and $X^{\prime}$ are hadronic initial/final states). The DUNE near detector
[279] (red dashed line) and a potential liquid argon detector at the Forward
Physics Facility [282, 132] (purple dashed line) offer great sensitivity for
these searches, as shown in Fig. 14 as well.

####  5.3.7 Neutrino Portal Dark Matter

Scenarios where sterile neutrinos interact with a dark sector containing the
DM have also been studied recently [284, 285, 286]. A simple example involves
augmenting the sterile neutrino’s coupling to active leptons in (7) with a
Yukawa interaction with SM singlets, ${\cal L}\supset-\lambda\phi\chi N$.
Because $N$ can decay invisibly into the dark sector, the allowed active-
sterile mixing can be relatively large, particularly in the case of mixing
with $\nu_{\tau}$. Despite this, it can be particularly difficult to test this
simple setup, although it could potentially be probed at neutrino facilities
through $\nu_{\tau}$ production and PMNS unitarity [287].

###  5.4 ALP Portal

####  5.4.1 Introduction

The axion is a well-motivated solution to the strong CP problem. The
experimental searches for axions are nowadays extended toward probing more
general pseudo-scalar axion-like particles (ALPs), which are ubiquitous in the
string theory (e.g., Refs. [288, 289]). Due to their rich structure, ALPs
often behave as mediators and allow dark-sector particles to communicate with
the SM particles in various dark-sector scenarios [290]. We here focus on the
search for ALP mediators whose production is related to photons. Among various
ALP interactions, many of the phenomenological considerations are predicated
upon their couplings described in the following interaction Lagrangian:

$\mathcal{L_{\rm
ALP}}\supset\frac{1}{4}g_{a\gamma\gamma}aF_{\mu\nu}\tilde{F}^{\mu\nu}+ig_{aee}a\bar{e}\gamma^{5}e+ia\bar{\psi}_{N}\gamma^{5}(g_{ann}^{(0)}+g_{ann}^{(1)})\psi_{N},$
(20)

where $g_{a\gamma\gamma}$, $g_{aee}$, $g_{ann}^{(0)}$, and $g_{ann}^{(1)}$
parametrize the coupling strengths of the ALP field $a$ to the SM photon,
electron, nucleon isoscalar, and nucleon isovector, respectively. Here, again
$\tilde{F}_{\mu\nu}$ is the dual field strength tensor of the SM photon, as
defined earlier, and $\psi_{N}=\left(\begin{matrix}p\\\ n\end{matrix}\right)$
denotes the nucleon field. Neutrino experiments provide a great platform to
explore the ALP parameter space associated with the interactions defined in
Eq. (20), as they generate copiously the fluxes of not only neutrinos but
photons.

Depending on the underlying model details, ALPs can couple to other SM
particles such as gluon and quarks and other production and/or detection
channels may become important. For example, in models of ALPs coupling to SM
gluon through the $aG_{\mu\nu}^{a}\tilde{G}^{a,\mu\nu}$ operator, the ALPs can
be produced via the mixing with SM pseudoscalar mesons or gluon-gluon fusion
in the process of the collision between an incoming beam proton and a proton
inside the target system. Therefore, neutrino facilities carry great potential
of testing these models [291].

####  5.4.2 Production

Depending on the ALP interaction under consideration, ALPs can be produced in
various ways in the neutrino facilities. In particular, wherever photons
emerge during the sequence of interactions between the proton beam and the
target material, production of ALPs can be induced via the couplings in Eq.
(20). Photons can be produced not only by standard mechanisms including
proton-beam bremsstrahlung and neutral meson decays but by the cascade
showering processes of charged particles (e.g., $e^{\pm}$) out of the primary
interaction between the beam proton and the target [116, 292]. The main ALP
production mechanisms include:

Primakoff process

For the ALPs interacting with photons, a photon can turn into an ALP through
the Primakoff-like scattering process with a nucleus $\mathcal{N}$, i.e.,
$\gamma+\mathcal{N}\to a+\mathcal{N}$. As it takes place via a $t$-channel
exchange of a photon, the typical momentum transfer to the target nucleus is
very small, and as a result, i) the whole nucleus participates in the process
coherently and the production scattering cross-section benefits from a $Z^{2}$
enhancement with $Z$ being the atomic number of the nucleus of interest and
ii) the momentum of the outgoing ALP inherits from the incoming photon.

Compton-like process

In the presence of the ALP-electron coupling $g_{aee}$, an ALP can be produced
by a Compton-like scattering process which is initiated by a photon, i.e.,
$\gamma+e^{-}\to a+e^{-}$. Unlike the Primakoff process above, the outgoing
electron can carry a sizable fraction of the incoming photon energy and the
ALP can be emitted at a large angle with respect to the initial-state photon.

Nuclear reactions

If the ALP-to-nucleon coupling $g_{ann}^{(0,1)}$ is non-zero, an ALP can be
produced by nuclear reactions; for example, neutron captures, i.e.,
$n+\mathcal{N}(Z,A)\to\mathcal{N}(Z,A+1)+a$ with $n$ and $A$ respectively
denoting neutron and atomic mass number, and nuclear de-excitations
(radioactive decays), i.e., $\mathcal{N}^{*}(Z,A)\to\mathcal{N}(Z,A)+a$. In
the SM, both neutron captures and nuclear de-excitations accompany a photon,
so any photons originating from these nuclear processes can be connected to
the production of ALPs with a non-zero value of $g_{ann}^{(0,1)}$.

Inside the target material, the processes described in the above three
mechanisms compete with ordinary SM processes; for example, the photons in the
first two mechanisms can go through a pair conversion or an ordinary Compton
process, and the nuclear reactions create a photon instead of an ALP in the
final state. For a given source particle, therefore, the likelihood of ALP
production is given by the competition between the ALP production rate and
other SM events rate.

####  5.4.3 Detection

In the presence of the couplings in Eq. (20), ALP can leave various signatures
in the experiments. Broadly speaking, three channels are available in the
neutrino experiments: ALPs can be detected through their i) decays, ii)
scattering, and iii) conversion. The three channels show best signal
sensitivity to ALPs in different mass regions, providing complementary
information in the exploration of ALP parameter space.

Decays

Once the ALP is massive enough and/or its coupling to SM particles is sizable
enough, a large fraction of the produced ALPs can decay within the detector
fiducial volume. With a non-zero value of $g_{a\gamma\gamma}$, an ALP can
leave a diphotonic decay signal (i.e., $a\to\gamma+\gamma$), whereas in the
presence of non-vanishing $g_{aee}$, an ALP can decay to a pair of electrons
(i.e., $a\to e^{+}+e^{-}$) as long as its mass is greater than twice the
electron mass.

Scattering

If an ALP produced at the target does not decay and reaches the detector, it
can scatter off the nucleus or the electrons inside the detector material. If
the coupling to photon $g_{a\gamma\gamma}$ is non-zero, the ALP can be
converted to a photon through the inverse Primakoff scattering process, i.e.,
$a+\mathcal{N}\to\gamma+\mathcal{N}$. The scattering process involves the
whole nucleus, resulting in $Z^{2}$ enhancement as in the ALP production by
the Primakoff process. Since typical nuclear recoils are soft, the detectable
experimental signature is a single photon signal unless the detector features
sensitivity to small energy deposits. By contrast, if the coupling to electron
$g_{aee}$ is non-vanishing, the ALP can undergo a Compton-like scattering
process, giving rise to an electron and a photon in the final state, i.e.,
$a+e^{-}\to\gamma+e^{-}$. Both the electron and the photon can carry sizable
energy fractions of the incoming ALP, and therefore, detectors can record and
identify both electron and photon, depending on their capability, which
provides an additional handle to reduce potential backgrounds.

Conversion

For the ALPs interacting with photons, there exists an additional detection
channel if a detector accompanies a magnetic field region. The detection
principle is the same as that in helioscopes such as CAST; an incoming ALP can
convert to a photon by the external magnetic field. In the beam-dump type
experiments, this idea was proposed as Particle Accelerator helioScopes for
Slim Axion-like-particle deTection, PASSAT [293, 294]. In the limits of
$m_{a}\to 0$ and $g_{a\gamma\gamma}\to 0$, the ALP-to-photon conversion
probability is proportional to $(g_{a\gamma\gamma}BL)^{2}$ with $B$ and $L$
being the strength of magnetic field and the length of magnetic field region,
respectively. Once $m_{a}$ becomes large, the probability is quickly
suppressed by the decoherency factor (see e.g., [295, 129]) and the conversion
channel starts losing its sensitivity. The conversion channel, therefore,
shows the best sensitivity to the ALP of a very small mass value.

####  5.4.4 Experimental Prospects

Most of the experimental prospects are based on the simplified approach in
which only the coupling of interest is turned on while the others are
suppressed enough to be irrelevant. Various types of neutrino facilities
including the reactor-based, the stopped-pion, and the beam-focusing neutrino
experiments have sensitivity to ALP signals. They are sensitive to ALPs in
different mass regimes, hence providing complementary information in
constraining ALP parameter space.

Figure 15: Existing constraints and future prospects of $g_{a\gamma\gamma}$
(upper panels), $g_{aee}$ (lower-left panel), and $g_{ann}^{(1)}$ (lower-right
panel) at various experiments including neutrino facilities. The limits for
$g_{a\gamma\gamma}$ are divided into the lower-mass regime (upper-left panel)
and the higher-mass regime (upper-right panel). The plots for
$g_{a\gamma\gamma}$ and $g_{aee}$ are adapted from [129] while that for
$g_{ann}^{(1)}$ is adapted from [124]. See the main text for more details.

ALP-photon coupling $g_{a\gamma\gamma}$

The ALP-photon coupling is most extensively studied, not only at neutrino
facilities but at colliders. The upper-right panel of Fig. 15 shows existing
(color-shaded regions) and future expected (dashed lines) limits in the
$m_{a}$-$g_{a\gamma\gamma}$ plane for $m_{a}\gtrsim 10$ MeV to which the decay
channels are relevant. The current constraints include
$e^{+}e^{-}\to\gamma+{\rm inv.}$ [296, 297, 298, 299, 300], Belle-II [301],
CHARM [302], E137 [303], E141 [304], LEP [305], LHC (Pb) [306, 307], NA64
[308], NuCaI [309], and PrimEx [310]. The limits from astrophysical and
cosmological considerations compiled in Ref. [311] are also displayed in gray-
shaded regions. Future sensitivity reaches at neutrino facilities include
DUNE-GAr with a 1-year exposure [292], PIP-II with a 5-year exposure [312],
and SHiP with $2\times 10^{20}$ POTs [166]. For purposes of complementarity,
we include the sensitivity reaches expected in non-neutrino experiments, e.g.,
Belle-II [313], FASER/FASER2 [3], Glue-X [310], LDMX [233], LHC (Pb) [314],
NA62 [315], NA64 [316], PrimEx [310], SeaQuest [200]. The limits in the lower
mass regime where the scattering and conversion channels are better suited are
shown in the upper-left panel of Fig. 15. The current constraints (color-
shaded regions) include $e^{+}e^{-}\to\gamma+{\rm inv.}$ [296, 297, 298, 299,
300], $\Upsilon\to\gamma+{\rm inv.}$ [317, 318], light-shining-through-wall
type experiments [319], NOMAD [320], and E137 [303], together with the limits
from helioscopes and astrophysical/cosmological considerations (gray-shaded
regions) compiled in Ref. [311]. Future sensitivity reaches (dashed lines) at
neutrino experiments include a PASSAT interpretation [293] of NOMAD [320],
PASSAT implementations at the BDF facility with the CAST or BabyIAXO magnets
with $2\times 10^{20}$ POTs [293], a PASSAT implementation at the DUNE MPD
with a 7-year exposure [294], PASSAT implementations at DUNE with the CAST or
BabyIAXO magnets with a 7-year exposure [294], IsoDAR with a 5-year exposure
[321], and reactor searches at CONNIE, CONUS, and MINER [116]. Similar
analyses for reactor neutrino experiments also appear in Ref. [124] by taking
sets of benchmark ALP production and detection parameters, not specifying
concrete experiments. We also include the expected sensitivity reaches of
LSW@FASER/FASER2 [322] and FLArE [322] for comparison.

ALP-electron coupling $g_{aee}$

The ALP-electron coupling space can be also readily explored in many of the
neutrino experiments, in both decay and scattering channels. The lower-left
panel of Fig. 15 displays the existing (color-shaded regions) and future
expected (dashed lines) limits in the $m_{a}$-$g_{aee}$ plane. The current
constraints include BaBar [323, 324], E137 [303, 325], E141 [304], E774 [326],
NA64 [327, 328, 329], Orsay [330], and astrophysical considerations (stellar
cooling [331] and SN1987a [332]). Future prospects include CCM (a stopped-pion
neutrino experiment) with beam-on backgrounds [109], IsoDAR with a 5-year
exposure [321], and reactor neutrino experiments (CONNIE, CONUS, MINER, and
$\nu$-cleus) [116]. For comparison, the expected LDMX are included [233]. The
reactor searches are sensitive to the ALP signals in the decay channel only
within a narrow mass range since most of the photons created in the reactor
cores are not energetic enough to overcome the production threshold
$s\geq(m_{a}+m_{e})^{2}$ [116]. By contrast, the scattering channel is more
promising in the search for light ALPs (i.e., $m_{a}<2m_{e}$) and it has been
investigated in reactor neutrino experiments [116, 124] and neutrino beam
experiments [292].

For the reactor neutrino experiments, the dark boson interaction through
various portals can be produced in the reactor core and detected by the
neutrino detector through the Compton-like scattering and its inversion
scattering. The precision of the light-dark boson measurement in the reactor
neutrino experiments is limited by the accidental background uncertainty. The
further improvement of the sensitivity to an ALP signal can be achieved with a
better background control, which is expected in the next generation of reactor
neutrino experiments such as JUNO-TAO [333].

ALP-nucleon couplings $g_{ann}$

The ALP-nucleon couplings were explored in reactor neutrino experiments, e.g.,
TEXONO [334]. The TEXONO Collaboration assumes that ALPs are produced via the
$pn\to d\gamma$ isovector M1 transition inside the reactor core [i.e.,
proportional to $(g_{ann}^{(1)})^{2}$] while ALP detection is done either via
the inverse Primakoff scattering process (with vanishing $g_{aee}$) or the
Compton-like scattering process (with vanishing $g_{a\gamma\gamma}$). As an
example, the lower-right panel of Fig. 15 shows the existing (color-shaded
regions) and future expected (dashed lines) limits in the
$(m_{a},g_{ann}^{(1)}\cdot g_{a\gamma\gamma})$ plane. TEXONO constrains models
of ALP in this parameter space [334], while more stringent limits from various
astrophysical considerations (e.g., Borexino [335, 336], HB stars [337], and
SN1987a [337]) are available. The reactor neutrino experiments have great
potential to probe this parameter space like TEXONO; for example, the blue
(red) dashed line represents the reactor-experiment limit expected from a 140
(50) cm long $10^{3}$ (10) kg Xe-(Ge-)based detector located 10 m away from
the reactor core with a 10 DRU (/kg/keV/day) background. Similar limits in
other parameter spaces, e.g., $(m_{a},g_{ann}^{(1)}\cdot g_{aee})$ plane,
$(g_{ann}^{(1)},g_{a\gamma\gamma})$ plane, $(g_{ann}^{(1)},g_{aee})$ plane,
etc, appear in literature [334, 124]. We also add the limits expected at
IsoDAR with a 5-year exposure [321].

###  5.5 Dark Neutrinos and Dipole Portal

In this section, we consider two types of BSM heavy neutral lepton models that
yield different signatures compared to the traditional heavy sterile neutrino
that mixes with SM flavors, discussed in Section 5.3. They are generally
described as Heavy Neutral Leptons with a Dipole Portal, and dark neutrinos,
described in the following subsections.

####  5.5.1 Heavy Neutral Leptons with a Dipole Portal

The dipole portal d to the heavy neutral lepton (HNL) N is contained within
the effective Lagrangian:

$\mathcal{L}\supset\bar{N}(i\not{\partial}-m_{N})N+(d\bar{\nu}_{L}\sigma_{\mu\nu}F^{\mu\nu}N+h.c.)$
(21)

The traditional neutrino portal coupling $NLH$ [90, 338] is assumed to be
absent, or subdominant, which allows the dipole portal operator to offer novel
signatures and features in the production and decay of $N$. The energy,
intensity, and astrophysical frontiers afford ideal probes for the sensitivity
of d and each case is studied within [339]. The main signal under
consideration is the decay $N$ $\rightarrow\gamma\nu$. At high energy
colliders, such as the LHC and LEP, the sensitivity for d is $\sim$ 10 TeV-1
and is largely independent of the $N$ mass, provided it is within the
kinematic reach of the collider. In the high intensity regime where beam dump
experiments dominate, such high masses are unattainable. Instead, beam dump
experiments explore low coupling for sub-GeV masses. Experiments such as LSND
[340, 341] and MiniBooNE [342] give sensitivity for d at $\sim$ (10-6–10-7)
GeV-1. The upcoming experiments, including, e.g., SBND [343], DUNE [93], and
SHiP [166] will provide increased sensitivity in this regime. At the
astrophysical frontier supernovae explosions restrict the parameter space, but
allow for probes for $m_{N}$ on the order of a few hundred MeV. This allows
for astrophysical constraints to probe d in the range of (10-7–10-10) GeV-1.
The dipole portal HNL has diverse phenomenological consequences [56, 344, 345,
346, 339, 347, 348], and could potentially explain an excess from the Xenon 1T
experiment [349, 350].

####  5.5.2 Heavy Neutral Leptons With Dark Forces

Figure 16: Signatures of heavy neutrinos that interact with additional dark
forces as a function of the new interaction strength. Stronger interactions
lead to shorter $N$ lifetimes and additional production modes.

Heavy neutral leptons may not be completely sterile and could engage in
beyond-the-SM gauge interactions. These interactions may be shared by the SM
fields, such as in $B-L$ or $L_{\alpha}-L_{\beta}$ gauge symmetries, or not,
such as in a secluded $U(1)$ gauge symmetry wherein SM particles only interact
with the dark photon via kinetic mixing. In the secluded case, the new
particles can often evade strong experimental constraints, as they only
communicate with the SM via the renormalizable portals: scalars, neutrino, and
vector portals. Nevertheless, the phenomenology of the heavy neutrinos can be
substantially different from that of the minimal models where one considers
each portal interaction individually.

In neutrino experiments, the new forces can lead to new production as well as
decay channels. If the new force is much weaker than the weak interactions
(further suppressed by mixing), then the phenomenology will be very similar to
that already discussed in 5.3. However, when it is stronger, it shortens the
lifetime of the heavy neutrino, enhancing the rate of decay-in-flight
signatures up until the new states become too short-lived to propagate between
the beam target and the detector. Still, in the latter scenario, heavy
neutrinos can still be searched for when they are produced by neutrino
scattering inside the detector. A schematic of the phenomenology in that case
is show in Fig. 16, where the new signatures are shown as a function of the
new interaction strengths.

Dark neutrinos have been investigated in various contexts. For instance, dark
neutrinos can provide an explanation for the long-standing excess of electron-
like events at MiniBooNE [351, 65, 66, 76, 352, 278, 71, 73, 70], long-range
vector-mediated neutrino self-interactions [353, 354, 355], and as an
explanation to the XENON1T electron recoil excess [356]. Dark neutrinos also
lead to active to sterile neutrino transition magnetic moments (dipole portal
HNL), which is further discussed in the previous section.

In general, this dark neutrino model may, in principle, also give
contributions to the muon $g-2$, to atomic parity violation, polarized
electron scattering, neutrinoless double $\beta$ decay, rare meson decays as
well as to other low energy observables such as the running of the weak mixing
angle $\sin^{2}\theta_{W}$. There may also be consequences to neutrino
experiments. It can, for instance, modify neutrino scatterings, such as
coherent neutrino-nucleus scattering, or impact neutrino oscillations
experimental results as this model may give rise to non-standard neutrino
interactions in matter.

###  5.6 $\nu$-philic Interactions (CE$\nu$NS, I$\nu$NS, Neutrino Tridents)

The study of neutrino interactions can be used to shed light on new physics
communicating to neutrinos, in particular in scenarios with $\nu-$philic
interactions, where the dark sector only communicates with neutrinos. New
$\nu-$philic physics can manifest itself through many distinctive signatures.
Focusing on neutrino beams, scattering measurements can probe the existence of
neutrino non-standard interactions or of new light dark sector states, whose
existence can also enhance rare SM processes such as trident events.

####  5.6.1 Coherent elastic neutrino-nucleus scattering (CE$\nu$NS)

CE$\nu$NS is a neutral-current process in which the neutrino interacts with
the nucleus as a whole [357, 358]. One basic requirement for the coherence of
this interaction is the smallness of the momentum transfer, which needs to be
smaller than the inverse size of the nucleus. The fact that all nucleons
recoil coherently gives rise to an increase in the scattering amplitude of the
process, in turn leading to an enhancement of the cross section proportional
to the number of nucleons squared. The tiny recoil energy transferred to the
nucleus is then observable, although it requires using low-threshold detectors
capable of observing $\sim\mathcal{O}($keV) recoil energies. Despite the
magnitude of the CE$\nu$NS cross section, the largest among neutrino
scattering channels for energies below $\sim$ 100 MeV and for most nuclei, its
detection has proven to be demanding because of the required low thresholds
and reduction of backgrounds. However, the use of intense, pulsed sources of
low-energy neutrinos in combination with low-threshold detectors and a low-
background environment allow for a successful measurement of the CE$\nu$NS
process. The first detection of the CE$\nu$NS process in 2017 in a sodium-
doped cesium-iodide (CsI[Na]) by the COHERENT experiment [359, 360], has
fuelled the interest in new physics opportunities which can be explored with
this channel. Then, the recent observation of CE$\nu$NS also in argon [361],
together with the new data collected by the COHERENT experiment using the
CsI[Na] detector [362] have further demonstrated that we are entering an era
of CE$\nu$NS precision measurements, allowing not only to perform accuracy
tests of the SM but also to probe physics beyond the SM [363, 364].

Accelerator-based experiments using low-energy neutrinos from pion decays at
rest ($\pi-$DAR), designed for the detection of the CE$\nu$NS process, have
the further advantage of offering several opportunities to probe dark sectors.
These may include light, weakly-coupled states such as sub-GeV dark matter
candidates, axion-like particles (ALPs), sterile neutrinos, new heavy or light
mediators in the neutrino sector and other new particles which can appear in
several extensions of the SM.

##### Non-standard neutrino interactions

The spectrum of coherent elastic neutrino–nucleus scattering events can be
used to probe new subdominant neutrino Non-Standard Interactions (NSI) with
matter fields mediated by a new heavy vector particle [365, 366]. These are
commonly parameterized by a matrix of parameters $\epsilon_{ij}^{q,P}$, with
$q=u,d$, $i,j=e,\mu,\tau$ and $P=V(\rm vector),A(\rm axial)$, describing
either “non-universal” ($i=j$) or flavor-changing ($i\neq j$) interactions of
neutrinos with quarks. (A scattering experiment using neutrinos from $\pi-$DAR
will have sensitivity only to NSI couplings with ($i=e,\mu$).) Neglecting the
axial contribution, the existence of non-zero NSI would result in an overall
scaling of the event rate, either enhancement or suppression. While a positive
signal would undoubtedly hint towards new physics, existing data already
constrain the effective NSI parameters [367, 368, 369, 370, 371, 372, 373,
374, 375, 362, 376] – encoding the magnitude of the new interaction in terms
of $G_{F}$ – and consequently disfavour models of new physics, as for instance
those that were motivated by the Dark-LMA solution [377, 378, 379]. Fig. 17
shows current constraints on non-zero vector-like neutrino-quark NSI couplings
$\epsilon_{\rm ee}^{\rm d,V}$ and $\epsilon_{\rm ee}^{\rm u,V}$, obtained with
COHERENT CsI [362] and LAr [361] data. In full generality, not only vector
operators but a larger set of interactions can be explored with CE$\nu$NS
experiments, including all Lorentz invariant non-derivative interactions of
neutrinos with first generation quarks [380, 381, 382].

Figure 17: COHERENT constraints on non-zero vector-like neutrino-quark NSI
couplings $\epsilon_{\rm ee}^{\rm d,V}$ and $\epsilon_{\rm ee}^{\rm u,V}$,
compared to the CHARM [383] constraint. Constraints in the left panel have
been obtained using data collected by the COHERENT experiment with the CsI[Na]
detector [362]. The right panel shows the bounds extracted from the argon
measurement [361] and plotted together with the previous COHERENT CsI[Na]
measurement [359].

##### CE$\nu$NS and reactor experiments

CE$\nu$NS can be investigated at the reactor experiments using electron type
anti-neutrino emerging from the reactors, e.g., [372]. Various reactor based
experiments, e.g., TEXONO [384], $\nu$GeN [119], CONUS [385], MINER [386],
CONNIE [113],RED-100 [387], Ricochet [122],NEON [388], $\nu$-cleus [118],
NCC-1701 at Dresden-II [128] etc (see also Table 1). Among these experiments,
recently, NCC-1701 at Dresden-II nuclear reactor has observed an excess of
events which is claimed to be compatible with the expectations from the SM
CE$\nu$NS signal. This observation will implement constraints on non-standard
neutrino interactions, neutrino electromagnetic properties and new light
mediators [389, 390, 391, 392].

##### Light mediators

CE$\nu$NS experiments are also ideal laboratories for searches of new physics
in the form of light mediators, since in these scenarios the scattering is
proportional to the inverse of the momentum transferred squared, which we
recall is small for the CE$\nu$NS process. For the case of vector mediators,
there is an interference with the SM vector couplings that can be either
constructive or destructive, thus leading also to a possible depletion of the
event rate [393, 394]. In scenarios with a scalar boson mediating the
CE$\nu$NS process, the new contribution has no interference with the SM one,
and it simply adds to it. Low-energy high-intensity measurements at CE$\nu$NS
experiments can provide a valuable probe of light mediator scenarios,
complementary to high-energy collider searches and electroweak precision
measurements [395, 396, 393, 371, 397, 398, 376, 399, 400, 401]. CP-violating
effects may also be investigated in the context of light vector mediator
scenarios with CE$\nu$NS [394]. It is possible to utilize detector with
directional sensitivities to CE$\nu$NS to various kinds of light mediators and
their interactions with neutrinos. Both stopped pion and reactor neutrino
sources can be used with gaseous helium and fluorine as possible detector
materials. It is shown that directional detectors show distinguishing spectral
features in the angular and the recoil energy spectrum for light mediators
even for nuclear recoil thresholds as high as 50 keV. Directional information
combined with energy and timing information, can help extracting new physics
from CE$\nu$NS experiments [402].

Apart from the CE$\nu$NS measurements, the light mediators can be constrained
at the reactor experiments utilizing electron recoil with low threshold
detectors.

##### Sterile neutrinos

Many SM extensions capable of accommodating neutrino masses and mixings call
upon the introduction of new neutral sterile leptons. From a theoretical point
of view, there is no limit on the number of these sterile states and their
masses can span over several orders of magnitude. Because they are flavor
blind, CE$\nu$NS experiments, are sensitive to the total flux of active
neutrinos and they can be used to probe neutrino oscillations to the sterile
states [403, 404, 405], in complementarity to neutrino-electron scattering
experiments. The sterile neutrino oscillation also can be probed at the
reactor based CE$\nu$NS experiments utilizing low threshold detectors [406].
Future, more ambitious CE$\nu$NS experiments can provide complementary
information to the conventional neutrino oscillation data, offering an
alternative way to search for light sterile neutrinos.

##### Low-mass dark matter

Utilizing the high intensity neutrino fluxes originated from pulsed proton
beams, detectors sensitive to CE$\nu$NS processes can search for light dark
matter [407, 82, 83]. Probing light dark matter with masses below $\sim 1$ GeV
this analysis can provide complementary information to direct detection
searches. The characteristic timing composition of $\pi-$DAR beams provide
useful opportunities to constrain systematic uncertainties, which, together
with the coherent enhancement of the CE$\nu$NS-like dark matter cross section
on nuclei allow for competitive sensitivities. Currently, both a scenario with
a vector portal that mixes kinetically with the photon (see also section 5.2)
[408] as well another scenario with a lepto-phobic portal coupling to any SM
baryon [408, 108] have been investigated with CE$\nu$NS experiments.

The production of dark matter $\chi$ can occur from the decay of a dark gauge
boson $X$ via a relevant Lagrangian given by

$\mathcal{L}_{\rm
prod}\supset\sum_{f}\kappa_{f}x_{f}X_{\mu}\bar{f}\gamma^{\mu}f+\kappa_{D}X_{\mu}\bar{\chi}\gamma^{\mu}\chi\,,$
(22)

where $x_{f}$ is the gauge charge of SM fermion species $f$ and $\kappa_{f}$
denotes the coupling constant associated with the dark gauge boson $X$. By
contrast, $\kappa_{D}$ parameterizes the dark-sector coupling of $X$ to
$\chi$. The dark matter can produce nuclear and electron recoils at the
detector. Using the energy and momentum, $E_{\chi}$ and $p_{\chi}$, of
incoming dark matter, the differential scattering cross section in recoil
energy $E_{r,N}$ of the target nucleus is expressed as [82]

$\frac{d\sigma}{dE_{r,N}}=\frac{(x_{f}\kappa_{f}\kappa_{D})^{2}Z^{2}\cdot|F_{X}|^{2}}{4\pi
p_{\chi}^{2}(2m_{N}E_{r,N}+m_{X}^{2})^{2}}\left\\{2E_{\chi}^{2}m_{N}\left(1-\frac{E_{r,N}}{E_{\chi}}-\frac{m_{N}E_{r,N}}{2E_{\chi}^{2}}\right)+m_{N}E_{r,N}^{2}\right\\},$
(23)

where $Z$ and $m_{N}$ are the atomic number and the mass of the target nucleus
and where $F_{X}$, which is a function over $2m_{N}E_{r,N}$, denotes the form
factor associated with the dark gauge boson $X$.

It has been shown that the timing information available in neutrino
experiments with pulsed beam from COHERENT, CCM and JSNS2 is a powerful probe
of new physics [82, 83]. A combination of energy and timing cuts can eliminate
SM neutrino events which emerge as prompt decays of pion with energy $\sim$ 30
MeV and delayed from the decays of the muons, thereby allowing the possibility
of isolating DM-induced events which are in the prompt window with larger
energy.

| Channel |  $E_{r}$ cut |  $t$ cut
---|---|---|---
COHERENT-CsI | Nucleus scattering | 14 keV$<E_{r}<$26 keV |  $t<1.5~{}\mu$s
COHERENT-LAr | Nucleus scattering |  $E_{r}>21$ keV |  $t<1.5~{}\mu$s
CCM | Nucleus scattering | $E_{r}>50$ keV |  $t<0.1~{}\mu$s (Tight WP)
$t<0.4~{}\mu$s (Loose WP)
JSNS2 | Electron scattering |  $E_{r}>30$ MeV |  $t<0.25~{}\mu$s

Table 5: A summary of the recoil energy and timing cuts that we use for our
data analysis. Figure 18: 90% C.L. projected experimental sensitivity to the
model couplings and mediator masses in the single-mediator scenario ($X=V$)
for our benchmark detectors. We take a dark photon $A^{\prime}$ as our
mediator, and conventionally plot the sensitivities on
$Y\equiv\epsilon^{2}\alpha_{D}(\frac{m_{\chi}}{m_{V}})^{4}$ where
$\alpha_{D}=(\kappa^{V}_{D})^{2}/(4\pi)=0.5$ and $m_{V}/m_{\chi}=3$. The
relevant existing limits from BaBar [409], LSND [18], MiniBooNE [410], and
NA64 [411] are shown by the shaded regions. The parameter sets that are
consistent with the observed dark matter relic abundance are shown by the
black solid line.

For Fig. 18, the energy and timing cuts are utilized as it allows for
eliminating a large portion of backgrounds. The choices for the cuts are
summarized in Table 5. In order to evaluate future sensitivities at COHERENT,
CCM, and JSNS2 to dark matter signals, a likelihood analysis is performed
using simulation data at each experiment for nominal choices of the expected
exposure. For COHERENT, we have utilized the CsI and LAr data as released by
the collaboration.

##### ALPs

Recently, it has been realized that the high intensity sources of photons,
electron-positrons at neutrino experiments (reactor and beam based) can
provide an excellent opportunity to probe ALP [116, 124, 292]. In this regard
the beam based CE$\nu$NS experiments, e.g., CCM, COHERENT, JSNS2 with proton
beam energies ranging from 800 MeV to 3 GeV can play important roles by
producing high intensity photon and electron-positron flux from
bremsstrahlung, cascades, meson decays etc. at the target. The photons can be
utilized via Primakoff processes (enhanced by a factor of $Z^{2}$ where $Z$ is
the atomic number of the target nucleus) for ALP production and similarly,
inverse Primakoff can be utilized for detection as shown in Figs. 19a, 19b.
Further, axions can also decay into two photons in the detector as shown in
Fig. 19c). ALPs, with couplings to electrons, can be produced via Compton-like
scattering (Fig. 19d), bremsstrahlung, and $e^{+}e^{-}$ annihilation and can
be detected via inverse-Compton scattering (Fig. 19h), decay to $e^{+}e^{-}$
(Fig. 19i).

$a$$\gamma$$N$$N$ (a) Primakoff

$\gamma$$a$$N$$N$ (b) Inverse Primakoff

$a$$\gamma$$\gamma$ (c) Diphoton Decay

$a$$e^{-}$$e^{-}$$\gamma$ (d) Compton

$e^{-}$$a$$\gamma$$e^{+}$ (e) Associated Production

$e^{-}$$e^{+}$$a$ (f) Resonance Production

$e^{\pm}$$e^{\pm}$$N$$N$$a$ (g) Bremsstrahlung

$e^{-}$$a$$\gamma$$e^{-}$ (h) Inverse Compton

$a$$e^{-}$$e^{+}$ (i) Dielectron Decay

$a$$e^{+}$$e^{-}$$N$$N$ (j) Pair Production

Figure 19: Contributions to ALP production and detection considered in this
analysis [109].

In order to search for ALPs, we use the Coherent CAPTAIN-Mills (CCM)
experiment, as an example where an 800 MeV proton beam hits a tungsten target
[412]. The GEANT4 10.7 along with the QGSP_BIC_HP library [413] is used to
model the photon and electron-positron production processes. The resulting
photon, electron/positron spectra are shown in Fig. 20 for the energy range
$E_{\gamma}=1\,\text{MeV}-1\,\text{GeV}$.

The ALP interactions are parametrized by the following Lagrangian terms for
this analysis:

$\mathcal{L}_{\rm
ALP}~{}\supset~{}-\frac{g_{a\gamma}}{4}\,aF_{\mu\nu}\tilde{F}^{\mu\nu}\,-\,g_{ae}\,a\,\bar{e}\,i\gamma_{5}\,e$
(24)

where $F_{\mu\nu}\tilde{F}^{\mu\nu}$ is the electromagnetic dual field-
strength operator.

Figure 20: $\gamma$ and $e^{\pm}$ energy spectrum at the Lujan source. GEANT4
10.5 is used with the QGSP_BIC_HP library [413] by generating $10^{5}$ protons
incident on a tungsten target [109].

In Fig. 21, the CCM reach for the ALP parameter space for the coupling
$g_{a\gamma}$ is shown where all the existing constraints from various
experiments and astrophysical bounds are included. CCM’s reach is shown in
dark red (with projected background based on the current measurement) and pink
(no backgrounds). However, the sensitivity would be as good as the zero
background limit once the purity of the LAr is improved. The “cosmological
triangle" [414, 415], can be explored at CCM via ALP decaying into two photons
which is not excluded by any lab based experiment or astrophysical constraint
at present. The upper region of the triangle overlaps some of the parameter
space allowed within various QCD axion models [416]. The parameter space
bounded by the horizontal line portion of the sensitivity graph is due to the
inverse Primakoff scattering and extends to a very low axion mass and in this
region of the parameter space, CCM would also be able to put the best
laboratory bound. The astrophysical bounds are generally dependent on the
underlying model assumed [417, 418, 419, 420, 421, 422, 423, 424].

In Fig. 21, we show the CCM reach for the ALP parameter space for the coupling
$g_{ae}$. CCM’s reach here is shown in navy blue (with projected background
based on the current measurement) and light blue (no background scenario). The
dotted line shows the projected limit. The sensitivity reaches the parameter
space where there exists no direct astrophysical or lab-based limits. The
sensitivity reach also covers some unexplored regions of the QCD axion models.

Figure 21: CCM sensitivities over the axion-photon coupling and electron
coupling parameter spaces are shown for 3 year ($2.25\cdot 10^{22}$ POT)
[109].

The Primakoff and Compton channels can be important to probe ALPs at reactors
[116, 124] both for production and detection. Experiments like MINER, CONUS,
CONNIE, $\nu$-cleus etc. dedicated to CE$\nu$NS observation can be utilized to
search for ALPs. The high intensity photon flux from the reactors can used to
produce ALP via Primakoff and Compton channels. Low-threshold detectors in
close proximity to the core will be sensitive to ALP decays and inverse
Primakoff and Compton scattering, providing sensitivity to the ALP-photon and
ALP-electron couplings.

##### “Bump" hunting using low energy proton beam based IsoDAR experiment

The photon flux from a low energy proton beam experiment, e.g., IsoDAR can
provide interesting BSM search prospects [110]. In this experiment the photon
flux exhibits interesting line-structures which emerge from the transitions of
excited nuclei Fig. 22(top-left). The transition lines can produce a light
mediator, $X$(scalar, pseudoscalar, vector etc), coupled to the nucleons and
the types of mediators determine the magnetic ($M_{i}$) and electric ($E_{i}$)
moments of these transitions [425, 426, 427]. The production rate of the new
mediator can be expressed as a branching ratio for a given transition which
depends on the coupling and the mass. One can assume that $X$ has couplings to
both quarks and neutrinos, e.g., [428, 429, 430].

Figure 22: Top-left: The photon spectrum from the IsoDAR target using Geant
4-QGSP_BIC_ALLHP library. Top-right: The IsoDAR 4-year livetime sensitivity
exclusion for the $N^{*}\to NX(\to\bar{\nu}\nu)$ branching ratio as a function
of the $m_{X}$ at 90% CL. The flat limit for $m_{X}\lesssim 5$ MeV can be
extended to arbitrarily small masses. [110].Bottom: The IBD
($\bar{\nu}_{e}+p\to e^{+}+n$) rates from the decaying
$X\to\bar{\nu}_{e}\nu_{e}$ arriving at the Yemilab detector plotted along with
the expected IBD background (gray). The spectral shape is due to the
convolution of the boosted 2-body decay spectrum with the IBD cross section
which is summed over all kinematically accessible nuclear transitions to
produce the $X$ states

In Fig. 22(top-right), the 90% CL sensitivity to the mediator $X$ is shown.
Here $X$ decays to $\bar{\nu}\nu$ pairs where the antineutrino is detected via
IBD. Fig. 22(bottom) shows $\bar{\nu}_{e}$ energy spectra for several masses
which are compared with the IBD rate from 8Li ( expected to be the only
significant background for this search). The edges in the spectrum emerge due
to the photon spectrum and IBD cross section convolution. From this analysis,
$X$-boson coupling can be constrained to be $\leq 10^{-3}$ for mass $O(10)$
MeV when the $X$ boson decays promptly into neutrinos with coupling values
$\geq 10^{-7}$. The existing constraints from COHERENT, CCM have not ruled out
this parameter space completely.

The “bump search” utilizing the transition lines at the low energy beam dump
experiments have many interesting consequences:
(i) We can probe low mass mediators which can provide positive and negative
contributions to $\Delta N_{eff}$ depending on its decay branching ratio into
neutrino-anti-neutrinos and electron-positrons, respectively [431]. Further,
the interactions involving the decay into neutrino final states have impact on
the neutrino floor for dark matter direct detection experiments [429, 430,
432].
(ii) We can achieve sensitivity to the light mediator claimed to explain the
Atomki anomaly [433, 434, 435, 436]. This is a reported excess of $e^{+}e^{-}$
pairs observed in the decay of the 18 MeV excited state of beryllium produced
through 7Li(p,n)8Be∗, and the set of 20 MeV excited states of helium produced
through 3H(p,$\gamma$)4He.
(iii) We can probe the origin of the 5 MeV reactor bump, which is observed in
the event distribution of most modern reactor experiments, e.g., PROSPECT
[437] STEREO [438], NEOS [439], RENO [440], Daya Bay [441] and Double Chooz
[442].

ALP at IsoDAR The M-type transition lines will be very useful to investigate
ALP at IsoDAR. We will be able to get world leading constraint in some of the
channels. In figure 23, the 5 year sensitivity exclusion plot is shown for the
product of couplings $g_{aNN}\times g_{a\gamma\gamma}$. We find that IsoDAR
will provide the best constraint in the parameter space which has constraints
from TEXONO, Borexino, SN1987A, HB stars etc. Similar exclusion plots can be
obtained for $g_{aNN}\times g_{aee}$ as a function of $m_{a}$.

ALPs at IsoDAR can be also obtained from the Primakoff process using the
bremsstrahlung and cascade photons and from the cascade electrons which would
provide constraints on $g_{a\gamma\gamma}$ and $g_{aee}$ separately. A
detailed study is underway [321]

Figure 23: [Preliminary]The IsoDAR sensitivity exclusion $g_{aNN}\times
g_{a\gamma\gamma}$ is shown as function of ALP mass $m_{a}$. [321].

####  5.6.2 Incoherent neutrino-nucleus scattering (I$\nu$NS)

Neutral-current neutrino-nucleus scattering also presents an inelastic
(incoherent) channel (I$\nu$NS), in which the quantum state of the nucleus in
the final state is changed. Contrary to the elastic channel, this cross
section has a linear dependence on the number of nucleons [443, 444, 445].
Going to higher neutrino energies, there is a smooth transition between the
coherent and incoherent neutrino-nucleus scattering regimes. The I$\nu$NS
channel can affect the high-energy tail of the recoil spectrum of neutrino
experiments like COHERENT [446]. A correct treatment of both channels requires
an accurate evaluation of the transition matrix elements describing the
various interaction channels between the initial and a final nuclear states.

In Fig.24(top-left) we show various neutrino-nucleus inelastic calculations.
The top left plot shows a comparison of multipole operator analysis, total
Gammow-Teller (GT) and 1st GT are compared with the CRPA [447] and free
nucleon [448] predictions for ${}^{40}Ar$ [449]. The full multipole operator
analysis and the GT transitions are calculated using the nuclear shell model
code BIGSTICK[450, 451]. For small momentum transfers, when a GT transition is
kinematically accessible, the inelastic cross section will be dominated by it
and in this limit the GT operator alone can then provide an efficient way to
approximate the scattering cross section. The multipole results only include
transitions to the first 15 excited states and thus it is not capturing all
accessible states. However it includes the first GT transition and one can see
the GT dominates the inelastic cross-section. Total GT includes all possible
GT transitions. Computing the complete multipole results would be the most
precise results, however, the total GT strength is sufficiently precise. GT
approximation makes large number of final states calculation a tractable more
computational task. The total elastic and inelastic cross-sections for the
133Cs and 127I targets are shown in Fig. 24 (top-right).

Figure 24: Comparison of multipole operator analysis, total GT and 1st GT are
compared with the CRPA [447] and free nucleon [448] predictions (top-left).
Total elastic and inelastic $\nu$-nucleus (top-right) DM-nucleus (bottom)
scattering cross section for 40Ar, 133Cs, and 127I nuclei are shown [449].

The elastic and inelastic cross section for dark matter scattering on the
target nuclei 40Ar, 133Cs and 127I are shown in Fig. 24(bottom). We assume
$m_{\chi}=30$MeV, $m_{A^{\prime}}=90$ MeV, $\epsilon=10^{-4}$ and
$g_{D}=\sqrt{2\pi}$ in the allowed parameter space. 133Cs and 127I have a
higher elastic cross section than 40Ar since $\sigma_{\rm el}$ has explicit
$Z^{2}$ (atomic number) dependence, but have a lower inelastic cross section
since the inelastic cross section is the largest for 40Ar and is the lowest
for 133Cs.

####  5.6.3 Neutrino tridents

Neutrino trident production is a rare SM process in which a pair of leptons
with opposite charge is produced from the scattering of a neutrino off the
Coulomb field of a heavy nucleus [452, 453, 454, 455, 456, 457]. Neutrino
trident production has been searched for in several neutrino beam experiments
and dimuon tridents have been observed at the CHARM-II [458] and CCFR [459]
experiments. NuTeV found no conclusive signal [460, 461]. While these
measurements are consistent with SM predictions, this process offers a
sensitive probe to constrain new physics, in particular new neutral currents
among leptons. For instance, it has been shown to be capable of imposing
stringent constraints on well-motivated extensions of the SM introducing a
$Z^{\prime}$ boson by gauging the difference of the lepton number between the
muon and tau flavor, $L_{\mu}-L_{\tau}$ [462, 463]. Sizeable number of trident
events are expected at future near detector experiments receiving intense
neutrino beams from accelerators [464, 465, 466], thus allowing to improve
current measurements, including measuring dielectron and mixed flavor trident
channels and to search for new physics effects [467, 468].

##  6 Tools

| Production |  | Dark $\rightarrow$ Standard |  |
---|---|---|---|---|---
Process | Brem. | Direct | Prompt | LL | Flux | Decay | $e$ |  $N$ El. |  $N$ Inel. | Det. | Reco.
MadDump |  | $\checkmark$ | $\checkmark$ |  | $\checkmark$ |  | $\checkmark$ |  | $\checkmark$ |  |
BdNMC | $\checkmark$ | $\checkmark$ | $\checkmark$ |  | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ |  |
GENIE |  |  |  |  |  |  | $\checkmark$ | $\checkmark$ | $\checkmark$ |  |
Geant4 |  |  | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ |  |  |  | $\checkmark$ |
ACHILLES |  |  |  |  |  | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ |  |
FORESEE | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ | $\checkmark$ |  |  |
Table 6: Summary of the capabilities of some tools that are currently
available. A green check mark indicates strong capabilities and full public
availability. A yellow check mark indicates either missing features or
inaccessibility. None of these tools can cover most dark sector models and
current tools are generally focused on a handful of models. Geant4 stands for
a suite of tools developed by experimental collaborations, such as those
within sbncode or G4edep-sim. The full labeling of the processes is dark
bremsstrahlung, direct production (deep inelastic scattering), prompt meson
decay, long-lived meson decay, flux, dark sector decay, electron scattering,
nucleon elastic scattering, nucleon inelastic scattering (resonant and deep
inelastic), detector simulation, reconstruction.

Assessment of the reach of neutrino beam experiments to dark sector models
requires detailed simulation of the signals. Several factors challenge efforts
to develop such simulations. First, the target geometry can play a significant
role in models where dark sector states arise from long-lived meson decays,
which can be challenging to model accurately. The beam energies are high but
not so high that nuclear effects in proton-target collisions are entirely
negligible. Finally, the slowness of detector simulation for LArTPC
experiments is a bottleneck on event generation for upcoming experiments.
Given these challenges, several different tools have been developed that
address the specific needs of given models. We describe several of these tools
in 6.1.

Beyond tools for event generation, dark sector signals may introduce unique
topologies that are not optimally detected by existing reconstruction tools,
which focus primarily on neutrino-like signals. Ongoing work in the
reconstruction of non-standard signals will require new tools, including
potentially harnessing the power of machine learning. These issues are
discussed more detail in 6.2.

###  6.1 Event Generation Tools

Event generation necessarily requires two components: generation of dark
sector states as the protons of the beam collide on target and generation of a
visible signal in the detector downstream. Each of these can pose unique
challenges.

Dark sector production

The targets at neutrino experiments are typically thin, in the 1-2 radiation
length range, leading to significant portions of the proton beam that go
through to a downstream absorber. Furthermore, any hadronic particles produced
in the collision may escape the target before decaying. Such decays can
produce dark sector particles in some models, such as the Higgs Portal model
(previously discussed in Section 5.1). Finally, magnetic horns are typically
employed to enhance the neutrino or anti-neutrino content of the beam. For
dark sector states that are produced promptly, either by short decays of, say,
$\pi^{0}$ or direct production such as in dark bremsstrahlung, these
challenges can be readily overcome. Tools like BdNMC [19] and MadDump [469]
can be used to accurately simulate such prompt processes for a number of dark
sector models.

For models such as the Higgs Portal model, where dark sector states are
produced via decays of long-lived kaons, a more comprehensive, Geant4-based
approach is typically required [470]. This can be done by appropriately
modifying the output of neutrino beam simulations. Unfortunately, this needs
to be done on a beam-by-beam basis but has been successfully implemented for
both the Booster Neutrino Beam (BNB) and Neutrinos at the Main Injector (NuMI)
beam [165].

Dark sector scattering and decay

Subsequent to the production of dark sector states, these particles need to be
propagated into the detector, which is a straightforward geometric exercise,
provided the geometry is accurately known. They can leave a visible signal
either by decay, which is generally straightforward to generate, or
scattering, which may be more complicated. Event generation is typically
straightforward if the dark sector state scatters electrons. Complications may
arise if the dark sector topology is non-trivial, say if the scattering is
inelastic and leads to a displaced decay. BdNMC and MadDump can handle
straightforward electron scattering, and even inelastic scattering could and
should be implemented without too much difficulty.

The more challenging situation is when the dark sector states scatter off of
nucleons. The energy of particles produced in neutrino beams is typically
around one to few GeV, leading to scattering with energy transfers around the
QCD scale. This is a challenging energy scale to simulate, as there is no
first-principles description of the physics. Instead, modeling and data-
fitting are required. Furthermore, in this energy regime, any hadrons produced
in the dark sector scattering can scatter as they exit the nuclear debris in a
process known as Final State Interactions (FSI). These FSI can significantly
distort both the particle IDs and spectra coming out of hadronic dark sector
collisions. For a broad class of dark matter models, namely those with a
spin-1 mediator, a tool has been developed to simulate hadronic scattering
[471]. This tool is built within the GENIE software [472], making it
straightforward to test different nuclear models and to connect with detector
simulation pipelines. Recently, a new tool (ACHILLES) was developed to
increase the flexibility of including arbitrary models into neutrino event
generators [473]. ACHILLES separates the nuclear current from the leptonic
current, providing an adaptable framework to quickly study new models.
Furthermore, ACHILLES is the first code that correctly propagates spin
correlations through the generation of $n$-body final state processes, instead
of generating $2\rightarrow 2$ processes with subsequent on-shell decays.

###  6.2 Necessary Experimental Capabilities

Event timing

Many models postulate BSM particles with longer time of flight than neutrinos.
In the usual case where the neutrino beam is pulsed, the time window
immediately after all the neutrinos have crossed the detector will offer a
sample without neutrino background. Despite only containing a fraction of the
signal, these kinds of samples exclude neutrinos which can mimic the signal
topologies and cannot be easily eliminated. In the search for heavy neutral
leptons produced from kaon decays at rest in BNB, the MicroBooNE experiment
adds a new configuration in the trigger system and thereby utilizes the data
collected 0.6 $\mathrm{\SIUnitSymbolMicro s}$ after the arrival of the
neutrinos produced in the same beam, which has an energy spectrum peaked at
$\sim$800 MeV [7]. As a result, the remaining background of this analysis is
the mis-reconstructed cosmic rays, which have different topologies from signal
and are much more straightforward to get rid of. In addition, it is possible
to employ the time structure of the proton extraction in data collected in the
arrival time window of neutrinos. This typically requires $\mathrm{ns}$ time
resolution, and detectors designed for light detection usually meet the
requirement.

Late signal events offer a particular challenge for the trigger system of
LArTPC experiments. Trigger systems are extremely important to LArTPC-based
experiments, whose millimeter spatial resolution results in a huge volume of
data and requires real-time selection to make it manageable. It is essential
to have a flexible trigger system allowing different configurations optimized
to different physics topics. While the complete MicroBooNE experiment and the
ongoing ICARUS experiment (the far detector of SBN) both have a trigger system
up to a certain degree of flexibility, a more sophisticated trigger system is
being developed. For instance, based on the nanosecond scale of the beam
structure, a trigger system with nanosecond time resolution will more
efficiently select neutrinos or BSM particles with longer time-of-flight. In a
LArTPC, only the scintillation light of liquid argon have such a time
resolution, and therefore light detectors required to have nanosecond time
resolution, for both the real-time trigger logics and data analyses.

As LArTPC-based experiments utilize the scintillation light to obtain
nanosecond-scale timing of interested activities and the ionization charge for
the spatial and kinematic information, matching the light and charge
originating from the same activity is crucial. An accurate, efficient matching
algorithm will allow us to determine the time-of-flight of a particle to the
level of a few nanoseconds and therefore distinguish heavy BSM particles from
SM neutrinos.

Fast detector simulation and its challenges

Unlike the particles produced in a collider experiment, the interactions or
decays of interests here can occur at every point inside (or outside) the
active volume of the neutrino detectors. Given the finite volume, it is
important to have a correct detector geometry configuration to assess the
containment and acceptance of the particles produced in the signal events, in
particular in the cases with non-uniform beam intensities and with the beam
off the axis of the detector. Further, a correct detector geometry will help
to assess the impacts or the systematic uncertainties from interactions with
other materials in the detectors, and from events occurring outside the active
volume of the detectors, while defining a fiducial volume can mitigate the
impacts.

The official simulation toolkits used in an experiment, such as LArSoft in SBN
and DUNE, typically have a driver to appropriately handle the detector
geometry. However, Monte Carlo generators for BSM signals are usually not
fully integrated, and the detector geometry hence needs to be carefully
handled. Instead of importing MC events into LArSoft and completing the full
detector simulation, it would be helpful to design an interface for easier
implementation of event generator, taking into account the detector geometry
in early stages.

Realistic sensitivity estimates are an important step in promoting and
developing analyses with real data. This typically requires kinematic
distributions or simplified MC simulation, combined with parameters of
detector efficiency and resolution. Detector efficiency and resolution in
neutrino experiments usually depend not only on the particle energy, but also
on its direction and the relative location in the detector, and therefore it
is complicated to obtain a parametrization matrix mapping all the phase space.
Nonetheless, it is desired to utilize realistic, approximate parametrization
matrices to quantify the sensitivity and compare with existing results. This
parametrization needs to be consistent with an understanding of the detector
geometry.

A fast detector response estimation will be an invaluable tool for both
experimentalists and theorists, but in order to search for a model, a full
modeling of particle trajectories through the detector volume and the
resulting energy deposits is necessary. In particular, simulation of this
response in LArTPCs with a multi-ten-ton scale is slow, limiting the number of
signals that will be simulated. Overcoming this bottleneck will be necessary
to provide a broad program of dark sector searches at LArTPC experiments.

One intermediate possibility between a full detector simulation and a
parametrized response is to use track and shower templates to model bypass the
slow step of propagating the particles through the detector medium using
Geant4. This could allow for study of more complicated in models in a
realistic way and, perhaps, to determine experimental sensitivity to more
models.

MeV-scale signatures

Many sub-GeV BSM particles can produce MeV-scale signatures. The scope of BSM
searches would be expanded if they were able to detect and reconstruct such
MeV-scale deposits. Furthermore, the search for exotic particles from their
decay products, such as a muon-pion pair decaying from a hypothesized heavy
neutral lepton, can also be separated from SM neutrino background by excluding
MeV-scale particles around the decay vertex. Lowering the detection threshold
of a LArTPC can be achieved mainly by shortening the pitches of the charge
detection system, and/or by enhancing the signal-to-noise ratio. As a particle
can be distinguished from noise by coincident energy depositions in two
adjacent detection channels, smaller pitches (below the typical 3 or 4
$\mathrm{mm}$) allow detection of particles with lower energy. A large signal-
to-noise ratio would further raise the likelihood to identify particles with
smaller energy deposit than minimal ionization particles, which either leave a
shorter track than the pitch width, or hypothetically carries fractional
charge such as millicharged particles discussed in Sec. 5.2.4.

A robust signal processing algorithm is required to disentangle the energy
deposition and the effect of the induced charge from the adjacent channels,
and provide more accurate information for hit finding and reconstruction
algorithms. It is also desired to increase the reconstruction efficiency of
MeV-scale energy deposits.

Reconstruction of complex topologies

Several topologies are of particular interests in search for BSM signals. They
can also occur in a SM neutrino interaction, and reconstruction algorithms
optimizing to such topologies will benefit the SM measurements. For example,
it would be very useful to characterize a electromagnetic shower containing an
electron and a positron from the decay of a boosted, long-lived scalar
particle, as illustrated in Sec. 5.1. Such characterization will improve the
reconstruction of $\pi^{0}$, the main background of $\nu_{e}$ appearance
measurements. In some cases, optimizing the reconstruction efficiency of
particles coming from non-standard beam direction, such as MicroBooNE with
respect to a particle produced at the hadron absorber of the NuMI beam (a
nearly opposite direction of the BNB neutrino beam), would help improve the
sensitivity.

For up-scattered BSM signals, an interaction and decay vertices occurring in
coincidence is a distinctive feature, and, in LArTPCs, only the light signals
have the required time resolution. It is therefore crucial to have charge-
light matching algorithms dealing with these cases. Reconstructing this kind
of signature may be particularly important for surface LArTPCs. For example,
the interaction or decay point may only attach to a single track or an
electromagnetic shower, and does not literally form a “vertex,” making the
events similar to an interaction overlaid with a cosmic ray track.
Nonetheless, it is another example which can benefit a SM neutrino
measurement. A neutrino interaction producing an electromagnetic shower can
have a radiated photon which travels a few tens of centimeters and then starts
the pair production; such a case would also have better resolution by
correctly associate the pair produced electrons and positrons with the
original electromagnetic shower.

###  6.3 Action Plan

Simulation pipeline

In order to streamline the process of simulating different dark sector models
and increase coverage of model space, a seamless and modular simulation
pipeline is necessary. As indicated in Table 6, there are several stages of
the pipeline and different tools for generation of the relevant physics at
each.

As an example, it would be highly useful to be able to interface the output of
dark matter scattering in the detector with different models of detector
simulation, from parametrized response to full detector simulation. Another
use case is that nuclear final state interactions and modeling of low-energy
inelastic scattering can have significant effects on sensitivity to
hadronically interacting dark sector particles, so it is important to also
have the flexibility to connect with different models of nuclear and hadronic
physics. A framework to connect different models of dark sector physics with
this challenging standard model physics is needed. A prototype of how this
framework could be expressed is outlined in Ref. [473], and implemented within
the ACHILLES tool. This framework separates the nuclear current from the
leptonic current, providing a realistic strategy for interfacing arbitrary
dark matter models with arbitrary nuclear models.

At present, these tools do not easily interface with one another or with the
pipeline used by neutrino experiment full simulation and reconstruction,
including notably LArSoft.

There are several ways in which this process could be streamlined. One option
is a fully Geant4-compatible package for the dark matter simulation which is
responsible for production of dark matter and its interaction inside (or
outside) of the detector geometry. Collaborators of NA64 experiment at CERN
developing such Geant4 extension package called DMG4 [474], for 100 GeV
electron beam and the newly added physics processes in this package are about
production of dark matter via electron and muon bremsstrahlung off nuclei,
resonant in-flight positron annihilation on atomic electrons and gamma to
axion-like particles conversions on nuclei. Currently, the DMG4 package
support dark matter productions from only electron and muon beam but if we can
extend this for proton beam, this will allow us to formulate an efficient
simulation pipeline and also provide additional opportunity of cross check
about the simulation results.

Similar full simulation from the production of new physics species to the
experimental signature, albeit currently with less detector simulation details
than Geant4 could offer, can be performed for far-forward physics searches at
the LHC with a dedicated FORESEE tool [475]. Currently, the package offers the
possibility to compare expected signal rates in selected BSM models for
different detector types, new physics models and experimental signatures that
can be varied by the user. A modified version of FORESEE is also included in
the FASER collaboration simulation pipeline, therefore making the tool an
ideal interface between theory and experiment.

Perhaps more flexible would be to standardize the output of each step of the
chain described by Table 6. The standard format for collider high-energy
experiments such as those at the Large Hadron Collider is the HepMC3 [476]
format, which contains enough flexibility to describe the output at each step
above given some common standards.

This does not necessarily solve all the problems, such as the problem of
connecting to different nuclear models and fully tracking systematic and
theoretical uncertainties through the process, but it would be an excellent
start. The HepMC3 format offers one way to handle the propagation of
systematic and theoretical uncertainties through the simulation pipeline,
though further work is needed to accurately quantify these uncertainties and
build them into the pipeline.

A process should be started to assess how to best standardize the simulation
pipeline and allow for easy interface between different models for the various
stages of simulation. As a first step, a workshop should be held to bring
together experts on the various stages of simulation, as well as
experimentalists and theorists who use these tools, to recommend a set of
standards and discuss their implementation.

It would also be helpful to ease connection of dark sector models into the
pipeline. None of the tools currently available allow for simple
implementation of new, fully general models. MadDump does allow for
implementation of models using the standard FeynRules package and UFO model
description format, but cannot cover models that have arbitrary kinds of
interactions, such as those with multiple vertices in the detector. ACHILLES
also allows for implementation of models using the standard FeynRules package
and UFO model description format, but is currently unable to handle particles
with spin $>$ 1\. Other tools generally focus on specific types of dark sector
particles and interactions. In order to ensure that the dark sector models
developed over the last several years are studied in upcoming searches, it is
important that more models are implemented. While recent work has made large
strides in this direction, there still exists a barrier to a robust dark
matter search program with neutrino beams.

Fast simulation and response

Many of the tools that would be helpful for simulating more complicated
production modes, such as via decay of long-lived mesons, are developed by
experimental collaborations and have a high barrier to entry. Incorporating
these processes in to the more theory-focused tools is challenging, as they
are dependent on the specific beam and target geometries. Furthermore, complex
analysis tools such as fine-grained timing of signals can be valuable and is
also highly dependent on the beam geometry. By standardizing the format,
theorists could be free to implement their model using the tool of their
choice of the underlying particle physics, with confidence that detailed
predictions for experiments could be derived.

Detector simulation and reconstruction are particularly intensive for upcoming
LArTPC experiments. Furthermore, the tools to perform these stages of the
simulation chain are not accessible to theorists, leading to crude estimations
of sensitivity. Development of fast simulation and reconstruction, either by a
simplified Geant4-based approach or by parameterized efficiencies and
resolutions, is needed by both the theory and experiment communities.

New trigger and reconstruction algorithms

On the experimental side, the wealth of complicated signals demands new
reconstruction algorithms. The trigger system will need the flexibility to
handle out-of-time signals. Timing can also help in distinguishing signals
from backgrounds, but, in LArTPC-based experiments for example, this requires
careful matching of light and charge signals. Low energy signals will require
new reconstruction strategies and the full capabilities for going below
“standard” reconstruction thresholds is unknown. Algorithms to pick out
complex topologies with multiple, separated vertices, such as from dark sector
up-scatter followed by decay, also need to be developed. Work on all of these
is ongoing and should be a high priority as the scope of dark sector searches
grows.

##  7 Outlook

During the next decade and beyond, a variety of neutrino beam experiments will
address basic questions about the nature of neutrinos. As we have spotlighted
in this whitepaper, these experiments also have the capability to pursue a
broad program of BSM searches for new light, weakly coupled states that are
part of a dark sector.

Dark sector theories are motivated on several accounts, as they may address
some of the outstanding mysteries in fundamental physics, including dark
matter and neutrino masses, or explain certain experimental anomalies. A wide-
ranging experimental program to probe the dark sector is emerging, and there
has been a growing realization that neutrino beam experiments are a vital part
of this enterprise. This is a consequence of their intense beams/sources,
large neutrino and secondary fluxes, and cutting-edge sensitive detectors.

Substantial progress has been made in recent years in terms of the
phenomenological and experimental developments needed to pursue a viable dark
sector search program at neutrino beam facilities, but there is still work to
be done. We have called attention to some of these needs, including accurate
and fast simulation tools that can be easily integrated into experimental
analyses, novel reconstruction and analyses methods, and improved modeling of
neutrino-nucleus interactions.

We anticipate this whitepaper will provide a broad snapshot of the state of
this subfield along with guidance on the next steps needed to realize a robust
dark sector search program at existing and future neutrino beam facilities.

## Acknowledgements

B. Batell is supported by U.S. Department of Energy (DOE) Grant DE–SC0007914
and by PITT PACC. F. Kling acknowledges support by the Deutsche
Forschungsgemeinschaft under Germany’s Excellence Strategy - EXC 2121 Quantum
Universe - 390833306. WJ and JY are supported by the U.S. DOE Grant No. DE-
SC0011686. JCP is supported by the National Research Foundation of Korea (NRF)
[NRF-2019R1C1C1005073 and NRF-2021R1A4A2001897]. TBS is supported by the
National Science Foundation Graduate Research Fellowship Program under Grant
No. 1839285. VDR acknowledges financial support by the SEJI/2020/016 grant
funded by Generalitat Valenciana, by the Universitat de València through the
sub-programme “Attracció de talent 2019” and by the Spanish grant
PID2020-113775GB-I00 (AEI/10.13039/501100011033). S. Trojanowski is supported
by the grant “AstroCeNT: Particle Astrophysics Science and Technology Centre”
carried out within the International Research Agendas programme of the
Foundation for Polish Science financed by the European Union under the
European Regional Development Fund, by the Polish Ministry of Science and
Higher Education through its scholarship for young and outstanding scientists
(decision no 1190/E-78/STYP/14/2019), and by the European Union’s Horizon 2020
research and innovation programme under grant agreement No. 952480 (DarkWave
24 project).

## Glossary

cluster on board (COB)

    An ATCA motherboard housing four RCEs
cathode plane assembly (CPA)

    The component of the SP detector module that provides the drift HV cathode
data acquisition (DAQ)

    The data acquisition system accepts data from the detector FE electronics, buffers the data, performs a , builds events from the selected data and delivers the result to the offline
data selector

    The portion of the DAQ front-end fragment that accepts trigger commands and returns the corresponding data fragment. Not to be confused with .
DAQ front-end readout (FER)

    The portion of a DAQ front-end fragment that accepts data from the detector electronics and provides it to the FEC.
DAQ front-end fragment

    The portion of one DAQ partition relating to a single front-end computer (FEC) and corresponding to an integral number of detector units. See also
DAQ partition

    A cohesive and coherent collection of DAQ hardware and software working together to trigger and read out some portion of one detector module; it consists of an integral number of . Multiple DAQ partitions may operate simultaneously, but each instance operates independently
DAQ run

    A period of time over which relevant data taking conditions and DAQ configuration are asserted to be unchanged. Multiple DAQ runs may occur simultaneously when multiple DAQ partitions are active. This term should not be confused with DUNE experiment or beam “runs” which typically span many DAQ runs.
data fragment

    A block of data read out from a single DAQ front-end fragment that span a contiguous period of time as requested by a trigger command
detector module

    The entire DUNE far detector is segmented into four modules, each with a nominal $10\text{\,}\mathrm{kt}$ fiducial mass
detector unit

    A may be partitioned into a number of similar parts. For example the single-phase TPC is made up of APA units
DUNE

    Deep Underground Neutrino Experiment
external trigger logic (ETL)

    Trigger processing that consumes detector module level information and other global sources of trigger input and emits information back to the
external trigger candidate

    Information provided to the about events external to a detector module so that it may be considered in forming
field cage (FC)

    The component of a LArTPC that contains and shapes the applied E field
front-end (FE)

    The front-end refers a point that is “upstream” of the data flow for a particular subsystem. For example the front-end electronics is where the cold electronics meet the sense wires of the TPC and the front-end DAQ is where the DAQ meets the output of the electronics
front-end computer (FEC)

    The portion of one DAQ partition that hosts the , and . It hosts the and corresponding portion of the .
inter-process communication (IPC)

    A system for software elements to exchange information between threads, local processes or across a data network. An IPC system is typically specified in terms of protocols composed of message types and their associated data schema.
large electron multiplier (LEM)

    A micro-pattern detector suitable for use in ultra-pure argon vapor; LEMs consist of copper-clad PCB boards with sub-millimeter-size holes through which electrons undergo amplification
one-pulse-per-second signal (1PPS signal)

    An electrical signal with a fast rise time and that arrives in real time with a precise period of one second
ProtoDUNE

    Either of the two DUNE prototype detectors constructed at CERN and operated in a CERN test beam (expected fall 2018). One prototype implements SP and the other DP technology
run control (RC)

    The system for configuring, starting and terminating the DAQ
single-phase (SP)

    Distinguishes one of the DUNE far detector technologies by the fact that it operates using argon in its liquid phase only
SP module

    single-phase detector module
trigger command message (TCM)

    A message flowing down the trigger hierarchy from global to local context. Also see
technical design report (TDR)

    A formal project document that describes the experiment at a technical level
trigger candidate

    Summary information derived from the full data stream and representing a contribution toward forming a
trigger command

    Information derived from one or more trigger candidates that directs elements of the detector module to read out a portion of the data stream
trigger notification

    Information provided by to external trigger logic (ETL) about its processing
Micro Telecommunications Computing Architecture ($\mu$TCA)

    The computer architecture specification followed by the crates that house charge and light readout electronics in the dual-phase module

## References

  * [1] J. Alexander et al. 2016\.  arXiv:1608.08632 [hep-ph].  https://inspirehep.net/record/1484628/files/arXiv:1608.08632.pdf.
  * [2] M. Battaglieri et al. arXiv:1707.04591 [hep-ph].
  * [3] J. Beacham et al. arXiv:1901.09966 [hep-ex].
  * [4] R. Kolb, H. Weerts, N. Toro, R. V. de Water, R. Essig, D. McKinsey, K. Zurek, A. Chou, P. Graham, J. Estrada, J. Incandela, and T. Tait, “Basic Research Needs for Dark-Matter Small Projects New Initiatives.” https://science.energy.gov/~/media/hep/pdf/Reports/Dark_Matter_New_Initiatives_rpt.pdf, 2019\.
  * [5] MiniBooNE Collaboration, A. Aguilar-Arevalo et al. Phys. Rev. Lett. 118 no. 22, (2017) 221803, arXiv:1702.02688 [hep-ex].
  * [6] MiniBooNE DM Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. D 98 no. 11, (2018) 112004, arXiv:1807.06137 [hep-ex].
  * [7] MicroBooNE Collaboration, P. Abratenko et al. Phys. Rev. D 101 no. 5, (2020) 052001, arXiv:1911.10545 [hep-ex].
  * [8] ArgoNeuT Collaboration, R. Acciarri et al. Phys. Rev. Lett. 127 no. 12, (2021) 121801, arXiv:2106.13684 [hep-ex].
  * [9] MicroBooNE Collaboration, P. Abratenko et al. Phys. Rev. Lett. 127 no. 15, (2021) 151803, arXiv:2106.00568 [hep-ex].
  * [10] B. Holdom Phys. Lett. 166B (1986) 196–198.
  * [11] B. Patt and F. Wilczek arXiv:hep-ph/0605188.
  * [12] P. Minkowski Phys. Lett. 67B (1977) 421–428.
  * [13] L. B. Okun Sov. Phys. JETP 56 (1982) 502.
  * [14] R. D. Peccei and H. R. Quinn Phys. Rev. Lett. 38 (1977) 1440–1443.
  * [15] S. Weinberg Phys. Rev. Lett. 40 (1978) 223–226.
  * [16] F. Wilczek Phys. Rev. Lett. 40 (1978) 279–282.
  * [17] B. W. Lee and S. Weinberg Phys. Rev. Lett. 39 (1977) 165–168.
  * [18] P. deNiverville et al. Phys. Rev. D84 (2011) 075020, arXiv:1107.4580 [hep-ph].
  * [19] P. deNiverville et al. Phys. Rev. D95 no. 3, (2017) 035006, arXiv:1609.01770 [hep-ph].
  * [20] L. Buonocore, C. Frugiuele, and P. deNiverville Phys. Rev. D 102 no. 3, (2020) 035006, arXiv:1912.09346 [hep-ph].
  * [21] A. Berlin, P. deNiverville, A. Ritz, P. Schuster, and N. Toro Phys. Rev. D 102 no. 9, (2020) 095011, arXiv:2003.03379 [hep-ph].
  * [22] B. Batell, J. L. Feng, A. Ismail, F. Kling, R. M. Abraham, and S. Trojanowski Phys. Rev. D 104 no. 3, (2021) 035036, arXiv:2107.00666 [hep-ph].
  * [23] B. Batell et al. Phys. Rev. D90 no. 11, (2014) 115014, arXiv:1405.7049 [hep-ph].
  * [24] P. Coloma et al. JHEP 04 (2016) 047, arXiv:1512.03852 [hep-ph].
  * [25] M. Gell-Mann, P. Ramond, and R. Slansky Conf. Proc. C790927 (1979) 315–321, arXiv:1306.4669 [hep-th].
  * [26] T. Yanagida Conf. Proc. C7902131 (1979) 95–99.
  * [27] S. L. Glashow NATO Sci. Ser. B 61 (1980) 687.
  * [28] R. N. Mohapatra and G. Senjanovic Phys. Rev. Lett. 44 (1980) 912. [,231(1979)].
  * [29] J. Schechter and J. W. F. Valle Phys. Rev. D 22 (1980) 2227.
  * [30] R. Foot, H. Lew, X. G. He, and G. C. Joshi Z. Phys. C 44 (1989) 441.
  * [31] MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. Lett. 102 (2009) 101802, arXiv:0812.2243 [hep-ex].
  * [32] MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. Lett. 121 no. 22, (2018) 221801, arXiv:1805.12028 [hep-ex].
  * [33] MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. D 103 no. 5, (2021) 052002, arXiv:2006.16883 [hep-ex].
  * [34] V. Brdar and J. Kopp Phys. Rev. D 105 no. 11, (2022) 115024, arXiv:2109.08157 [hep-ph].
  * [35] MicroBooNE Collaboration, P. Abratenko et al. arXiv:2110.00409 [hep-ex].
  * [36] G. Karagiorgi, Z. Djurcic, J. M. Conrad, M. H. Shaevitz, and M. Sorel Phys. Rev. D 80 (2009) 073001, arXiv:0906.1997 [hep-ph]. [Erratum: Phys.Rev.D 81, 039902 (2010)].
  * [37] G. H. Collin, C. A. Arg$\ddot{\rm u}$elles, J. M. Conrad, and M. H. Shaevitz Phys. Rev. Lett. 117 no. 22, (2016) 221801, arXiv:1607.00011 [hep-ph].
  * [38] C. Giunti and M. Laveder Phys. Rev. D 84 (2011) 073008, arXiv:1107.1452 [hep-ph].
  * [39] C. Giunti and M. Laveder Phys. Lett. B 706 (2011) 200–207, arXiv:1111.1069 [hep-ph].
  * [40] S. Gariazzo, C. Giunti, M. Laveder, and Y. F. Li JHEP 06 (2017) 135, arXiv:1703.00860 [hep-ph].
  * [41] S. Böser, C. Buck, C. Giunti, J. Lesgourgues, L. Ludhova, S. Mertens, A. Schukraft, and M. Wurm arXiv:1906.01739 [hep-ex].
  * [42] J. Kopp, M. Maltoni, and T. Schwetz Phys. Rev. Lett. 107 (2011) 091801, arXiv:1103.4570 [hep-ph].
  * [43] J. Kopp, P. A. N. Machado, M. Maltoni, and T. Schwetz JHEP 05 (2013) 050, arXiv:1303.3011 [hep-ph].
  * [44] M. Dentler, A. Hernández-Cabezudo, J. Kopp, P. A. N. Machado, M. Maltoni, I. Martinez-Soler, and T. Schwetz JHEP 08 (2018) 010, arXiv:1803.10661 [hep-ph].
  * [45] K. Abazajian et al. arXiv:1204.5379 [hep-ph].
  * [46] J. M. Conrad, C. M. Ignarra, G. Karagiorgi, M. H. Shaevitz, and J. Spitz Adv. High Energy Phys. 2013 (2013) 163897, arXiv:1207.4765 [hep-ex].
  * [47] A. Diaz, C. A. Arg$\ddot{\rm u}$elles, G. H. Collin, J. M. Conrad, and M. H. Shaevitz arXiv:1906.00045 [hep-ex].
  * [48] J. Asaadi, E. Church, R. Guenette, B. J. P. Jones, and A. M. Szelc Phys. Rev. D 97 no. 7, (2018) 075021, arXiv:1712.08019 [hep-ph].
  * [49] G. Karagiorgi, M. H. Shaevitz, and J. M. Conrad arXiv:1202.1024 [hep-ph].
  * [50] H. Pas, S. Pakvasa, and T. J. Weiler Phys. Rev. D 72 (2005) 095017, arXiv:hep-ph/0504096.
  * [51] D. Döring, H. Päs, P. Sicking, and T. J. Weiler Eur. Phys. J. C 80 no. 12, (2020) 1202, arXiv:1808.07460 [hep-ph].
  * [52] V. Kostelecky and M. Mewes Phys. Rev. D69 (2004) 016005, arXiv:hep-ph/0309025 [hep-ph].
  * [53] T. Katori et al. Phys. Rev. D74 (2006) 105009, arXiv:hep-ph/0606154 [hep-ph].
  * [54] J. S. Diaz and V. A. Kostelecky Phys. Lett. B 700 (2011) 25–28, arXiv:1012.5985 [hep-ph].
  * [55] J. Diaz and A. Kostelecky Phys. Rev. D85 (2012) 016013, arXiv:1108.1799 [hep-ph].
  * [56] S. Gninenko Phys. Rev. Lett. 103 (2009) 241802, arXiv:0902.3802 [hep-ph].
  * [57] S. N. Gninenko and D. S. Gorbunov Phys. Rev. D 81 (2010) 075013, arXiv:0907.4666 [hep-ph].
  * [58] Y. Bai, R. Lu, S. Lu, J. Salvado, and B. A. Stefanek Phys. Rev. D 93 no. 7, (2016) 073004, arXiv:1512.05357 [hep-ph].
  * [59] J. Liao and D. Marfatia Phys. Rev. Lett. 117 no. 7, (2016) 071802, arXiv:1602.08766 [hep-ph].
  * [60] M. Carena, Y.-Y. Li, C. S. Machado, P. A. N. Machado, and C. E. M. Wagner Phys. Rev. D 96 no. 9, (2017) 095014, arXiv:1708.09548 [hep-ph].
  * [61] Z. Moss, M. H. Moulai, C. A. Arg$\ddot{\rm u}$elles, and J. M. Conrad Phys. Rev. D97 no. 5, (2018) 055017, arXiv:1711.05921 [hep-ph].
  * [62] A. de Gouvêa, O. L. G. Peres, S. Prakash, and G. V. Stenico JHEP 07 (2020) 141, arXiv:1911.01447 [hep-ph].
  * [63] M. H. Moulai, C. A. Arg$\ddot{\rm u}$elles, G. H. Collin, J. M. Conrad, A. Diaz, and M. H. Shaevitz Phys. Rev. D 101 no. 5, (2020) 055020, arXiv:1910.13456 [hep-ph].
  * [64] M. Dentler, I. Esteban, J. Kopp, and P. Machado Phys. Rev. D 101 no. 11, (2020) 115013, arXiv:1911.01427 [hep-ph].
  * [65] E. Bertuzzo et al. Phys. Rev. Lett. 121 no. 24, (2018) 241801, arXiv:1807.09877 [hep-ph].
  * [66] P. Ballett, S. Pascoli, and M. Ross-Lonergan Phys. Rev. D99 (2019) 071701, arXiv:1808.02915 [hep-ph].
  * [67] O. Fischer, A. Hernández-Cabezudo, and T. Schwetz Phys. Rev. D 101 no. 7, (2020) 075045, arXiv:1909.09561 [hep-ph].
  * [68] A. Datta, S. Kamali, and D. Marfatia Phys. Lett. B 807 (2020) 135579, arXiv:2005.08920 [hep-ph].
  * [69] B. Dutta, S. Ghosh, and T. Li Phys. Rev. D 102 no. 5, (2020) 055017, arXiv:2006.01319 [hep-ph].
  * [70] W. Abdallah, R. Gandhi, and S. Roy JHEP 12 (2020) 188, arXiv:2006.01948 [hep-ph].
  * [71] A. Abdullahi, M. Hostert, and S. Pascoli Phys. Lett. B 820 (2021) 136531, arXiv:2007.11813 [hep-ph].
  * [72] V. Brdar, O. Fischer, and A. Y. Smirnov Phys. Rev. D 103 no. 7, (2021) 075008, arXiv:2007.14411 [hep-ph].
  * [73] W. Abdallah, R. Gandhi, and S. Roy Phys. Rev. D 104 no. 5, (2021) 055028, arXiv:2010.06159 [hep-ph].
  * [74] N. W. Kamp, M. Hostert, A. Schneider, S. Vergani, C. A. Arg$\ddot{\rm u}$elles, J. M. Conrad, M. H. Shaevitz, and M. A. Uchida arXiv:2206.07100 [hep-ph].
  * [75] B. Dutta, D. Kim, A. Thompson, R. T. Thornton, and R. G. Van de Water arXiv:2110.11944 [hep-ph].
  * [76] C. A. Arg$\ddot{\rm u}$elles, M. Hostert, and Y.-D. Tsai Phys. Rev. Lett. 123 no. 26, (2019) 261801, arXiv:1812.08768 [hep-ph].
  * [77] MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. Lett. 118 no. 22, (2017) 221803, arXiv:1702.02688 [hep-ex].
  * [78] A. Bhattarai, V. Brdar, B. Dutta, W. Jang, D. Kim, I. M. Shoemaker, Z. Tabrizi, A. Thompson, and J. Yu arXiv:2206.06380 [hep-ph].
  * [79] LSND Collaboration, A. Aguilar-Arevalo et al. Phys. Rev. D 64 (2001) 112007, arXiv:hep-ex/0104049.
  * [80] MINOS+ Collaboration, P. Adamson et al. Phys. Rev. Lett. 122 no. 9, (2019) 091803, arXiv:1710.06488 [hep-ex].
  * [81] IceCube Collaboration, M. G. Aartsen et al. Phys. Rev. D 102 no. 5, (2020) 052009, arXiv:2005.12943 [hep-ex].
  * [82] B. Dutta, D. Kim, S. Liao, J.-C. Park, S. Shin, and L. E. Strigari Phys. Rev. Lett. 124 no. 12, (2020) 121802, arXiv:1906.10745 [hep-ph].
  * [83] B. Dutta, D. Kim, S. Liao, J.-C. Park, S. Shin, L. E. Strigari, and A. Thompson JHEP 01 (2022) 144, arXiv:2006.09386 [hep-ph].
  * [84] Z. Chacko, H.-S. Goh, and R. Harnik Phys. Rev. Lett. 96 (2006) 231802, arXiv:hep-ph/0506256.
  * [85] B. Batell, M. Low, E. T. Neil, and C. B. Verhaaren in 2022 Snowmass Summer Study.  3, 2022.  arXiv:2203.05531 [hep-ph].
  * [86] P. W. Graham, D. E. Kaplan, and S. Rajendran Phys. Rev. Lett. 115 no. 22, (2015) 221801, arXiv:1504.07551 [hep-ph].
  * [87] T. Flacke, C. Frugiuele, E. Fuchs, R. S. Gupta, and G. Perez JHEP 06 (2017) 050, arXiv:1610.02025 [hep-ph].
  * [88] F. Bezrukov and D. Gorbunov JHEP 05 (2010) 010, arXiv:0912.0390 [hep-ph].
  * [89] E. K. Akhmedov, V. A. Rubakov, and A. Yu. Smirnov Phys. Rev. Lett. 81 (1998) 1359–1362, arXiv:hep-ph/9803255 [hep-ph].
  * [90] T. Asaka and M. Shaposhnikov Phys. Lett. B620 (2005) 17–26, arXiv:hep-ph/0505013 [hep-ph].
  * [91] G. Elor, M. Escudero, and A. Nelson Phys. Rev. D 99 no. 3, (2019) 035031, arXiv:1810.00880 [hep-ph].
  * [92] DUNE Collaboration, R. Acciarri et al. arXiv:1601.05471 [physics.ins-det].
  * [93] R. Acciarri and _et. al._ arXiv:1512.06148. http://arxiv.org/abs/1512.06148.
  * [94] A. De Roeck, D. Kim, Z. G. Moghaddam, J.-C. Park, S. Shin, and L. H. Whitehead JHEP 11 (2020) 043, arXiv:2005.08979 [hep-ph].
  * [95] D. Kim et al. Phys. Rev. Lett. 119 no. 16, (2017) 161801, arXiv:1612.06867 [hep-ph].
  * [96] T2K Collaboration, K. Abe et al. arXiv:1901.03750 [physics.ins-det].
  * [97] A. Korzenev, F. Barao, S. Bordoni, D. Breton, F. Cadoux, Y. Favre, M. Khabibullin, A. Khotyantsev, Y. Kudenko, T. Lux, J. Maalmi, P. Mermod, O. Mineev, and F. Sanchez Journal of Instrumentation 17 no. 01, (Jan, 2022) P01016. http://dx.doi.org/10.1088/1748-0221/17/01/P01016.
  * [98] J. Yu et al., Concept for a Neutral-Rich Three-Dimensional Sign-Selecting Focusing System, manuscript in preparation.
  * [99] CCM Collaboration, A. A. Aguilar-Arevalo et al. arXiv:2105.14020 [hep-ex].
  * [100] NOvA Collaboration, D. S. Ayres et al.
  * [101] DUNE Collaboration, “TDR Volume 1: The LBNF and DUNE Projects,” tech. rep., 2018.  http://docs.dunescience.org/cgi-bin/ShowDocument?docid=nnnn.
  * [102] DUNE Collaboration, A. Abed Abud et al. Instruments 5 no. 4, (2021) 31, arXiv:2103.13910 [physics.ins-det].
  * [103] T2K Collaboration, K. Abe et al. Nucl. Instrum. Meth. A 659 (2011) 106–135, arXiv:1106.1238 [physics.ins-det].
  * [104] Hyper-Kamiokande Collaboration, K. Abe et al. arXiv:1805.04163 [physics.ins-det].
  * [105] MicroBooNE, LAr1-ND, ICARUS-WA104 Collaboration, M. Antonello et al. arXiv:1503.01520 [physics.ins-det].
  * [106] S. Ajimura et al. arXiv:1705.08629 [physics.ins-det].
  * [107] S. Ajimura et al. arXiv:2012.10807 [hep-ex].
  * [108] A. A. Aguilar-Arevalo et al. arXiv:2109.14146 [hep-ex].
  * [109] CCM Collaboration, A. A. Aguilar-Arevalo et al. arXiv:2112.09979 [hep-ph].
  * [110] J. Alonso et al. arXiv:2111.09480 [hep-ex].
  * [111] J. R. Alonso et al. arXiv:2201.10040 [physics.ins-det].
  * [112] G. Fernandez Moroni, J. Estrada, E. E. Paolini, G. Cancelo, J. Tiffenberg, and J. Molina Phys. Rev. D 91 no. 7, (2015) 072001, arXiv:1405.5761 [physics.ins-det].
  * [113] CONNIE Collaboration, A. Aguilar-Arevalo et al. J. Phys. Conf. Ser. 761 no. 1, (2016) 012057, arXiv:1608.01565 [physics.ins-det].
  * [114] J. Hakenm$\ddot{\rm u}$ller et al. arXiv:1903.09269 [physics.ins-det].
  * [115] MINER Collaboration, G. Agnolet et al. Nucl. Instrum. Meth. A853 (2017) 53–60, arXiv:1609.02066 [physics.ins-det].
  * [116] J. B. Dent, B. Dutta, D. Kim, S. Liao, R. Mahapatra, K. Sinha, and A. Thompson Phys. Rev. Lett. 124 no. 21, (2020) 211804, arXiv:1912.05733 [hep-ph].
  * [117] NEON Collaboration, J. J. Choi, “The Neutrino Elastic-scattering Observation experiment with NaI[Tl] crystal (NEON).” https://indico.cern.ch/event/773605/contributions/3494452/attachments/1897629/3131255/NuFact_NEON_190827_v5.pdf, 2019\.
  * [118] R. Strauss et al. Eur. Phys. J. C 77 (2017) 506, arXiv:1704.04320 [physics.ins-det].
  * [119] V. Belov et al. JINST 10 no. 12, (2015) P12011.
  * [120] D. Y. Akimov et al. Instrum. Exp. Tech. 60 no. 2, (2017) 175–181.
  * [121] D. Y. Akimov et al. JINST 12 no. 06, (2017) C06018.
  * [122] J. Billard et al. J. Phys. G44 no. 10, (2017) 105101, arXiv:1612.09035 [physics.ins-det].
  * [123] SBC Collaboration, P. Giampa, “The Scintillating Bubble Chamber (SBC) Experiment For Dark Matter and Reactor CEvNS.” https://indico.cern.ch/event/868940/contributions/3814886/attachments/2080921/3495190/ICHEP2020_PietroGiampa.pdf, 2020\.
  * [124] D. Aristizabal Sierra, V. De Romeri, L. J. Flores, and D. K. Papoulias JHEP 03 (2021) 294, arXiv:2010.15712 [hep-ph].
  * [125] SoLid Collaboration, Y. Abreu et al. JINST 16 no. 02, (2021) P02025, arXiv:2002.05914 [physics.ins-det].
  * [126] H. T.-K. Wong The Universe 3 no. 4, (2015) 22–37, arXiv:1608.00306 [hep-ex].
  * [127] G. Fernandez-Moroni, P. A. N. Machado, I. Martinez-Soler, Y. F. Perez-Gonzalez, D. Rodrigues, and S. Rosauro-Alcaraz JHEP 03 (2021) 186, arXiv:2009.10741 [hep-ph].
  * [128] J. Colaresi, J. I. Collar, T. W. Hossbach, C. M. Lewis, and K. M. Yocum arXiv:2202.09672 [hep-ex].
  * [129] J.-F. Fortin, H.-K. Guo, S. P. Harris, D. Kim, K. Sinha, and C. Sun Int. J. Mod. Phys. D 30 no. 07, (2021) 2130002, arXiv:2102.12503 [hep-ph].
  * [130] R. Mammen Abraham et al.
  * [131] L. A. Anchordoqui et al. Phys. Rept. 968 (2022) 1–50, arXiv:2109.10905 [hep-ph].
  * [132] J. L. Feng et al. in 2022 Snowmass Summer Study.  3, 2022.  arXiv:2203.05090 [hep-ex].
  * [133] FASER Collaboration, A. Ariga et al. arXiv:1811.10243 [physics.ins-det].
  * [134] FASER Collaboration, A. Ariga et al. arXiv:1812.09139 [physics.ins-det].
  * [135] J. Feng et al. Phys. Rev. D97 no. 3, (2018) 035001, arXiv:1708.09389 [hep-ph].
  * [136] FASER Collaboration, A. Ariga et al. Phys. Rev. D 99 no. 9, (2019) 095011, arXiv:1811.12522 [hep-ph].
  * [137] J. Arakawa, J. L. Feng, A. Ismail, F. Kling, and M. Waterbury arXiv:2206.09932 [hep-ph].
  * [138] FASER Collaboration, H. Abreu et al. Eur. Phys. J. C 80 no. 1, (2020) 61, arXiv:1908.02310 [hep-ex].
  * [139] FASER Collaboration, H. Abreu et al. Phys. Rev. D 104 no. 9, (2021) L091101, arXiv:2105.06197 [hep-ex].
  * [140] V. Brdar, A. de Gouvêa, P. A. N. Machado, and R. Plestid arXiv:2112.03283 [hep-ph].
  * [141] FASER Collaboration, H. Abreu et al. arXiv:2001.03073 [physics.ins-det].
  * [142] FASER Collaboration, “FASER$\nu$ 2: A Forward Neutrino Experiment at the HL LHC.”  https://www.snowmass21.org/docs/files/summaries/NF/SNOWMASS21-NF10_NF6-EF6_EF9-IF0_FASERnu2-006.pdf.
  * [143] F. Kling and L. J. Nevay Phys. Rev. D 104 no. 11, (2021) 113008, arXiv:2105.08270 [hep-ph].
  * [144] SHiP Collaboration, C. Ahdida et al. arXiv:2002.08722 [physics.ins-det].
  * [145] B. Batell, J. L. Feng, and S. Trojanowski Phys. Rev. D 103 no. 7, (2021) 075023, arXiv:2101.10338 [hep-ph].
  * [146] F. Kling, J.-L. Kuo, S. Trojanowski, and Y.-D. Tsai arXiv:2205.09137 [hep-ph].
  * [147] S. Foroughi-Abari, F. Kling, and Y.-D. Tsai arXiv:2010.07941 [hep-ph].
  * [148] M. Toups et al. in 2022 Snowmass Summer Study.  3, 2022.  arXiv:2203.08079 [hep-ex].
  * [149] R. Ainsworth et al. arXiv:2106.02133 [physics.acc-ph].
  * [150] Hyper-Kamiokande Collaboration, K. Abe et al. PTEP 2018 no. 6, (2018) 063C01, arXiv:1611.06118 [hep-ex].
  * [151] Hyper-Kamiokande Collaboration, K. Abe et al. arXiv:1805.04163 [physics.ins-det].
  * [152] R. Catherall et al. Nucl. Instrum. Meth. B 317 (2013) 204–207.
  * [153] Facility for Rare Isotope Beams, https://frib.msu.edu.
  * [154] D. Jeon et al. J. Korean Phys. Soc. 65 no. 7, (2014) 1010–1019.
  * [155] V. Silveira and A. Zee Phys. Lett. B 161 (1985) 136–140.
  * [156] J. McDonald Phys. Rev. D 50 (1994) 3637–3649, arXiv:hep-ph/0702143.
  * [157] C. P. Burgess, M. Pospelov, and T. ter Veldhuis Nucl. Phys. B 619 (2001) 709–728, arXiv:hep-ph/0011335.
  * [158] M. Pospelov et al. Phys. Lett. B662 (2008) 53–61, arXiv:0711.4866 [hep-ph].
  * [159] G. Krnjaic Phys. Rev. D94 no. 7, (2016) 073009, arXiv:1512.04119 [hep-ph].
  * [160] S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy JHEP 08 (2007) 010, arXiv:0705.2425 [hep-ph].
  * [161] D. Croon, J. N. Howard, S. Ipek, and T. M. P. Tait Phys. Rev. D 101 no. 5, (2020) 055042, arXiv:1911.01432 [hep-ph].
  * [162] R. S. Willey and H. L. Yu Phys. Rev. D 26 (1982) 3086.
  * [163] H. Leutwyler and M. A. Shifman Nucl. Phys. B 343 (1990) 369–397.
  * [164] J. F. Gunion, H. E. Haber, G. L. Kane, and S. Dawson, vol. 80.  2000\.
  * [165] B. Batell, J. Berger, and A. Ismail arXiv:1909.11670 [hep-ph].
  * [166] S. Alekhin et al. Rept. Prog. Phys. 79 no. 12, (2016) 124201, arXiv:1504.04855 [hep-ph].
  * [167] I. Boiarska, K. Bondarenko, A. Boyarsky, V. Gorkavenko, M. Ovchynnikov, and A. Sokolenko JHEP 11 (2019) 162, arXiv:1904.10447 [hep-ph].
  * [168] S. Foroughi-Abari and A. Ritz Phys. Rev. D 105 no. 9, (2022) 095045, arXiv:2108.05900 [hep-ph].
  * [169] B. Batell, J. A. Evans, S. Gori, and M. Rai JHEP 05 (2021) 049, arXiv:2008.08108 [hep-ph].
  * [170] P. deNiverville et al. Phys. Rev. D86 (2012) 035022, arXiv:1205.3499 [hep-ph].
  * [171] M. B. Voloshin Sov. J. Nucl. Phys. 44 (1986) 478.
  * [172] J. F. Donoghue, J. Gasser, and H. Leutwyler Nucl. Phys. B 343 (1990) 341–368.
  * [173] M. W. Winkler Phys. Rev. D 99 no. 1, (2019) 015018, arXiv:1809.01876 [hep-ph].
  * [174] S. Foroughi-Abari and A. Ritz Phys. Rev. D 102 no. 3, (2020) 035015, arXiv:2004.14515 [hep-ph].
  * [175] CHARM Collaboration, F. Bergsma et al. Phys. Lett. B 157 (1985) 458–462.
  * [176] D. Egana-Ugrinovic, S. Homiller, and P. Meade Phys. Rev. Lett. 124 no. 19, (2020) 191801, arXiv:1911.10203 [hep-ph].
  * [177] E. Goudzovski et al. arXiv:2201.07805 [hep-ph].
  * [178] G. Bernardi et al. Phys. Lett. 166B (1986) 479–483.
  * [179] G. Bernardi et al. Phys. Lett. B203 (1988) 332–334.
  * [180] D. Gorbunov, I. Krasnov, and S. Suvorov Phys. Lett. B 820 (2021) 136524, arXiv:2105.11102 [hep-ph].
  * [181] LHCb Collaboration, R. Aaij et al. Phys. Rev. Lett. 115 no. 16, (2015) 161802, arXiv:1508.04094 [hep-ex].
  * [182] LHCb Collaboration, R. Aaij et al. Phys. Rev. D 95 no. 7, (2017) 071101, arXiv:1612.07818 [hep-ex].
  * [183] NA62 Collaboration, E. Cortina Gil et al. JHEP 06 (2021) 093, arXiv:2103.15389 [hep-ex].
  * [184] NA62 Collaboration, E. Cortina Gil et al. JHEP 03 (2021) 058, arXiv:2011.11329 [hep-ex].
  * [185] NA62 Collaboration, E. Cortina Gil et al. JHEP 02 (2021) 201, arXiv:2010.07644 [hep-ex].
  * [186] P. S. B. Dev, R. N. Mohapatra, and Y. Zhang JCAP 08 (2020) 003, arXiv:2005.00490 [hep-ph]. [Erratum: JCAP 11, E01 (2020)].
  * [187] J. M. Berryman, A. de Gouvea, P. J. Fox, B. J. Kayser, K. J. Kelly, and J. L. Raaf JHEP 02 (2020) 174, arXiv:1912.07622 [hep-ph].
  * [188] J. L. Feng, I. Galon, F. Kling, and S. Trojanowski Phys. Rev. D 97 no. 5, (2018) 055034, arXiv:1710.09387 [hep-ph].
  * [189] FASER Collaboration, A. Ariga et al. arXiv:1901.04468 [hep-ex].
  * [190] A. Kachanovich, U. Nierste, and I. Niˇsandžić arXiv:2003.01788 [hep-ph].
  * [191] A. Filimonova, R. Schäfer, and S. Westhoff Phys. Rev. D 101 no. 9, (2020) 095006, arXiv:1911.03490 [hep-ph].
  * [192] D. Craik, P. Ilten, D. Johnson, and M. Williams in 2022 Snowmass Summer Study.  3, 2022.  arXiv:2203.07048 [hep-ph].
  * [193] J. A. Evans, A. Gandrakota, S. Knapen, and H. Routray Phys. Rev. D 103 no. 1, (2021) 015026, arXiv:2008.06918 [hep-ph].
  * [194] J. L. Pinfold, “MAPP Phase-1 Technical Proposal,” tech. rep., CERN, Geneva, Nov, 2021.  https://cds.cern.ch/record/2791293.
  * [195] M. Staelens, “MoEDAL-MAPP – The Monopole and Exotics Detector at the LHC: Progress, Plans and Prospects,” 2022.  https://indico.cern.ch/event/1077282/contributions/4832639/attachments/2452184/4202216/MoEDAL%20—%20IPP%2050th%20Anniversary%20Symposium%20%28No%20Sequencing%29%20-%202022-05-26.pdf.
  * [196] G. Aielli et al. arXiv:2203.07316 [hep-ex].
  * [197] D. Curtin et al. arXiv:1806.07396 [hep-ph].
  * [198] G. Lanfranchi, “SHADOWS – Search for Hidden And Dark Objects With the SPS.” https://indico.cern.ch/event/1137723/contributions/4773516/attachments/2404601/4152201/shadows_SPSC_April2022_Lanfranchi.pdf, 2022\.
  * [199] LSND Collaboration, C. Athanassopoulos et al. Phys. Rev. C 58 (1998) 2489–2511, arXiv:nucl-ex/9706006.
  * [200] A. Berlin, S. Gori, P. Schuster, and N. Toro Phys. Rev. D 98 no. 3, (2018) 035011, arXiv:1804.00661 [hep-ph].
  * [201] J. o. Chang JHEP 01 (2017) 107, arXiv:1611.03864 [hep-ph].
  * [202] M. Pospelov Phys. Rev. D 80 (2009) 095002, arXiv:0811.1030 [hep-ph].
  * [203] Muon g-2 Collaboration, B. Abi et al. Phys. Rev. Lett. 126 no. 14, (2021) 141801, arXiv:2104.03281 [hep-ex].
  * [204] Muon g-2 Collaboration, G. W. Bennett et al. Phys. Rev. D 73 (2006) 072003, arXiv:hep-ex/0602035.
  * [205] T. Aoyama et al. Phys. Rept. 887 (2020) 1–166, arXiv:2006.04822 [hep-ph].
  * [206] S. Baek et al. Phys. Rev. D64 (2001) 055006, arXiv:hep-ph/0104141 [hep-ph].
  * [207] J. A. Dror, R. Lasenby, and M. Pospelov Phys. Rev. Lett. 119 no. 14, (2017) 141803, arXiv:1705.06726 [hep-ph].
  * [208] J. Heeck, M. Lindner, W. Rodejohann, and S. Vogl SciPost Phys. 6 no. 3, (2019) 038, arXiv:1812.04067 [hep-ph].
  * [209] F. Kling Phys. Rev. D 102 no. 1, (2020) 015007, arXiv:2005.03594 [hep-ph].
  * [210] B. Batell, J. L. Feng, M. Fieg, A. Ismail, F. Kling, R. M. Abraham, and S. Trojanowski Phys. Rev. D 105 no. 7, (2022) 075001, arXiv:2111.10343 [hep-ph].
  * [211] J. Blümlein and J. Brunner Phys. Lett. B 731 (2014) 320–326, arXiv:1311.3870 [hep-ph].
  * [212] D. Gorbunov, A. Makarov, and I. Timiryasov Phys. Rev. D 91 no. 3, (2015) 035027, arXiv:1411.4007 [hep-ph].
  * [213] Y.-D. Tsai, P. deNiverville, and M. X. Liu Phys. Rev. Lett. 126 no. 18, (2021) 181801, arXiv:1908.07525 [hep-ph].
  * [214] B. Batell et al. Phys. Rev. D80 (2009) 095024, arXiv:0906.5614 [hep-ph].
  * [215] A. de Gouvêa et al. JHEP 01 (2019) 001, arXiv:1809.06388 [hep-ph].
  * [216] E. Izaguirre, G. Krnjaic, P. Schuster, and N. Toro Phys. Rev. D 90 no. 1, (2014) 014052, arXiv:1403.6826 [hep-ph].
  * [217] E. Izaguirre et al. Phys. Rev. D96 no. 5, (2017) 055007, arXiv:1703.06881 [hep-ph].
  * [218] M. Dobroliubov and A. Yu. Ignatiev Phys. Rev. Lett. 65 (1990) 679–682.
  * [219] G. Magill et al. arXiv:1806.03310 [hep-ph].
  * [220] ArgoNeuT Collaboration, R. Acciarri et al. Phys. Rev. Lett. 124 no. 13, (2020) 131801, arXiv:1911.07996 [hep-ex].
  * [221] G. Marocco and S. Sarkar SciPost Phys. 10 no. 2, (2021) 043, arXiv:2011.08153 [hep-ph].
  * [222] R. Plestid, V. Takhistov, Y.-D. Tsai, T. Bringmann, A. Kusenko, and M. Pospelov arXiv:2002.11732 [hep-ph].
  * [223] D. Gorbunov, I. Krasnov, Y. Kudenko, and S. Suvorov Phys. Lett. B 822 (2021) 136641, arXiv:2103.11814 [hep-ph].
  * [224] R. Harnik, Z. Liu, and O. Palamara arXiv:1902.03246 [hep-ph].
  * [225] A. Haas, C. S. Hill, E. Izaguirre, and I. Yavin Phys. Lett. B746 (2015) 117–120, arXiv:1410.6816 [hep-ph].
  * [226] K. J. Kelly and Y.-D. Tsai Phys. Rev. D100 no. 1, (2019) 015043, arXiv:1812.03998 [hep-ph].
  * [227] S. Choi et al. arXiv:2007.06329 [physics.ins-det].
  * [228] P. Ilten, Y. Soreq, M. Williams, and W. Xue JHEP 06 (2018) 004, arXiv:1801.04847 [hep-ph].
  * [229] R. Essig et al. Phys. Rev. D82 (2010) 113008, arXiv:1008.0636 [hep-ph].
  * [230] Belle-II Collaboration, W. Altmannshofer et al. PTEP 2019 no. 12, (2019) 123C01, arXiv:1808.10567 [hep-ex]. [Erratum: PTEP 2020, 029201 (2020)].
  * [231] T. Ferber, C. Garcia-Cely, and K. Schmidt-Hoberg arXiv:2202.03452 [hep-ph].
  * [232] N. Baltzell et al. arXiv:2203.08324 [hep-ex].
  * [233] A. Berlin et al. arXiv:1807.01730 [hep-ph].
  * [234] R. Essig, P. Schuster, N. Toro, and B. Wojtsekhowski JHEP 02 (2011) 009, arXiv:1001.2557 [hep-ph].
  * [235] B. Echenard, R. Essig, and Y.-M. Zhong JHEP 01 (2015) 113, arXiv:1411.1770 [hep-ph].
  * [236] K. Pachal, “The DarkLight experiment at TRIUMF and the hunt for a new boson.” https://meetings.triumf.ca/event/269/contributions/3449/attachments/2635/3413/pachal_darklight_wnppc.pdf, 2019\.
  * [237] S. Cerci et al. arXiv:2201.00019 [hep-ex].
  * [238] REDTOP Collaboration, J. Elam et al. arXiv:2203.07651 [hep-ex].
  * [239] I. Galon, D. Shih, and I. R. Wang arXiv:2202.08843 [hep-ph].
  * [240] SHiP Collaboration, C. Ahdida et al. Eur. Phys. J. C 81 no. 5, (2021) 451, arXiv:2011.05115 [hep-ex].
  * [241] C. Cesarotti, S. Homiller, R. K. Mishra, and M. Reece arXiv:2202.12302 [hep-ph].
  * [242] J. L. Feng and J. Smolinsky Phys. Rev. D 96 no. 9, (2017) 095022, arXiv:1707.03835 [hep-ph].
  * [243] V. De Romeri et al. arXiv:1903.10505 [hep-ph].
  * [244] DUNE Collaboration, B. Abi et al. arXiv:2002.03005 [hep-ex].
  * [245] DUNE Collaboration, B. Abi et al. Eur. Phys. J. C 81 no. 4, (2021) 322, arXiv:2008.12769 [hep-ex].
  * [246] LDMX Collaboration, T. Åkesson et al. arXiv:1808.05219 [hep-ex].
  * [247] COHERENT Collaboration, D. Akimov et al. arXiv:2110.11453 [hep-ex].
  * [248] T. Hapitas, D. Tuckler, and Y. Zhang arXiv:2108.12440 [hep-ph].
  * [249] B. Batell, J. Berger, L. Darmé, and C. Frugiuele Phys. Rev. D 104 no. 7, (2021) 075026, arXiv:2106.04584 [hep-ph].
  * [250] J. Jordan et al. Phys. Rev. D98 no. 7, (2018) 075020, arXiv:1806.05185 [hep-ph].
  * [251] A. Berlin and F. Kling Phys. Rev. D 99 no. 1, (2019) 015021, arXiv:1810.01879 [hep-ph].
  * [252] A. Boyarsky, O. Mikulenko, M. Ovchynnikov, and L. Shchutska JHEP 03 (2022) 006, arXiv:2104.09688 [hep-ph].
  * [253] P. Schuster, N. Toro, and K. Zhou Phys. Rev. D 105 no. 3, (2022) 035036, arXiv:2112.02104 [hep-ph].
  * [254] G. Krnjaic et al. arXiv:2207.00597 [hep-ph].
  * [255] J. Orloff, A. N. Rozanov, and C. Santoni Phys. Lett. B 550 (2002) 8–15, arXiv:hep-ph/0208075.
  * [256] NOMAD Collaboration, P. Astier et al. Phys. Lett. B 506 (2001) 27–38, arXiv:hep-ex/0101041.
  * [257] T2K Collaboration, K. Abe et al. Phys. Rev. D 100 no. 5, (2019) 052006, arXiv:1902.07598 [hep-ex].
  * [258] C. A. Arg$\ddot{\rm u}$elles, N. Foppiani, and M. Hostert arXiv:2109.03831 [hep-ph].
  * [259] K. J. Kelly and P. A. N. Machado Phys. Rev. D 104 no. 5, (2021) 055015, arXiv:2106.06548 [hep-ph].
  * [260] A. Kusenko, S. Pascoli, and D. Semikoz JHEP 11 (2005) 028, arXiv:hep-ph/0405198.
  * [261] O. Ruchayskiy and A. Ivashko JHEP 06 (2012) 100, arXiv:1112.3319 [hep-ph].
  * [262] E949 Collaboration, A. V. Artamonov et al. Phys. Rev. D91 no. 5, (2015) 052001, arXiv:1411.3963 [hep-ex]. [Erratum: Phys. Rev.D91,no.5,059903(2015)].
  * [263] NA62 Collaboration, E. Cortina Gil et al. Phys. Lett. B 807 (2020) 135599, arXiv:2005.09575 [hep-ex].
  * [264] NA62 Collaboration, E. Cortina Gil et al. Phys. Lett. B 816 (2021) 136259, arXiv:2101.12304 [hep-ex].
  * [265] D. A. Bryman and R. Shrock Phys. Rev. D 100 (2019) 073011, arXiv:1909.11198 [hep-ph].
  * [266] A. de Gouvêa and A. Kobach Phys. Rev. D93 no. 3, (2016) 033005, arXiv:1511.00683 [hep-ph].
  * [267] R. S. Hayano et al. Phys. Rev. Lett. 49 (1982) 1305.
  * [268] DELPHI Collaboration, P. Abreu et al. Z. Phys. C74 (1997) 57–71. [Erratum: Z. Phys.C75,580(1997)].
  * [269] I. Boiarska, A. Boyarsky, O. Mikulenko, and M. Ovchynnikov Phys. Rev. D 104 no. 9, (2021) 095019, arXiv:2107.14685 [hep-ph].
  * [270] P. Ballett et al. JHEP 04 (2017) 102, arXiv:1610.08512 [hep-ph].
  * [271] P. Ballett, T. Boschi, and S. Pascoli arXiv:1905.00284 [hep-ph].
  * [272] P. Coloma, E. Fernández-Martínez, M. González-López, J. Hernández-García, and Z. Pavlovic Eur. Phys. J. C 81 no. 1, (2021) 78, arXiv:2007.03701 [hep-ph].
  * [273] F. Kling and S. Trojanowski arXiv:1801.08947 [hep-ph].
  * [274] A. Baha Balantekin and B. Kayser Ann. Rev. Nucl. Part. Sci. 68 (2018) 313–338, arXiv:1805.00922 [hep-ph].
  * [275] A. B. Balantekin, A. de Gouvêa, and B. Kayser Phys. Lett. B789 (2019) 488–495, arXiv:1808.10518 [hep-ph].
  * [276] A. de Gouvêa, P. J. Fox, B. J. Kayser, and K. J. Kelly Phys. Rev. D 104 no. 1, (2021) 015038, arXiv:2104.05719 [hep-ph].
  * [277] A. de Gouvêa, P. J. Fox, B. J. Kayser, and K. J. Kelly arXiv:2109.10358 [hep-ph].
  * [278] P. Ballett, M. Hostert, and S. Pascoli arXiv:1903.07589 [hep-ph].
  * [279] K. Kelly and Y. Zhang Phys. Rev. D99 no. 5, (2019) 055034, arXiv:1901.01259 [hep-ph].
  * [280] A. De Gouvêa, M. Sen, W. Tangarife, and Y. Zhang Phys. Rev. Lett. 124 no. 8, (2020) 081802, arXiv:1910.04901 [hep-ph].
  * [281] J. M. Berryman et al. in 2022 Snowmass Summer Study.  3, 2022.  arXiv:2203.01955 [hep-ph].
  * [282] K. J. Kelly, F. Kling, D. Tuckler, and Y. Zhang arXiv:2111.05868 [hep-ph].
  * [283] I. Esteban, S. Pandey, V. Brdar, and J. F. Beacom Phys. Rev. D 104 no. 12, (2021) 123014, arXiv:2107.13568 [hep-ph].
  * [284] B. Bertoni et al. JHEP 04 (2015) 170, arXiv:1412.3113 [hep-ph].
  * [285] B. Batell, T. Han, and B. Shams Es Haghi Phys. Rev. D 97 no. 9, (2018) 095020, arXiv:1704.08708 [hep-ph].
  * [286] B. Batell et al. Phys. Rev. D97 no. 7, (2018) 075016, arXiv:1709.07001 [hep-ph].
  * [287] A. De Gouvêa, K. J. Kelly, G. V. Stenico, and P. Pasquini Phys. Rev. D 100 no. 1, (2019) 016004, arXiv:1904.07265 [hep-ph].
  * [288] A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell Phys. Rev. D 81 (2010) 123530, arXiv:0905.4720 [hep-th].
  * [289] M. Cicoli, M. Goodsell, and A. Ringwald JHEP 10 (2012) 146, arXiv:1206.0819 [hep-th].
  * [290] J.-C. Park and S. C. Park Phys. Dark Univ. 14 (2016) 4–10, arXiv:1512.08117 [hep-ph].
  * [291] K. J. Kelly, S. Kumar, and Z. Liu Phys. Rev. D 103 no. 9, (2021) 095002, arXiv:2011.05995 [hep-ph].
  * [292] V. Brdar, B. Dutta, W. Jang, D. Kim, I. M. Shoemaker, Z. Tabrizi, A. Thompson, and J. Yu arXiv:2011.07054 [hep-ph].
  * [293] W. M. Bonivento, D. Kim, and K. Sinha Eur. Phys. J. C 80 no. 2, (2020) 164, arXiv:1909.03071 [hep-ph].
  * [294] P. S. B. Dev, D. Kim, K. Sinha, and Y. Zhang Phys. Rev. D 104 no. 3, (2021) 035037, arXiv:2101.08781 [hep-ph].
  * [295] I. G. Irastorza and J. Redondo Prog. Part. Nucl. Phys. 102 (2018) 89–159, arXiv:1801.08127 [hep-ph].
  * [296] OPAL Collaboration, G. Abbiendi et al. Eur. Phys. J. C 18 (2000) 253–272, arXiv:hep-ex/0005002.
  * [297] ALEPH Collaboration, A. Heister et al. Eur. Phys. J. C 28 (2003) 437–449, arXiv:hep-ex/0301034.
  * [298] L3 Collaboration, P. Achard et al. Phys. Lett. B 587 (2004) 16–32, arXiv:hep-ex/0402002.
  * [299] DELPHI Collaboration, J. Abdallah et al. Eur. Phys. J. C 38 (2005) 395–411, arXiv:hep-ex/0406019.
  * [300] J. L. Hewett et al. 5, 2012.  arXiv:1205.2671 [hep-ex].
  * [301] Belle-II Collaboration, F. Abudinén et al. Phys. Rev. Lett. 125 no. 16, (2020) 161806, arXiv:2007.13071 [hep-ex].
  * [302] CHARM Collaboration, F. Bergsma et al. Phys. Lett. B 157 (1985) 458–462.
  * [303] J. Bjorken et al. Phys. Rev. D38 (1988) 3375.
  * [304] E. M. Riordan et al. Phys. Rev. Lett. 59 (1987) 755.
  * [305] OPAL Collaboration, G. Abbiendi et al. Eur. Phys. J. C 26 (2003) 331–344, arXiv:hep-ex/0210016.
  * [306] CMS Collaboration, A. M. Sirunyan et al. Phys. Lett. B 797 (2019) 134826, arXiv:1810.04602 [hep-ex].
  * [307] ATLAS Collaboration, G. Aad et al. JHEP 11 (2021) 050, arXiv:2008.05355 [hep-ex].
  * [308] NA64 Collaboration, D. Banerjee et al. Phys. Rev. Lett. 125 no. 8, (2020) 081801, arXiv:2005.02710 [hep-ex].
  * [309] J. Blumlein et al. Z. Phys. C 51 (1991) 341–350.
  * [310] D. Aloni, C. Fanelli, Y. Soreq, and M. Williams Phys. Rev. Lett. 123 no. 7, (2019) 071801, arXiv:1903.03586 [hep-ph].
  * [311] M. Bauer, M. Heiles, M. Neubert, and A. Thamm Eur. Phys. J. C 79 no. 1, (2019) 74, arXiv:1808.10323 [hep-ph].
  * [312] PIP-II Collaboration, 2022.  (to appear).
  * [313] M. J. Dolan, T. Ferber, C. Hearty, F. Kahlhoefer, and K. Schmidt-Hoberg JHEP 12 (2017) 094, arXiv:1709.00009 [hep-ph]. [Erratum: JHEP 03, 190 (2021)].
  * [314] S. Knapen, T. Lin, H. K. Lou, and T. Melia Phys. Rev. Lett. 118 no. 17, (2017) 171801, arXiv:1607.06083 [hep-ph].
  * [315] B. Döbrich, J. Jaeckel, and T. Spadaro JHEP 05 (2019) 213, arXiv:1904.02091 [hep-ph]. [Erratum: JHEP 10, 046 (2020)].
  * [316] R. R. Dusaev, D. V. Kirpichnikov, and M. M. Kirsanov Phys. Rev. D 102 no. 5, (2020) 055018, arXiv:2004.04469 [hep-ph].
  * [317] CLEO Collaboration, R. Balest et al. Phys. Rev. D 51 (1995) 2053–2060.
  * [318] BaBar Collaboration, P. del Amo Sanchez et al. Phys. Rev. Lett. 107 (2011) 021804, arXiv:1007.4646 [hep-ex].
  * [319] J. Redondo and A. Ringwald Contemp. Phys. 52 (2011) 211–236, arXiv:1011.3741 [hep-ph].
  * [320] NOMAD Collaboration, P. Astier et al. Phys. Lett. B 479 (2000) 371–380.
  * [321] L. Waites, A. Conrad, J.and Bungau, B. Dutta, W.-C. Huang, D. Kim, M. Shaevitz, J. Sptz, and A. Thompson, “Axion-like particle production at the isodar experiment,” 2022.  (to appear).
  * [322] F. Kling and P. Quílez arXiv:2204.03599 [hep-ph].
  * [323] BaBar Collaboration, J. P. Lees et al. Phys. Rev. D 94 no. 1, (2016) 011102, arXiv:1606.03501 [hep-ex].
  * [324] M. Bauer, M. Neubert, and A. Thamm JHEP 12 (2017) 044, arXiv:1708.00443 [hep-ph].
  * [325] S. Andreas, O. Lebedev, S. Ramos-Sanchez, and A. Ringwald JHEP 08 (2010) 003, arXiv:1005.3978 [hep-ph].
  * [326] A. Bross, M. Crisler, S. H. Pordes, J. Volk, S. Errede, and J. Wrbanek Phys. Rev. Lett. 67 (1991) 2942–2945.
  * [327] NA64 Collaboration, Y. M. Andreev et al. Phys. Rev. D 104 no. 11, (2021) L111102, arXiv:2104.13342 [hep-ex].
  * [328] Y. M. Andreev et al. Phys. Rev. D 104 no. 9, (2021) L091701, arXiv:2108.04195 [hep-ex].
  * [329] S. N. Gninenko, D. V. Kirpichnikov, M. M. Kirsanov, and N. V. Krasnikov Phys. Lett. B 782 (2018) 406–411, arXiv:1712.05706 [hep-ph].
  * [330] D. J. Bechis, T. W. Dombeck, R. W. Ellsworth, E. V. Sager, P. H. Steinberg, L. J. Teig, J. K. Yoh, and R. L. Weitz Phys. Rev. Lett. 42 (1979) 1511. [Erratum: Phys.Rev.Lett. 43, 90 (1979)].
  * [331] E. Hardy and R. Lasenby JHEP 02 (2017) 033, arXiv:1611.05852 [hep-ph].
  * [332] G. Lucente and P. Carenza Phys. Rev. D 104 no. 10, (2021) 103007, arXiv:2107.12393 [hep-ph].
  * [333] M. Smirnov, G. Yang, J. Liao, Z. Hu, and J. Ling Phys. Rev. D 104 (Dec, 2021) 116024. https://link.aps.org/doi/10.1103/PhysRevD.104.116024.
  * [334] TEXONO Collaboration, H. M. Chang et al. Phys. Rev. D 75 (2007) 052004, arXiv:hep-ex/0609001.
  * [335] Borexino Collaboration, G. Bellini et al. Eur. Phys. J. C 54 (2008) 61–72.
  * [336] Borexino Collaboration, G. Bellini et al. Phys. Rev. D 85 (2012) 092003, arXiv:1203.6258 [hep-ex].
  * [337] J. S. Lee arXiv:1808.10136 [hep-ph].
  * [338] D. Gorbunov and M. Shaposhnikov JHEP 10 (2007) 015, arXiv:0705.1729 [hep-ph]. [Erratum: JHEP11,101(2013)].
  * [339] G. Magill et al. Phys. Rev. D98 no. 11, (2018) 115015, arXiv:1803.03262 [hep-ph].
  * [340] LSND Collaboration, C. Athanassopoulos et al. Nucl. Instrum. Meth. A388 (1997) 149–172, arXiv:nucl-ex/9605002 [nucl-ex].
  * [341] M. Pospelov and Y. Tsai Phys. Lett. B785 (2018) 288–295, arXiv:1706.00424 [hep-ph].
  * [342] MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al. Phys. Rev. Lett. 98 (2007) 231801, arXiv:0704.1500 [hep-ex].
  * [343] LAr1-ND, ICARUS-WA104, MicroBooNE Collaboration, M. Antonello et al. arXiv:1503.01520 [physics.ins-det].
  * [344] S. Gninenko Phys. Rev. D83 (2011) 015015, arXiv:1009.5536 [hep-ph].
  * [345] D. McKeen and M. Pospelov Phys. Rev. D82 (2010) 113018, arXiv:1011.3046 [hep-ph].
  * [346] S. Gninenko Phys. Lett. B710 (2012) 86–90, arXiv:1201.5194 [hep-ph].
  * [347] K. Jodłowski and S. Trojanowski JHEP 05 (2021) 191, arXiv:2011.04751 [hep-ph].
  * [348] A. Ismail, S. Jana, and R. M. Abraham Phys. Rev. D 105 no. 5, (2022) 055008, arXiv:2109.05032 [hep-ph].
  * [349] I. M. Shoemaker, Y.-D. Tsai, and J. Wyenberg Phys. Rev. D 104 no. 11, (2021) 115026, arXiv:2007.05513 [hep-ph].
  * [350] V. Brdar, A. Greljo, J. Kopp, and T. Opferkuch JCAP 01 (2021) 039, arXiv:2007.15563 [hep-ph].
  * [351] E. Bertuzzo et al. Phys. Lett. B791 (2019) 210–214, arXiv:1808.02500 [hep-ph].
  * [352] P. Ballett, M. Hostert, and S. Pascoli Phys. Rev. D99 no. 9, (2019) 091701, arXiv:1903.07590 [hep-ph].
  * [353] M. Berbig, S. Jana, and A. Trautner Phys. Rev. D 102 no. 11, (2020) 115008, arXiv:2004.13039 [hep-ph].
  * [354] N. Schöneberg, G. Franco Abellán, A. Pérez Sánchez, S. J. Witte, V. Poulin, and J. Lesgourgues arXiv:2107.10291 [astro-ph.CO].
  * [355] M. Archidiacono, S. Gariazzo, C. Giunti, S. Hannestad, and T. Tram JCAP 12 (2020) 029, arXiv:2006.12885 [astro-ph.CO].
  * [356] A. Bally, S. Jana, and A. Trautner Phys. Rev. Lett. 125 no. 16, (2020) 161802, arXiv:2006.11919 [hep-ph].
  * [357] D. Freedman Phys. Rev. D9 (1974) 1389–1392.
  * [358] V. B. Kopeliovich and L. L. Frankfurt JETP Lett. 19 (1974) 145–147.
  * [359] COHERENT Collaboration, D. Akimov et al. Science 357 no. 6356, (2017) 1123–1126, arXiv:1708.01294 [nucl-ex].
  * [360] COHERENT Collaboration, D. Akimov et al. arXiv:1804.09459 [nucl-ex].
  * [361] COHERENT Collaboration, D. Akimov et al. Phys. Rev. Lett. 126 no. 1, (2021) 012002, arXiv:2003.10630 [nucl-ex].
  * [362] D. Akimov et al. arXiv:2110.07730 [hep-ex].
  * [363] J. Barranco, O. G. Miranda, and T. I. Rashba JHEP 12 (2005) 021, arXiv:hep-ph/0508299.
  * [364] D. K. Papoulias, T. S. Kosmas, and Y. Kuno Front. in Phys. 7 (2019) 191, arXiv:1911.00916 [hep-ph].
  * [365] Y. Farzan and M. Tortola Front.in Phys. 6 (2018) 10, arXiv:1710.09360 [hep-ph].
  * [366] P. S. Bhupal Dev et al. vol. 2, p. 001.  2019\.  arXiv:1907.00991 [hep-ph].
  * [367] D. K. Papoulias and T. S. Kosmas Phys. Rev. D 97 no. 3, (2018) 033003, arXiv:1711.09773 [hep-ph].
  * [368] P. Coloma et al. Phys. Rev. D96 no. 11, (2017) 115007, arXiv:1708.02899 [hep-ph].
  * [369] J. Liao and D. Marfatia Phys. Lett. B775 (2017) 54–57, arXiv:1708.04255 [hep-ph].
  * [370] P. Coloma et al. JHEP 04 (2017) 116, arXiv:1701.04828 [hep-ph].
  * [371] P. Denton et al. JHEP 07 (2018) 037, arXiv:1804.03660 [hep-ph].
  * [372] J. Dent et al. Phys. Rev. D97 no. 3, (2018) 035009, arXiv:1711.03521 [hep-ph].
  * [373] M. Abdullah et al. Phys. Rev. D98 no. 1, (2018) 015005, arXiv:1803.01224 [hep-ph].
  * [374] B. Dutta, S. Liao, S. Sinha, and L. E. Strigari arXiv:1903.10666 [hep-ph].
  * [375] P. Coloma, I. Esteban, M. C. Gonzalez-Garcia, and M. Maltoni JHEP 02 (2020) 023, arXiv:1911.09109 [hep-ph]. [Addendum: JHEP 12, 071 (2020)].
  * [376] O. G. Miranda, D. K. Papoulias, G. Sanchez Garcia, O. Sanders, M. Tórtola, and J. W. F. Valle JHEP 05 (2020) 130, arXiv:2003.12050 [hep-ph]. [Erratum: JHEP 01, 067 (2021)].
  * [377] O. Miranda et al. JHEP 10 (2006) 008, arXiv:hep-ph/0406280 [hep-ph].
  * [378] F. J. Escrihuela, O. G. Miranda, M. A. Tortola, and J. W. F. Valle Phys. Rev. D 80 (2009) 105009, arXiv:0907.2630 [hep-ph]. [Erratum: Phys.Rev.D 80, 129908 (2009)].
  * [379] M. C. Gonzalez-Garcia and M. Maltoni JHEP 09 (2013) 152, arXiv:1307.3092 [hep-ph].
  * [380] M. Lindner et al. JHEP 03 (2017) 097, arXiv:1612.04150 [hep-ph].
  * [381] D. Aristizabal Sierra et al. Phys. Rev. D98 (2018) 075018, arXiv:1806.07424 [hep-ph].
  * [382] L. J. Flores, N. Nath, and E. Peinado Phys. Rev. D 105 no. 5, (2022) 055010, arXiv:2112.05103 [hep-ph].
  * [383] CHARM Collaboration, J. Dorenbosch et al. Phys. Lett. B 180 (1986) 303–307.
  * [384] TEXONO Collaboration, H. T. Wong Mod. Phys. Lett. A 19 (2004) 1207–1214.
  * [385] CONUS Collaboration, H. Bonet et al. Phys. Rev. Lett. 126 no. 4, (2021) 041804, arXiv:2011.00210 [hep-ex].
  * [386] MINER Collaboration, G. Agnolet et al. Nucl. Instrum. Meth. A 853 (2017) 53–60, arXiv:1609.02066 [physics.ins-det].
  * [387] RED-100 Collaboration, D. Y. Akimov et al. JINST 15 no. 02, (2020) P02020, arXiv:1910.06190 [physics.ins-det].
  * [388] J. J. Choi PoS NuFact2019 (2020) 047.
  * [389] P. Coloma, I. Esteban, M. C. Gonzalez-Garcia, L. Larizgoitia, F. Monrabal, and S. Palomares-Ruiz arXiv:2202.10829 [hep-ph].
  * [390] D. Aristizabal Sierra, V. De Romeri, and D. K. Papoulias arXiv:2203.02414 [hep-ph].
  * [391] J. Liao, H. Liu, and D. Marfatia arXiv:2202.10622 [hep-ph].
  * [392] M. Atzori Corona, M. Cadeddu, N. Cargioli, F. Dordei, C. Giunti, Y. F. Li, C. A. Ternes, and Y. Y. Zhang arXiv:2205.09484 [hep-ph].
  * [393] J. Billard, J. Johnston, and B. J. Kavanagh JCAP 11 (2018) 016, arXiv:1805.01798 [hep-ph].
  * [394] D. Aristizabal Sierra, V. De Romeri, and N. Rojas JHEP 09 (2019) 069, arXiv:1906.01156 [hep-ph].
  * [395] B. Dutta, R. Mahapatra, L. E. Strigari, and J. W. Walker Phys. Rev. D 93 no. 1, (2016) 013015, arXiv:1508.07981 [hep-ph].
  * [396] J. B. Dent, B. Dutta, S. Liao, J. L. Newstead, L. E. Strigari, and J. W. Walker Phys. Rev. D 96 no. 9, (2017) 095007, arXiv:1612.06350 [hep-ph].
  * [397] M. Cadeddu, N. Cargioli, F. Dordei, C. Giunti, Y. F. Li, E. Picciau, and Y. Y. Zhang JHEP 01 (2021) 116, arXiv:2008.05022 [hep-ph].
  * [398] B. Dutta, S. Ghosh, and J. Kumar Phys. Rev. D 102 no. 7, (2020) 075041, arXiv:2007.16191 [hep-ph].
  * [399] O. G. Miranda, D. K. Papoulias, M. Tórtola, and J. W. F. Valle Phys. Rev. D 101 no. 7, (2020) 073005, arXiv:2002.01482 [hep-ph].
  * [400] H. Banerjee, B. Dutta, and S. Roy Phys. Rev. D 104 no. 1, (2021) 015015, arXiv:2103.10196 [hep-ph].
  * [401] M. Atzori Corona, M. Cadeddu, N. Cargioli, F. Dordei, C. Giunti, Y. F. Li, E. Picciau, C. A. Ternes, and Y. Y. Zhang JHEP 05 (2022) 109, arXiv:2202.11002 [hep-ph].
  * [402] M. Abdullah, D. Aristizabal Sierra, B. Dutta, and L. E. Strigari Phys. Rev. D 102 no. 1, (2020) 015009, arXiv:2003.11510 [hep-ph].
  * [403] A. J. Anderson, J. M. Conrad, E. Figueroa-Feliciano, C. Ignarra, G. Karagiorgi, K. Scholberg, M. H. Shaevitz, and J. Spitz Phys. Rev. D 86 (2012) 013004, arXiv:1201.3805 [hep-ph].
  * [404] C. Blanco, D. Hooper, and P. Machado Phys. Rev. D 101 no. 7, (2020) 075051, arXiv:1901.08094 [hep-ph].
  * [405] O. G. Miranda, D. K. Papoulias, O. Sanders, M. Tórtola, and J. W. F. Valle Phys. Rev. D 102 (2020) 113014, arXiv:2008.02759 [hep-ph].
  * [406] B. Dutta, Y. Gao, R. Mahapatra, N. Mirabolfathi, L. E. Strigari, and J. W. Walker Phys. Rev. D 94 no. 9, (2016) 093002, arXiv:1511.02834 [hep-ph].
  * [407] P. deNiverville et al. Phys. Rev. D92 no. 9, (2015) 095005, arXiv:1505.07805 [hep-ph].
  * [408] COHERENT Collaboration, D. Akimov et al. Phys. Rev. D 102 no. 5, (2020) 052007, arXiv:1911.06422 [hep-ex].
  * [409] BaBar Collaboration, J. Lees et al. Phys. Rev. Lett. 119 no. 13, (2017) 131804, arXiv:1702.03327 [hep-ex].
  * [410] MiniBooNE DM Collaboration, A. Aguilar-Arevalo et al. arXiv:1807.06137 [hep-ex].
  * [411] D. Banerjee et al. Phys. Rev. Lett. 123 no. 12, (2019) 121801, arXiv:1906.00176 [hep-ex].
  * [412] C. collaboration (2021(to appear)) .
  * [413] GEANT4 Collaboration, S. Agostinelli et al. Nucl. Instrum. Meth. A506 (2003) 250–303.
  * [414] P. Carenza, O. Straniero, B. Döbrich, M. Giannotti, G. Lucente, and A. Mirizzi Phys. Lett. B 809 (2020) 135709, arXiv:2004.08399 [hep-ph].
  * [415] P. F. Depta, M. Hufnagel, and K. Schmidt-Hoberg JCAP 05 (2020) 009, arXiv:2002.08370 [hep-ph].
  * [416] L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli Phys. Rept. 870 (2020) 1–117, arXiv:2003.01100 [hep-ph].
  * [417] J. Jaeckel, E. Masso, J. Redondo, A. Ringwald, and F. Takahashi Phys. Rev. D 75 (2007) 013004, arXiv:hep-ph/0610203 [hep-ph].
  * [418] J. Khoury and A. Weltman Phys. Rev. Lett. 93 (2004) 171104, arXiv:astro-ph/0309300 [astro-ph].
  * [419] E. Masso and J. Redondo JCAP 0509 (2005) 015, arXiv:hep-ph/0504202 [hep-ph].
  * [420] E. Masso and J. Redondo Phys. Rev. Lett. 97 (2006) 151802, arXiv:hep-ph/0606163 [hep-ph].
  * [421] A. Dupays, E. Masso, J. Redondo, and C. Rizzo Phys. Rev. Lett. 98 (2007) 131802, arXiv:hep-ph/0610286 [hep-ph].
  * [422] R. N. Mohapatra and S. Nasri Phys. Rev. Lett. 98 (2007) 050402, arXiv:hep-ph/0610068 [hep-ph].
  * [423] P. Brax, C. van de Bruck, and A.-C. Davis Phys. Rev. Lett. 99 (2007) 121103, arXiv:hep-ph/0703243 [HEP-PH].
  * [424] W. DeRocco, P. W. Graham, and S. Rajendran arXiv:2006.15112 [hep-ph].
  * [425] F. T. Avignone, C. Baktash, W. C. Barker, F. P. Calaprice, R. W. Dunford, W. C. Haxton, D. Kahana, R. T. Kouzes, H. S. Miley, and D. M. Moltz Phys. Rev. D 37 (1988) 618–630.
  * [426] J. L. Feng, B. Fornal, I. Galon, S. Gardner, J. Smolinsky, T. M. P. Tait, and P. Tanedo Phys. Rev. D 95 no. 3, (2017) 035017, arXiv:1608.03591 [hep-ph].
  * [427] J. B. Dent et al. Phys. Rev. D 105 no. 1, (2022) 015030, arXiv:2105.07007 [hep-ph].
  * [428] A. Datta, B. Dutta, S. Liao, D. Marfatia, and L. E. Strigari JHEP 01 (2019) 091, arXiv:1808.02611 [hep-ph].
  * [429] D. Aristizabal Sierra, B. Dutta, S. Liao, and L. E. Strigari JHEP 12 (2019) 124, arXiv:1910.12437 [hep-ph].
  * [430] C. Bœhm, D. G. Cerdeño, P. A. N. Machado, A. Olivares-Del Campo, E. Perdomo, and E. Reid JCAP 01 (2019) 043, arXiv:1809.06385 [hep-ph].
  * [431] M. Escudero JCAP 02 (2019) 007, arXiv:1812.05605 [hep-ph].
  * [432] D. Aristizabal Sierra, V. De Romeri, L. J. Flores, and D. K. Papoulias JCAP 01 no. 01, (2022) 055, arXiv:2109.03247 [hep-ph].
  * [433] A. J. Krasznahorkay et al. Phys. Rev. Lett. 116 no. 4, (2016) 042501, arXiv:1504.01527 [nucl-ex].
  * [434] J. Gulyás, T. J. Ketel, A. J. Krasznahorkay, M. Csatlós, L. Csige, Z. Gácsi, M. Hunyadi, A. Krasznahorkay, A. Vitéz, and T. G. Tornyi Nucl. Instrum. Meth. A 808 (2016) 21–28, arXiv:1504.00489 [nucl-ex].
  * [435] A. Aleksejevs, S. Barkanova, Y. G. Kolomensky, and B. Sheff arXiv:2102.01127 [hep-ph].
  * [436] L. Delle Rose, S. Khalil, S. J. D. King, and S. Moretti Front. in Phys. 7 (2019) 73, arXiv:1812.05497 [hep-ph].
  * [437] PROSPECT Collaboration, J. Ashenfelter et al. Phys. Rev. Lett. 122 no. 25, (2019) 251801, arXiv:1812.10877 [nucl-ex].
  * [438] STEREO Collaboration Collaboration, H. Almazán et al. Phys. Rev. D 102 (Sep, 2020) 052002. https://link.aps.org/doi/10.1103/PhysRevD.102.052002.
  * [439] NEOS Collaboration, Y. J. Ko et al. Phys. Rev. Lett. 118 no. 12, (2017) 121802, arXiv:1610.05134 [hep-ex].
  * [440] RENO Collaboration Collaboration, J. H. Choi et al. Phys. Rev. Lett. 116 (May, 2016) 211801. https://link.aps.org/doi/10.1103/PhysRevLett.116.211801.
  * [441] Daya Bay Collaboration Collaboration, F. P. An et al. Phys. Rev. Lett. 116 (Feb, 2016) 061801. https://link.aps.org/doi/10.1103/PhysRevLett.116.061801.
  * [442] Double Chooz Collaboration, Y. Abe et al. JHEP 01 (2016) 163, arXiv:1510.08937 [hep-ex].
  * [443] V. A. Bednyakov and D. V. Naumov Phys. Rev. D 98 no. 5, (2018) 053004, arXiv:1806.08768 [hep-ph].
  * [444] P. Pirinen, J. Suhonen, and E. Ydrefors Adv. High Energy Phys. 2018 (2018) 9163586, arXiv:1804.08995 [nucl-th].
  * [445] V. A. Bednyakov and D. V. Naumov Phys. Part. Nucl. Lett. 16 no. 6, (2019) 638–646, arXiv:1904.03119 [hep-ph].
  * [446] R. Sahu, D. K. Papoulias, V. K. B. Kota, and T. S. Kosmas Phys. Rev. C 102 no. 3, (2020) 035501, arXiv:2004.04055 [nucl-th].
  * [447] N. Van Dessel, V. Pandey, H. Ray, and N. Jachowicz arXiv:2007.03658 [nucl-th].
  * [448] V. A. Bednyakov and D. V. Naumov Phys. Rev. D 98 (Sep, 2018) 053004. https://link.aps.org/doi/10.1103/PhysRevD.98.053004.
  * [449] B. Dutta, W.-C. Huang, J. L. Newstead, and V. Pandey arXiv:2206.08590 [hep-ph].
  * [450] C. W. Johnson, W. E. Ormand, K. S. McElvain, and H. Shan arXiv:1801.08432 [physics.comp-ph].
  * [451] C. W. Johnson, W. E. Ormand, and P. G. Krastev Comput. Phys. Commun. 184 (2013) 2761–2774, arXiv:1303.0905 [nucl-th].
  * [452] W. Czyz et al. Nuovo Cim. 34 (1964) 404–435.
  * [453] K. Fujikawa Annals Phys. 68 (1971) 102–162.
  * [454] J. Lovseth and M. Radomiski Phys. Rev. D3 (1971) 2686–2706.
  * [455] K. Koike et al. Prog. Theor. Phys. 46 (1971) 1150–1169.
  * [456] K. Koike et al. Prog. Theor. Phys. 46 (1971) 1799–1804.
  * [457] R. W. Brown, R. H. Hobbs, J. Smith, and N. Stanko Phys. Rev. D 6 (1972) 3273–3292.
  * [458] CHARM-II Collaboration, D. Geiregat et al. Phys. Lett. B 245 (1990) 271–275.
  * [459] CCFR Collaboration, S. R. Mishra et al. Phys. Rev. Lett. 66 (1991) 3117–3120.
  * [460] NuTeV Collaboration, T. Adams et al. in 29th International Conference on High-Energy Physics, pp. 631–634.  7, 1998.  arXiv:hep-ex/9811012.
  * [461] NuTeV Collaboration, T. Adams et al. Phys. Rev. D 61 (2000) 092001, arXiv:hep-ex/9909041.
  * [462] W. Altmannshofer et al. Phys. Rev. Lett. 113 (2014) 091801, arXiv:1406.2332 [hep-ph].
  * [463] Y. Kaneta and T. Shimomura PTEP 2017 no. 5, (2017) 053B04, arXiv:1701.00156 [hep-ph].
  * [464] P. Ballett, M. Hostert, S. Pascoli, Y. F. Perez-Gonzalez, Z. Tabrizi, and R. Zukanovich Funchal JHEP 01 (2019) 119, arXiv:1807.10973 [hep-ph].
  * [465] W. Altmannshofer et al. arXiv:1902.06765 [hep-ph].
  * [466] P. Ballett, M. Hostert, S. Pascoli, Y. F. Perez-Gonzalez, and Z. Tabrizi arXiv:1902.08579 [hep-ph].
  * [467] G. Magill and R. Plestid Phys. Rev. D 95 no. 7, (2017) 073004, arXiv:1612.05642 [hep-ph].
  * [468] G. Magill and R. Plestid Phys. Rev. D 97 no. 5, (2018) 055003, arXiv:1710.08431 [hep-ph].
  * [469] L. Buonocore et al. arXiv:1812.06771 [hep-ph].