmic and we have verified that increasing it
by as much as one order of magnitude results in weakening the bounds in eq.
(34) by less than 25%.

CE$\nu$NS at the COHERENT experiment provides information on magnetic moments
for both $\nu_{e}$ and $\nu_{\mu}$. In the right panel of figure 4, we show
their 90% CL (2 dof, one-sided) excluded values, obtained with our combined
analysis of CE$\nu$NS at COHERENT with both CsI and Ar targets. Because there
is no interference between the contributions from $\mu_{\nu_{\mu}}$ and
$\mu_{\nu_{e}}$, the resulting allowed region is just a square with a rounded
upper-right corner. The 90% CL (1 dof, one-sided) upper bound from the
Dresden-II reactor experiment on $\mu_{\nu_{e}}$, eq. (34), is indicated by
vertical lines. As seen in the figure, the sensitivity of COHERENT to
$\mu_{\nu_{e}}$ is ${\cal O}(10)$ weaker. The combination of the two
experiments results in the 90% CL excluded regions (2 dof, one-sided) shown in
the figure in color. The corresponding combined bounds on each neutrino
magnetic moment (after profiling over the other) at 90% CL (1 dof) are

$\displaystyle\left|\mu_{\nu_{e}}\right|$ $\displaystyle<$
$\displaystyle\left\\{\begin{array}[]{c}1.8\;(2.8)\times
10^{-10}\;\mu_{B}\quad\textrm{(one-sided~{}limit)}\\\\[6.45831pt]
2.2\;(3.2)\times 10^{-10}\;\mu_{B}\quad\textrm{(two-
sided~{}limit)}\end{array}\right.~{},$ (37)
$\displaystyle\left|\mu_{\nu_{\mu}}\right|$ $\displaystyle<$
$\displaystyle\left\\{\begin{array}[]{c}2.4\;(2.4)\times
10^{-9}\;\mu_{B}\quad\;\,\textrm{(one-sided~{}limit)}\\\\[6.45831pt]
2.7\;(2.7)\times 10^{-9}\;\mu_{B}\quad\;\textrm{(two-
sided~{}limit)}\end{array}\right.~{},$ (40)

for the combination of data from the COHERENT and the Dresden-II reactor
experiments performed with the Fef (YBe) quenching factor for germanium.

###  4.3 Bounds on light scalar mediator models

Figure 5: Left panel: 90% CL (2 dof, two-sided, $\Delta\chi^{2}=4.61$)
excluded regions for models with light scalar mediators coupled universally to
all relevant fermions. Right panel: 90% CL (2 dof, two-sided,
$\Delta\chi^{2}=4.61$) excluded regions for models with light scalar mediators
coupled only to leptons. The thick blue and red dotted lines show the boundary
of the region excluded by the Dresden-II reactor experiment with the Fef and
YBe quenching factors, respectively. The black dashed line shows the boundary
of region excluded from the analysis of COHERENT CsI and Ar data. The filled
regions are those excluded by the combined COHERENT+Dresden-II analysis.

The results of the analysis of the data from the Dresden-II reactor experiment
and its combination with COHERENT, including the contribution of the events
induced by a new light scalar mediator, are shown in figure 5. We depict the
excluded region at 90% CL (2 dof, two-sided) for the parameter space of the
scalar models $\left(\left|g^{\rm mod}_{\phi}\right|,M_{\phi}\right)$, for the
two models with charges listed in table 2. On the left panel, we show the
results for a scalar coupling universally coupled to all relevant fermions,
while on the right panel we focus on a scalar which only interacts with
leptons.

The thick blue and red thick dotted lines in figure 5 show the boundaries of
the regions excluded by the Dresden-II reactor data with with the Fef and YBe
quenching factor, respectively. These results are obtained after profiling
over the background model parameters (i.e., for each value of
$\left(\left|g^{\rm mod}_{\phi}\right|,M_{\phi}\right)$). For light mediator
masses, the experiment has no sensitivity to the mediator mass and the limit
of the regions approaches a horizontal line of constant $\left|g^{\rm
mod}_{\phi}\right|$. For these effectively massless scalar mediators it is
possible to derive an upper bound on the coupling constant regardless the
mediator mass, which for the considered models, reads at 90% CL (1 dof),

$\displaystyle\left|g_{\phi}^{\rm univ}\right|$ $\displaystyle\leq$
$\displaystyle\left\\{\begin{array}[]{c}1.6\;(1.9)\times
10^{-6}\quad\textrm{(one-sided)}\\\\[6.45831pt] 1.7\;(2.0)\times
10^{-6}\quad\textrm{(two-sided)}\end{array}\right.~{},$ (43)
$\displaystyle\left|g_{\phi}^{\ell}\right|$ $\displaystyle\leq$
$\displaystyle\left\\{\begin{array}[]{c}4.9\;(5.5)\times
10^{-6}\quad\textrm{(one-sided)}\\\\[6.45831pt] 5.5\;(6.1)\times
10^{-6}\quad\textrm{(two-sided)}\end{array}\right.~{},$ (46)

for the Fef (YBe) quenching factor for germanium. As done above, we indicate
both, one-sided and two-sided (1 dof) bounds.

Conversely, for larger mediator masses, the boundary is a diagonal,
characteristic of the contact-interaction limit. In that case, the event rates
depend on $(g_{\phi}/M_{\phi})^{4}$, which we find to be well approximated by

$\displaystyle\frac{\left|g_{\phi}^{\rm univ}\right|}{M_{\phi}/{\rm MeV}}$
$\displaystyle\gtrsim$ $\displaystyle 3.4\;(3.6)\times 10^{-7}~{},\quad{\rm
for\;}M_{\phi}\gtrsim 10\;{\rm MeV}~{},$
$\displaystyle\frac{\left|g_{\phi}^{\ell}\right|}{M_{\phi}/{\rm MeV}}$
$\displaystyle\gtrsim$ $\displaystyle 1.1\;(1.1)\times 10^{-4}~{},\quad{\rm
for\;}M_{\phi}\gtrsim 0.1\;{\rm MeV}~{},$ (47)

for the Fef (YBe) quenching factor for germanium.

In summary, we find that for sufficiently light mediators ($M_{\phi}\lesssim
10^{-2}~{}\mathrm{MeV}$), the bound on the coupling constant is about a factor
${\cal O}(3)$ stronger if the interaction is coupled to quarks than if it
couples only to leptons. This is so because scalar-mediated CE$\nu$NS always
dominates over the corresponding scalar-mediated incoherent scattering off
electrons for the low-energy part of the spectrum, where statistics is best
(see figure 1). Equivalently, in the contact-interaction limit, the bound on
$\left|g^{\rm univ}_{\phi}\right|/M_{\phi}$ is more than two orders of
magnitude better than on $\left|g^{\ell}_{\phi}\right|/M_{\phi}$.

In figure 5, we also show the boundary of the regions excluded from the
analysis of COHERENT CsI and Ar data (black dashed lines). For most of the
parameter space we consider, the bounds imposed by the Dresden-II reactor
experiment dominate in either model. COHERENT bounds only become competitive
for the universal model for $\left|g_{\phi}^{\rm univ}\right|\gtrsim 5\times
10^{-5}$. Consequently, the results in eqs. (46) and (47) hold to good
approximation for the combination of COHERENT and Dresden-II reactor
experiments.

###  4.4 Bounds on light vector mediator models

The results of the analysis of the data from the Dresden-II reactor experiment
and its combination with COHERENT, including the contribution of the events
induced by a new light vector mediator, are shown in figure 6. The figure
displays the regions excluded at 90% CL (2 dof, two-sided) corresponding to
the parameter space of vector mediator models $\left(\left|g^{\rm
mod}_{Z^{\prime}}\right|,M_{Z^{\prime}}\right)$, for the three cases with
charges listed in table 2.

Figure 6: Upper left panel: 90% CL (2 dof, two-sided, $\Delta\chi^{2}=4.61$)
excluded regions for models with light vector mediators coupled universally to
all relevant fermions. Upper right panel: 90% CL (2 dof, two-sided,
$\Delta\chi^{2}=4.61$) excluded regions for models with light vector mediators
coupled only to $L_{e}$. Lower panel: 90% CL (2 dof, two-sided,
$\Delta\chi^{2}=4.61$) excluded regions for models with light vector mediators
coupled only to $B-L$. The thick blue and red dotted lines show the boundary
of the region excluded by the Dresden-II reactor experiment with the Fef and
YBe quenching factors, respectively. The black dashed line shows the boundary
of region excluded from the analysis of COHERENT CsI and Ar data. The filled
regions are those excluded by the combined COHERENT+Dresden-II analysis.

As above, the thick blue and red thick dotted lines in the figures indicate
the boundaries of the regions excluded at 90% CL by the Dresden-II reactor
data with the Fef and YBe quenching factor, respectively, after profiling over
the background model parameters. The black dashed lines indicate the boundary
of the regions excluded from the analysis of COHERENT CsI and Ar data and the
filled regions correspond to the results of the COHERENT + Dresden-II
combination. We see that COHERENT bounds only give some contribution for the
universal and $B-L$ models for $\left\\{\left|g_{Z^{\prime}}^{\rm
univ}\right|,\left|g_{Z^{\prime}}^{B-L}\right|\right\\}\gtrsim 5\times
10^{-4}$.

Again, we find that for sufficiently light mediator masses ($M_{\phi}\lesssim
10^{-2}~{}\mathrm{MeV}$) the region becomes independent of the mediator mass.
For these effectively massless vector mediators, the corresponding 90% CL (1
dof) upper bounds on the coupling constant read

$\displaystyle\left|g_{Z^{\prime}}^{\rm univ}\right|$ $\displaystyle\leq$
$\displaystyle\left\\{\begin{array}[]{c}0.87\;(1.0)\times
10^{-6}\quad\textrm{(one-sided)}\\\\[6.45831pt] 0.92\;(1.1)\times
10^{-6}\quad\textrm{(two-sided)}\end{array}\right.~{},$
$\displaystyle\left|g_{Z^{\prime}}^{L_{e}}\right|$ $\displaystyle\leq$
$\displaystyle\left\\{\begin{array}[]{c}0.90\;(1.0)\times
10^{-6}\quad\textrm{(one-sided)}\\\\[6.45831pt] 0.95\;(1.1)\times
10^{-6}\quad\textrm{(two-sided)}\end{array}\right.~{},$ (52)
$\displaystyle\left|g_{Z^{\prime}}^{B-L}\right|$ $\displaystyle\leq$
$\displaystyle\left\\{\begin{array}[]{c}0.90\;(1.1)\times
10^{-6}\quad\textrm{(one-sided)}\\\\[6.45831pt] 0.95\;(1.1)\times
10^{-6}\quad\textrm{(two-sided)}\end{array}\right.~{},$

for the Fef (YBe) quenching factor for germanium. As done above, we indicate
both, one-sided and two-sided (1 dof) bounds.

Unlike the case of scalar mediators, in the small-mass limit, the bounds for
vector mediators are very similar regardless of whether quarks are charged
under the new interaction. This is so because in this limit the $Z^{\prime}$
contribution to the event rates is dominated by the incoherent scattering off
electrons, as seen in figure 1. We also notice that for all models, the
regions obtained with the YBe quenching factor present a dip around
$M_{Z^{\prime}}\sim 0.03$ MeV and $\left|g_{Z^{\prime}}\right|\sim 10^{-6}$.
This arises because the inclusion of scattering off electrons mediated by such
a particle provides a fit which is better than the SM one at $\sim$
1.5$\sigma$. Comparing the two upper panels, we also see that constraints on
the universal model become more stringent than those on the $L_{e}$ model for
$M_{Z^{\prime}}\gtrsim 0.2$ MeV. For these masses, CE$\nu$NS starts dominating
over scattering off electrons.

For sufficiently large mediator masses, the contact-interaction approximation
is recovered and the event rates vary with a power of
$\left|g_{Z^{\prime}}\right|/M_{Z^{\prime}}$, which ranges from a power of
two, due the interference with the SM, to a power of four, when the new vector
contribution is the dominant one (the interplay between the interference and
quadratic contributions is responsible for the disconnected island observed in
the upper right excluded region of the $B-L$ model). From the figure, we read
that, in this regime, the boundaries of the 90% CL excluded regions for the
Dresden-II reactor experiment are approximately described by

$\displaystyle\frac{\left|g_{Z^{\prime}}^{\rm
univ}\right|}{M_{Z^{\prime}}/{\rm MeV}}$ $\displaystyle\gtrsim$ $\displaystyle
7.5\;(9.0)\times 10^{-7}~{},\quad{\rm for\;}M_{Z^{\prime}}\gtrsim 10\;{\rm
MeV}~{},$
$\displaystyle\frac{\left|g_{Z^{\prime}}^{L_{e}}\right|}{M_{Z^{\prime}}/{\rm
MeV}}$ $\displaystyle\gtrsim$ $\displaystyle 1.7\;(2.9)\times
10^{-5}~{},\quad{\rm for\;}M_{Z^{\prime}}\gtrsim 0.1\;{\rm MeV}~{},$ (55)
$\displaystyle\frac{\left|g_{Z^{\prime}}^{B-L}\right|}{M_{Z^{\prime}}/{\rm
MeV}}$ $\displaystyle\gtrsim$ $\displaystyle\quad\;\;(6.5)\times
10^{-7}~{},\quad{\rm for\;}M_{Z^{\prime}}\gtrsim 10\;{\rm MeV}~{},$

for the Fef (YBe) quenching factor for germanium. For the $B-L$ model, the
interplay between scattering off electrons and nucleus and between the
interference and quadratic pieces makes the region obtained with the Fef
quenching factor not well described by this approximation. Also, as mentioned
above, for the universal and $B-L$ models, the combination with COHERENT
slightly extends the large-mass part of the excluded region beyond these
values as seen in the figure.

##  5 Summary and conclusions

The first evidence of observation of CE$\nu$NS with reactor electron
antineutrinos has been recently reported by an experiment conducted at the
Dresden-II reactor site, using the NCC-1701 germanium detector
Colaresi2022suggestive . This adds to the previous measurements performed by
the COHERENT experiment, which uses neutrinos from a spallation neutron source
and has observed CE$\nu$NS using both CsI[Na] and Ar nuclei COHERENT:2017ipa ;
COHERENT:2018imc ; COHERENT:2020iec ; COHERENT:2020ybo .

The very low momentum transfer produced by CE$\nu$NS renders this process an
excellent probe of new interactions in the neutrino sector. In this paper, we
have performed a detailed analysis of the new data from the Dresden-II
experiment, with the aim of deriving powerful constraints on a variety of BSM
scenarios. In particular, we have derived new bounds on neutrino NSI with
quarks, magnetic moments for electron and muon neutrinos, and several models
with light neutral scalar or vector mediators. Our analysis includes the
contributions to the event rates from CE$\nu$NS and from elastic scattering
off electrons.

In our analysis of the Dresden-II data, we have taken special care in
profiling over the parameters required to accurately model the background,
closely following the data release of the experimental collaboration
Colaresi2022suggestive . We have also quantified the dependence of the results
on the quenching factor by considering two models: one based on the use iron-
filtered monochromatic neutrons (Fef) and another one based on photoneutron
source measurements (YBe). The impact on the results of the uncertainty on
this parameter is approximately indicated by the spread between the bounds
obtained for these two models. As for COHERENT, our analysis includes both
timing and energy information in the case of CsI, while in the case of the Ar
data, we perform a $\chi^{2}$ analysis using time, energy and F90 information.
A careful treatment of systematic uncertainties is performed, following the
prescriptions provided by the collaboration in refs. COHERENT:2018imc ;
COHERENT:2020ybo .

We have also quantified the impact of the combination of the new data from the
Dresden-II reactor experiment with COHERENT data. From the phenomenological
point of view, the main difference between these two experiments arises from
the different flavor composition of the neutrino flux: while a nuclear reactor
only emits $\bar{\nu}_{e}$, at a spallation neutron source neutrinos are
primarily produced from pion decay at rest and therefore, the flux contains an
equal admixture of $\nu_{\mu}$, $\bar{\nu}_{\mu}$, and $\nu_{e}$, with higher
energies than the reactor $\bar{\nu}_{e}$ flux. Therefore, generically, for
models with lepton-flavor dependent effects (such as NSI), COHERENT is a
priori sensitive to a larger number of parameters. Nevertheless, the flavor
discrimination with COHERENT comes from the timing information and is only
partial. Thus, within the current experimental precision, this results in
degeneracies among the $\mu$-flavor and $e$-flavor parameters. The new
Dresden-II data bring in complementary information in this respect, as they
provide independent constraints on the $e$-flavor parameters. As a result, the
combination of both experiments allows breaking (or at least alleviating)
degeneracies present in the case of NSI, as illustrated in figure 3. Moreover,
the combination of data obtained for scattering off different nuclei (Ar and
CsI for COHERENT, Ge for the Dresden-II experiment) also adds additional
synergies since, for a given set of NSI parameters, the impact on the weak
charge is different depending on the particular nucleus under consideration
(see eq. (4)).

In the case of neutrino magnetic moment and light mediators with masses below
${\cal O}(100\;{\rm MeV})$, we generically find that the Dresden-II experiment
outperforms the bounds obtained for COHERENT (an obvious exception is the
magnetic moment of muon neutrinos, which is only constrained by COHERENT,
since for the Dresden-II experiment only a $\bar{\nu}_{e}$ flux is available).
This is a priori expected, since the Dresden-II experiment is sensitive to
much lower values of the momentum transfer, a critical feature which drives
the experimental reach of these scenarios. On the other hand, for mediators
with masses above ${\cal O}(100\;{\rm MeV})$, we find that COHERENT and
Dresden-II lead to similar bounds for the universal and $B-L$ scenarios, while
if the new interaction is coupled only to leptons, the Dresden-II bound is
more restrictive.

We finish by commenting on the role of ES. While the event rates from this
process are insignificant in the SM, their contribution could be significantly
enhanced in the presence of new physics effects. Most notably, such
contribution could pass the signal selection cuts for both the Dresden-II
experiment and the COHERENT CsI detector. In fact, for the analysis of
COHERENT CsI, this is a novel point of our analysis with respect to previous
works in the literature. Our results show that the inclusion of ES is
particularly relevant in scenarios with light vector mediators. In the case of
COHERENT CsI, this improves the bound on the coupling obtained from CE$\nu$NS
alone for the $B-L$ and universal models by at least a factor $\sim 5$, for
mediator masses below $\sim 20$ MeV. And a similar improvement is obtained on
the bounds derived from the Dresden-II reactor data when taking ES into
account. Conversely, in the reconstructed energy range of the Dresden-II
experiment, the contribution of ES induced by a neutrino magnetic moment and
by light scalar mediators is smaller than that from CE$\nu$NS. At higher
energies, however, ES would also dominate over CE$\nu$NS at the Dresden-II
reactor experiment. Therefore, extending the reconstructed energy region to
higher energies could enhance the reach of the Dresden-II experiment within
these BSM scenarios.

###### Acknowledgements.

We warmly thank Juan Collar for all the help with the new Dresden-II data
release. We also thank Nicola Cargioli for noticing a plotting bug in figure
1. This project has received funding/support from the European Union’s Horizon
2020 research and innovation program under the Marie Skłodowska-Curie grant
agreement No 860881-HIDDeN, and from grants RTI2018-095979,
PID2019-108892RB-I00, PID2019-105614GB-C21, PID2020-113334GB-I00,
PID2020-113644GB-I00, CEX2019-000918-M and CEX2020-001007-S, funded by
MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. PC is
also supported by Grant RYC2018-024240-I funded by MCIN/AEI/
10.13039/501100011033 and by “ESF Investing in your Investing in your future”.
M.C.G-G is also supported by U.S.A.-NSF grant PHY-1915093, and by AGAUR
(Generalitat de Catalunya) grant 2017-SGR-929. LL is supported by the
predoctoral training program non-doctoral research personnel of the Department
of Education of the Basque Government. LL and FM are also supported by the
European Research Council (ERC) under Grant Agreement No. 101039048-GanESS and
the Severo Ochoa Program grant CEX2018-000867-S. SPR is also partially
supported by the Portuguese FCT (CERN/FIS-PAR/0004/2019).

##  Appendix A Binding energies for neutrino scattering off electrons

For germanium we use x-ray

$Z_{\rm eff}^{\rm Ge}(T_{e})=\left\\{\begin{array}[]{lcl}32&&T_{e}>11.11\;{\rm
keV}\\\ 30&&11.11\;{\rm keV}>T_{e}>1.4146\;{\rm keV}\\\ 28&&1.4146\;{\rm
keV}>T_{e}>1.248\;{\rm keV}\\\ 26&&1.248\;{\rm keV}>T_{e}>1.217\;{\rm keV}\\\
22&&1.217\;{\rm keV}>T_{e}>0.1801\;{\rm keV}\\\ 20&&0.1801\;{\rm
keV}>T_{e}>0.1249\;{\rm keV}\\\ 18&&0.1249\;{\rm keV}>T_{e}>0.1208\;{\rm
keV}\\\ 14&&0.1208\;{\rm keV}>T_{e}>0.0298\;{\rm keV}\\\ 4&&0.0298\;{\rm
keV}>T_{e}\end{array}\right.$ (56)

while for caesium and for iodine we use x-ray

$\begin{array}[]{cc}Z^{\mathrm{Cs}}_{\rm
eff}(T_{e})=\left\\{\begin{array}[]{lcl}55&&T_{e}>35.99\;{\rm keV}\\\
53&&35.99\;{\rm keV}>T_{e}>5.71\;{\rm keV}\\\ 51&&5.71\;{\rm
keV}>T_{e}>5.36\;{\rm keV}\\\ 49&&5.36\;{\rm keV}>T_{e}>5.01\;{\rm keV}\\\
45&&5.01\;{\rm keV}>T_{e}>1.21\;{\rm keV}\\\ 43&&1.21\;{\rm
keV}>T_{e}>1.07\;{\rm keV}\\\ 41&&1.07\;{\rm keV}>T_{e}>1\;{\rm keV}\\\
37&&1\;{\rm keV}>T_{e}>0.74\;{\rm keV}\\\ 33&&0.74\;{\rm keV}>T_{e}>0.73\;{\rm
keV}\\\ 27&&0.73\;{\rm keV}>T_{e}>0.23\;{\rm keV}\\\ 25&&0.23\;{\rm
keV}>T_{e}>0.17\;{\rm keV}\\\ 23&&0.17\;{\rm keV}>T_{e}>0.16\;{\rm keV}\\\
19&&0.16\;{\rm keV}>T_{e}\end{array}\right.&Z^{\mathrm{I}}_{\rm
eff}(T_{e})=\left\\{\begin{array}[]{lcl}53&&T_{e}>33.17\;{\rm keV}\\\
51&&33.17\;{\rm keV}>T_{e}>5.19\;{\rm keV}\\\ 49&&5.19\;{\rm
keV}>T_{e}>4.86\;{\rm keV}\\\ 47&&4.86\;{\rm keV}>T_{e}>4.56\;{\rm keV}\\\
43&&4.56\;{\rm keV}>T_{e}>1.07\;{\rm keV}\\\ 41&&1.07\;{\rm
keV}>T_{e}>0.93\;{\rm keV}\\\ 39&&0.93\;{\rm keV}>T_{e}>0.88\;{\rm keV}\\\
35&&0.88\;{\rm keV}>T_{e}>0.63\;{\rm keV}\\\ 31&&0.63\;{\rm
keV}>T_{e}>0.62\;{\rm keV}\\\ 25&&0.62\;{\rm keV}>T_{e}>0.19\;{\rm keV}\\\
23&&0.19\;{\rm keV}>T_{e}>0.124\;{\rm keV}\\\ 21&&0.124\;{\rm
keV}>T_{e}>0.123\;{\rm keV}\\\ 17&&0.123\;{\rm
keV}>T_{e}\end{array}\right.\end{array}$ (57)

noting that $Z_{\rm eff}^{\mathrm{CsI}}(T_{e})=\frac{1}{2}\left[Z_{\rm
eff}^{\mathrm{Cs}}(T_{e})+Z_{\rm eff}^{\mathrm{I}}(T_{e})\right]$.

## References

  * (1) D. Z. Freedman, _Coherent effects of a weak neutral current_ , _Physical Review D_ 9 (1974) 1389.
  * (2) COHERENT collaboration, D. Akimov et al., _Observation of coherent elastic neutrino-nucleus scattering_ , _Science_ 357 (2017) 1123 [1708.01294].
  * (3) COHERENT collaboration, D. Akimov et al., _COHERENT Collaboration data release from the first observation of coherent elastic neutrino-nucleus scattering_ , 1804.09459.
  * (4) COHERENT collaboration, D. Akimov et al., _First measurement of coherent elastic neutrino-nucleus scattering on Argon_ , _Phys. Rev. Lett._ 126 (2021) 012002 [2003.10630].
  * (5) COHERENT collaboration, D. Akimov et al., _COHERENT Collaboration data release from the first detection of coherent elastic neutrino-nucleus scattering on Argon_ , 2006.12659.
  * (6) TEXONO collaboration, H. T. Wong, _The TEXONO research program on neutrino and astroparticle physics_ , _Mod. Phys. Lett. A_ 19 (2004) 1207.
  * (7) $\nu$GeN collaboration, V. Belov et al., _The $\nu$GeN experiment at the Kalinin nuclear power plant_, _JINST_ 10 (2015) P12011.
  * (8) CONNIE collaboration, A. Aguilar-Arevalo et al., _The CONNIE experiment_ , _J. Phys. Conf. Ser._ 761 (2016) 012057 [1608.01565].
  * (9) 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].
  * (10) 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].
  * (11) $\nu$-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].
  * (12) 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].
  * (13) J. J. Choi, _Neutrino elastic-scattering observation with NaI[Tl] (NEON)_ , _PoS_ NuFact2019 (2020) 047.
  * (14) 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].
  * (15) J. Colaresi et al., _First results from a search for coherent elastic neutrino-nucleus scattering at a reactor site_ , _Phys. Rev. D_ 104 (2021) 072003 [2108.02880].
  * (16) J. Colaresi, J. I. Collar, T. W. Hossbach, C. M. Lewis and K. M. Yocum, _Suggestive evidence for coherent elastic neutrino-nucleus scattering from reactor antineutrinos_ , 2202.09672.
  * (17) 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].
  * (18) M. Cadeddu and F. Dordei, _Reinterpreting the weak mixing angle from atomic parity violation in view of the Cs neutron rms radius measurement from COHERENT_ , _Phys. Rev. D_ 99 (2019) 033010 [1808.10202].
  * (19) X.-R. Huang and L.-W. Chen, _Neutron skin in CsI and low-energy effective weak mixing angle from COHERENT data_ , _Phys. Rev. D_ 100 (2019) 071301 [1902.07625].
  * (20) M. Cadeddu, F. Dordei, C. Giunti, Y. F. Li and Y. Y. Zhang, _Neutrino, electroweak, and nuclear physics from COHERENT elastic neutrino-nucleus scattering with refined quenching factor_ , _Phys. Rev. D_ 101 (2020) 033004 [1908.06045].
  * (21) M. Cadeddu, F. Dordei, C. Giunti, Y. F. Li, E. Picciau and Y. Y. Zhang, _Physics results from the first COHERENT observation of coherent elastic neutrino-nucleus scattering in argon and their combination with cesium-iodide data_ , _Phys. Rev. D_ 102 (2020) 015030 [2005.01645].
  * (22) M. Cadeddu et al., _New insights into nuclear physics and weak mixing angle using electroweak probes_ , _Phys. Rev. C_ 104 (2021) 065502 [2102.06153].
  * (23) M. Cadeddu, C. Giunti, Y. F. Li and Y. Y. Zhang, _Average CsI neutron density distribution from COHERENT data_ , _Phys. Rev. Lett._ 120 (2018) 072501 [1710.02730].
  * (24) E. Ciuffoli, J. Evslin, Q. Fu and J. Tang, _Extracting nuclear form factors with coherent neutrino scattering_ , _Phys. Rev. D_ 97 (2018) 113003 [1801.02166].
  * (25) D. K. Papoulias, T. S. Kosmas, R. Sahu, V. K. B. Kota and M. Hota, _Constraining nuclear physics parameters with current and future COHERENT data_ , _Phys. Lett. B_ 800 (2020) 135133 [1903.03722].
  * (26) P. Coloma, I. Esteban, M. C. Gonzalez-Garcia and J. Menéndez, _Determining the nuclear neutron distribution from coherent elastic neutrino-nucleus scattering: current results and future prospects_ , _JHEP_ 08 (2020) 030 [2006.08624].
  * (27) 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].
  * (28) 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) 013009 [1107.3512].
  * (29) A. J. Anderson et al., _Measuring active-to-sterile neutrino oscillations with neutral current coherent neutrino-nucleus scattering_ , _Phys. Rev. D_ 86 (2012) 013004 [1201.3805].
  * (30) 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) 093002 [1511.02834].
  * (31) 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].
  * (32) 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) 095007 [1612.06350].
  * (33) P. Coloma, P. B. Denton, M. C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, _Curtailing the dark side in non-standard neutrino interactions_ , _JHEP_ 04 (2017) 116 [1701.04828].
  * (34) T. S. Kosmas, D. K. Papoulias, M. Tórtola and J. W. F. Valle, _Probing light sterile neutrino signatures at reactor and spallation neutron source neutrino experiments_ , _Phys. Rev. D_ 96 (2017) 063013 [1703.00054].
  * (35) S.-F. Ge and I. M. Shoemaker, _Constraining photon portal dark matter with TEXONO and COHERENT data_ , _JHEP_ 11 (2018) 066 [1710.10889].
  * (36) I. M. Shoemaker, _COHERENT search strategy for beyond standard model neutrino interactions_ , _Phys. Rev. D_ 95 (2017) 115028 [1703.05774].
  * (37) P. Coloma, M. C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, _COHERENT enlightenment of the neutrino dark side_ , _Phys. Rev. D_ 96 (2017) 115007 [1708.02899].
  * (38) J. Liao and D. Marfatia, _COHERENT constraints on nonstandard neutrino interactions_ , _Phys. Lett. B_ 775 (2017) 54 [1708.04255].
  * (39) 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].
  * (40) 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) 035009 [1711.03521].
  * (41) D. K. Papoulias and T. S. Kosmas, _COHERENT constraints to conventional and exotic neutrino physics_ , _Phys. Rev. D_ 97 (2018) 033003 [1711.09773].
  * (42) 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].
  * (43) 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].
  * (44) 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].
  * (45) M. Chaves and T. Schwetz, _Resolving the LMA-dark NSI degeneracy with coherent neutrino-nucleus scattering_ , _JHEP_ 05 (2021) 042 [2102.11981].
  * (46) D. Aristizabal Sierra, V. De Romeri and N. Rojas, _COHERENT analysis of neutrino generalized interactions_ , _Phys. Rev. D_ 98 (2018) 075018 [1806.07424].
  * (47) 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].
  * (48) 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].
  * (49) 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) 075051 [1901.08094].
  * (50) 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) 061801 [1903.10666].
  * (51) 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].
  * (52) CONNIE collaboration, A. Aguilar-Arevalo et al., _Exploring low-energy neutrino physics with the Coherent Neutrino Nucleus Interaction Experiment_ , _Phys. Rev. D_ 100 (2019) 092005 [1906.02200].
  * (53) B. Dutta, D. Kim, S. Liao, J.-C. Park, S. Shin and L. E. Strigari, _Dark matter signals from timing spectra at neutrino experiments_ , _Phys. Rev. Lett._ 124 (2020) 121802 [1906.10745].
  * (54) D. K. Papoulias, _COHERENT constraints after the COHERENT-2020 quenching factor measurement_ , _Phys. Rev. D_ 102 (2020) 113004 [1907.11644].
  * (55) A. N. Khan and W. Rodejohann, _New physics from COHERENT data with an improved quenching factor_ , _Phys. Rev. D_ 100 (2019) 113003 [1907.12444].
  * (56) C. Giunti, _General COHERENT constraints on neutrino nonstandard interactions_ , _Phys. Rev. D_ 101 (2020) 035039 [1909.00466].
  * (57) D. Baxter et al., _Coherent elastic neutrino-nucleus scattering at the European Spallation Source_ , _JHEP_ 02 (2020) 123 [1911.00762].
  * (58) B. C. Cañas, E. A. Garcés, O. G. Miranda, A. Parada and G. Sánchez García, _Interplay between nonstandard and nuclear constraints in coherent elastic neutrino-nucleus scattering experiments_ , _Phys. Rev. D_ 101 (2020) 035012 [1911.09831].
  * (59) 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].
  * (60) L. J. Flores, N. Nath and E. Peinado, _Non-standard neutrino interactions in U(1)’ model after COHERENT data_ , _JHEP_ 06 (2020) 045 [2002.12342].
  * (61) O. G. Miranda, D. K. Papoulias, G. Sánchez García, O. Sanders, M. Tórtola and J. W. F. Valle, _Implications of the first detection of coherent elastic neutrino-nucleus scattering (CE $\nu$NS) with Liquid Argon_, _JHEP_ 05 (2020) 130 [2003.12050].
  * (62) N. Hurtado, H. Mir, I. M. Shoemaker, E. Welch and J. Wyenberg, _Dark matter-neutrino interconversion at COHERENT, direct detection, and the early Universe_ , _Phys. Rev. D_ 102 (2020) 015006 [2005.13384].
  * (63) O. G. Miranda, D. K. Papoulias, O. Sanders, M. Tórtola and J. W. F. Valle, _Future CE $\nu$NS experiments as probes of lepton unitarity and light-sterile neutrinos_, _Phys. Rev. D_ 102 (2020) 113014 [2008.02759].
  * (64) M. Cadeddu et al., _Constraints on light vector mediators through coherent elastic neutrino nucleus scattering data from COHERENT_ , _JHEP_ 01 (2021) 116 [2008.05022].
  * (65) I. M. Shoemaker and E. Welch, _Sailing the CE $\nu$NS seas of non-standard neutrino interactions with the coherent CAPTAIN Mills experiment_, 2103.08401.
  * (66) L. M. G. de la Vega, L. J. Flores, N. Nath and E. Peinado, _Complementarity between dark matter direct searches and CE $\nu$NS experiments in U(1)’ models_, _JHEP_ 09 (2021) 146 [2107.04037].
  * (67) 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].
  * (68) CONUS collaboration, H. Bonet et al., _Novel constraints on neutrino physics beyond the standard model from the CONUS experiment_ , _JHEP_ 05 (2022) 085 [2110.02174].
  * (69) L. J. Flores, N. Nath and E. Peinado, _CE $\nu$NS as a probe of flavored generalized neutrino interactions_, _Phys. Rev. D_ 105 (2022) 055010 [2112.05103].
  * (70) Y.-F. Li and S.-y. Xia, _Constraining light mediators via detection of coherent elastic solar neutrino nucleus scattering_ , _Nucl. Phys. B_ 977 (2022) 115737 [2201.05015].
  * (71) D. Aristizabal Sierra, J. Liao and D. Marfatia, _Impact of form factor uncertainties on interpretations of coherent elastic neutrino-nucleus scattering data_ , _JHEP_ 06 (2019) 141 [1902.07398].
  * (72) M. Abdullah, D. Aristizabal Sierra, B. Dutta and L. E. Strigari, _Coherent elastic neutrino-nucleus scattering with directional detectors_ , _Phys. Rev. D_ 102 (2020) 015009 [2003.11510].
  * (73) G. Fernandez-Moroni et al., _The physics potential of a reactor neutrino experiment with Skipper-CCDs: searching for new physics with light mediators_ , _JHEP_ 02 (2022) 127 [2108.07310].
  * (74) E. Bertuzzo, G. Grilli di Cortona and L. M. D. Ramos, _Probing light vector mediators with coherent scattering at future facilities_ , _JHEP_ 06 (2022) 075 [2112.04020].
  * (75) H. Bonet et al., _First limits on neutrino electromagnetic properties from the CONUS experiment_ , 2201.12257.
  * (76) M. Lindner, W. Rodejohann and X.-J. Xu, _Coherent neutrino-nucleus scattering and new neutrino interactions_ , _JHEP_ 03 (2017) 097 [1612.04150].
  * (77) J. Erler and M. J. Ramsey-Musolf, _The weak mixing angle at low energies_ , _Phys. Rev. D_ 72 (2005) 073003 [hep-ph/0409169].
  * (78) J. Erler and R. Ferro-Hernández, _Weak mixing angle in the Thomson limit_ , _JHEP_ 03 (2018) 196 [1712.09146].
  * (79) S. Klein and J. Nystrand, _Exclusive vector meson production in relativistic heavy ion collisions_ , _Phys. Rev. C_ 60 (1999) 014903 [hep-ph/9902259].
  * (80) R. H. Helm, _Inelastic and elastic scattering of 187-MeV electrons from selected even-even nuclei_ , _Phys. Rev._ 104 (1956) 1466.
  * (81) P. Klos, J. Menéndez, D. Gazit and A. Schwenk, _Large-scale nuclear structure calculations for spin-dependent WIMP scattering with chiral effective field theory currents_ , _Phys. Rev. D_ 88 (2013) 083516 [1304.7684].
  * (82) M. Hoferichter, P. Klos, J. Menéndez and A. Schwenk, _Nuclear structure factors for general spin-independent WIMP-nucleus scattering_ , _Phys. Rev. D_ 99 (2019) 055031 [1812.05617].
  * (83) M. Hoferichter, P. Klos, J. Menéndez and A. Schwenk, _Analysis strategies for general spin-independent WIMP-nucleus scattering_ , _Phys. Rev. D_ 94 (2016) 063505 [1605.08043].
  * (84) Particle Data Group collaboration, P. A. Zyla et al., _Review of Particle Physics_ , _PTEP_ 2020 (2020) 083C01.
  * (85) I. Angeli and K. P. Marinova, _Table of experimental nuclear ground state charge radii: An update_ , _Atom. Data Nucl. Data Tabl._ 99 (2013) 69.
  * (86) C. G. Payne, S. Bacca, G. Hagen, W. Jiang and T. Papenbrock, _Coherent elastic neutrino-nucleus scattering on 40Ar from first principles_, _Phys. Rev. C_ 100 (2019) 061304 [1908.09739].
  * (87) P. Vogel and J. Engel, _Neutrino electromagnetic form-factors_ , _Phys. Rev. D_ 39 (1989) 3378.
  * (88) O. Tomalak and R. J. Hill, _Theory of elastic neutrino-electron scattering_ , _Phys. Rev. D_ 101 (2020) 033006 [1907.03379].
  * (89) 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].
  * (90) K. Scholberg, _Prospects for measuring coherent neutrino-nucleus elastic scattering at a stopped-pion neutrino source_ , _Phys. Rev. D_ 73 (2006) 033005 [hep-ex/0511042].
  * (91) M. Hoferichter, J. Menéndez and A. Schwenk, _Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses_ , _Phys. Rev. D_ 102 (2020) 074018 [2007.08529].
  * (92) W. Rodejohann, X.-J. Xu and C. E. Yaguna, _Distinguishing between Dirac and Majorana neutrinos in the presence of general interactions_ , _JHEP_ 05 (2017) 024 [1702.05721].
  * (93) M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, _Remarks on Higgs boson interactions with nucleons_ , _Phys. Lett. B_ 78 (1978) 443.
  * (94) M. Cirelli, E. Del Nobile and P. Panci, _Tools for model-independent bounds in direct dark matter searches_ , _JCAP_ 10 (2013) 019 [1307.5955].
  * (95) J. Ellis, N. Nagata and K. A. Olive, _Uncertainties in WIMP dark matter scattering revisited_ , _Eur. Phys. J. C_ 78 (2018) 569 [1805.09795].
  * (96) P. Huber, _On the determination of anti-neutrino spectra from nuclear reactors_ , _Phys. Rev. C_ 84 (2011) 024617 [1106.0687].
  * (97) T. A. Mueller et al., _Improved predictions of reactor antineutrino spectra_ , _Phys. Rev. C_ 83 (2011) 054615 [1101.2663].
  * (98) X. Qian and J.-C. Peng, _Physics with reactor neutrinos_ , _Rept. Prog. Phys._ 82 (2019) 036201 [1801.05386].
  * (99) SuperCDMS collaboration, R. Agnese et al., _New results from the search for low-mass weakly interacting massive particles with the CDMS low ionization threshold experiment_ , _Phys. Rev. Lett._ 116 (2016) 071301 [1509.02448].
  * (100) R. B. Firestone and V. S. Shirley. New York: Wiley, 1996.
  * (101) S. O. W. Antman, D. A. Landis and R. H. Pehl, _Measurements of the Fano factor and the energy per hole-electron pair in Germanium_ , _Nucl. Instrum. Methods_ 40 (1966) 272.
  * (102) W. Z. Wei, L. Wang and D. M. Mei, _Average energy expended per e-h pair for Germanium-based dark matter experiments_ , _JINST_ 12 (2017) P04022 [1602.08005].
  * (103) 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].
  * (104) J. I. Collar, A. R. L. Kavner and C. M. Lewis, _Response of CsI[Na] to nuclear recoils: impact on coherent elastic neutrino-nucleus scattering (CE $\nu$NS)_, _Phys. Rev. D_ 100 (2019) 033003 [1907.04828].
  * (105) W. Creus, _Light yield in liquid Argon for dark matter detection_ , Ph.D. thesis, Zurich U., 2013.  10.5167/uzh-86639.
  * (106) I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and J. Salvado, _Updated constraints on non-standard interactions from global analysis of oscillation data_ , _JHEP_ 08 (2018) 180 [1805.04530].
  * (107) GEMMA collaboration, A. G. Beda et al., _The results of search for the neutrino magnetic moment in GEMMA experiment_ , _Adv. High Energy Phys._ 2012 (2012) 350150.
  * (108) GEMMA collaboration, A. G. Beda et al., _Gemma experiment: the results of neutrino magnetic moment search_ , _Phys. Part. Nucl. Lett._ 10 (2013) 139.
  * (109) A. Thompson et al., _X-ray data booklet_ , _https://xdb.lbl.gov/_ (2009) .