# Mono-Neutrino at DUNE: New Signals From Neutrinophilic Thermal Dark Matter

Kevin J. Kelly  Theoretical Physics Department, Fermilab, P.O. Box 500,
Batavia, IL 60510, USA  Yue Zhang  Theoretical Physics Department, Fermilab,
P.O. Box 500, Batavia, IL 60510, USA  Department of Physics and Astronomy,
Northwestern University, Evanston, IL 60208, USA

###### Abstract

We introduce the mono-neutrino signal at neutrino detectors as a smoking gun
of sub-GeV scale dark matter candidates that mainly interact with standard
model neutrinos. In a mono-neutrino process, invisible particles, either dark
matter themselves or the mediator particle, are radiated off a neutrino when
it undergoes the charged-current weak interaction. The associated signals
include a missing transverse momentum with respect to the incoming neutrino
beam direction and the production of wrong-sign charged leptons. We
demonstrate the potential leading role of the future DUNE experiment, using
its proposed liquid and gas argon near detectors, in probing these new signals
and the thermal origins of neutrinophilic dark matter.

††preprint: FERMILAB-PUB-19-002-T

##  I Introduction

The coming decade is about to witness impressive progress at the neutrino
frontier, with new experiments to be built for further exploring the present
unknowns in the neutrino sector, as well as any associated new physics. One in
particular is the DUNE experiment Acciarri et al. (2016a); Acciarri et al.
(2015); Acciarri et al. (2016b), which will be equipped with a high intensity
beam and liquid argon neutrino detectors. With these new facilities, the door
is open for exploring a broader range of physics beyond the standard model
(SM), and hunting for the corresponding new signals.

One of the exciting and well-motivated opportunities for DUNE as a
multipurpose experiment is to probe the nature of dark matter. While there is
enormous evidence from cosmology suggesting the existence of dark matter
Jungman et al. (1996); Bertone et al. (2005), the burning question is how to
look for it in our laboratories. In terms of energy deposition, neutrino
detectors typically have much higher energy thresholds than dedicated dark
matter detectors and thus are not tailored for probing dark matter scattering
as in the traditional direct detection picture Goodman and Witten (1985). Many
variations to this conventional picture have been proposed, such as searching
for a more energetic component of dark matter (or dark radiation) in our
galaxy which arises from astrophysical processes Agashe et al. (2014);
Chatterjee et al. (2018); Bringmann and Pospelov (2018); Ema et al. (2018), or
a man-made dark matter beam created via fixed-target collisions which then
strikes the detector to scatter elastically Batell et al. (2009); Coloma et
al. (2016); Aguilar-Arevalo et al. (2017, 2018) or causes charged lepton pair
creations de Gouvêa et al. (2018). It has also been envisioned that a fraction
of the halo dark matter may live in a metastable bound state and release much
more than its kinetic energy once it interacts Grossman et al. (2017). Note
that, in all scenarios mentioned above, dark matter particles originate
outside the neutrino detectors. Despite using a neutrino facility for
detection, the key interactions between dark matter and the SM sector here do
not involve neutrinos.

New dark-matter-neutrino interactions can leave important imprint in various
aspects of cosmology, such as the cosmic microwave background (CMB) Serra et
al. (2010); Wilkinson et al. (2014); Di Valentino et al. (2018), and the
structure formation from large to small scales Mangano et al. (2006);
Hannestad et al. (2014); Dasgupta and Kopp (2014); Bringmann et al. (2014);
Cherry et al. (2014); Bertoni et al. (2015); Binder et al. (2016); Davoudiasl
et al. (2018). Experimentally, neutrinos from dark matter annihilation at the
center of the galaxy or the sun have long been proposed and searched for using
neutrino telescopes Desai et al. (2004); Choi et al. (2015); Aartsen et al.
(2015); Adrian-Martinez et al. (2015); Srednicki et al. (1987); Zentner
(2009); Chen and Zhang (2011); Gao et al. (2011); Batell et al. (2018);
Olivares-Del Campo et al. (2018); Berryman et al. (2017); McKeen and Raj
(2018). The attenuation effect in the flux of high energy neutrinos from
distant astrophysical sources due to the travel through the cosmic dark matter
background has also been explored in Refs. Ng and Beacom (2014); Cherry et al.
(2016); Argüelles et al. (2016); Capozzi et al. (2017); Kelly and Machado
(2018). The direct impact of dark-matter-neutrino interactions on the observed
neutrino oscillation probabilities Berlin (2016); Krnjaic et al. (2018); Brdar
et al. (2018) has been recently investigated in the context of fuzzy dark
matter models Hu et al. (2000); Hui et al. (2017); Davoudiasl and Murphy
(2017). These existing works represent the wide range of dark matter theory
space and the corresponding signals that can be searched for using
multipurpose neutrino detectors.

In this work, we present a new type of dark matter signal at neutrino
experiments from neutrinophilic dark matter candidates, which mainly interact
with neutrinos rather than other SM particles. We introduce the mono-neutrino
process where invisible particles, either dark matter themselves or the
mediator to dark matter, are radiated away while the neutrino undergoes a
charged-current (CC) interaction and gets detected. The final states of such a
process are similar to the normal neutrino CC interaction, but there is an
imbalance of the final state momenta transverse to the neutrino beam
direction. This can be viewed as an expansion of the mono-$X$ search concept
for dark matter at high energy collider experiments Abercrombie et al. (2015),
where $X$ is now a neutrino and the search could only be performed at neutrino
detectors. The next-generation liquid argon detectors seem to be the best
places for this search thanks to their unprecedented particle identification
and energy resolution capabilities. We will examine several neutrinophilic
dark matter models, and then identify the parameter space where DUNE using its
near detectors will be at the frontier of probing the thermal origin of these
dark matter candidates.

This paper is organized as follows. In section II and III, we present the
benchmark models for neutrinophilic dark matter and calculate their thermal
relic abundance through the annihilation into neutrinos, respectively. We
present the mono-neutrino process in section IV, discuss the characteristic
signatures, and then explore the prospects of probing the associated signals
at the future DUNE near detectors. In the models under consideration, the
mono-neutrino signal is always accompanied with the “wrong-sign” charged
lepton production. We point out that the DUNE reach can be further improved
with a charge identification capability. We wrap up after commenting on a few
other existing constraints in section V.

##  II Benchmark models

To set the stage, we introduce a complex scalar particle $\phi$ which carries
lepton number (or the $B-L$ quantum number) equal to $-2$ ($2$) and couples to
SM neutrinos through the Weinberg operator portal

$\mathcal{L}_{\rm
portal}=\frac{(L_{\alpha}H)(L_{\beta}H)}{\Lambda_{\alpha\beta}^{2}}\phi+{\rm
h.c.}\to\frac{1}{2}\sum_{\alpha,\beta=e,\mu,\tau}\lambda_{\alpha\beta}\nu_{\alpha}\nu_{\beta}\phi+{\rm
h.c.}\ .$ (1)

After electroweak symmetry breaking, the Higgs vacuum expectation value (VEV)
projects out only neutrinos in the unitary gauge, as shown in the second step,
making $\phi$ neutrinophilic. The dimensionless coupling
$\lambda_{\alpha\beta}$ is defined as $v^{2}/\Lambda_{\alpha\beta}^{2}$ with
$v=246\,$GeV.

The above $\phi$ coupling looks similar to that of a Majoron Gelmini and
Roncadelli (1981); Barger et al. (1982), the goldstone boson (real scalar)
from spontaneously broken lepton number (or $B-L$) symmetry. If such a
symmetry breaking is responsible for generating the neutrino mass (Majorana in
this case), the Majoron coupling will be equal to $\lambda=im_{\nu}/f$, where
$f$ is the symmetry breaking scale. In this work, we are interested in sizable
couplings $\lambda\sim\mathcal{O}(1)$, which in turn imply very low $f\sim
m_{\nu}$. Therefore, for processes occurring at much higher energies, e.g., at
neutrino experiments, one should observe the effect of symmetry restoration.
In other words, we must consider neutrinos coupling to the whole complex
scalar field containing both the Majoron as well as the radial excitations
along the $f$ direction. The corresponding Lagrangian is identical to that of
$\phi$ in Eq. (1).

Alternatively, one could assume that the $\phi$ field does not develop a VEV.
As argued in Berryman et al. (2018), introducing a $\phi$-like scalar is the
easiest way of restoring the $B-L$ as an exact global symmetry of the standard
model effective theory. Eq. (1) is the lowest dimensional non-renormalizable
operator for $\phi$ to couple to standard model particles. In such a context,
the neutrino mass has to be Dirac, and one must introduce at least two right-
handed neutrinos (denoted as $\nu_{R}$), with Yukawa coupling to the SM lepton
doublets. A marginal operator, $\lambda^{\prime}\nu_{R}\nu_{R}\phi$, is also
allowed. In the presence of both $\lambda$ and $\lambda^{\prime}$ couplings,
the right-handed neutrinos could be produced through the $\phi$ exchange in
the early universe. To avoid an excessive contribution to the neutrino degrees
of freedom ($\Delta N_{\mathrm{eff}}$), which is tightly constrained by the
CMB observations Aghanim et al. (2018), the product of couplings,
$\lambda\lambda^{\prime}$ must be tiny, $\lesssim 10^{-9}$ for GeV scale
$m_{\phi}$ Berryman et al. (2018).

Within the parameter space of interest to this work, the new phenomena we are
going to explore based on Eq. (1) do not depend on the details of neutrino
mass generation, whether Dirac or Majorana.

We continue by assuming $B-L$ conservation at the Lagrangian level, and
further consider the above neutrinophilic $\phi$ boson as the portal to dark
matter. We will examine a few simple models where the dark matter is
stabilized by various symmetries, $\mathbb{Z}_{2}$, $\mathbb{Z}_{3}$ and
$U(1)$.

$\begin{split}{\it Model\ IA}:\hskip
28.45274pt&\mathcal{L}=\frac{1}{2}y_{IA}\chi^{2}\phi+{\rm h.c.}\\\ {\it Model\
IB}:\hskip 28.45274pt&\mathcal{L}=\frac{1}{2}y_{IB}\bar{\chi}^{c}\chi\phi+{\rm
h.c.}\\\ {\it Model\ II}:\hskip
28.45274pt&\mathcal{L}=\frac{1}{6}y_{II}\chi^{3}\phi+{\rm h.c.}\\\ {\it Model\
III}:\hskip 28.45274pt&\mathcal{L}=y_{III}\bar{\chi}_{1}\chi_{2}\phi+{\rm
h.c.}\\\ \end{split}$ (2)

In model IA, the dark matter $\chi$ is a complex scalar carrying lepton number
$+1$ and is stabilized by a $\mathbb{Z}_{2}$ symmetry. The coupling $y_{IA}$
in this model has mass dimension 1. Model IB is similar to IA but with $\chi$
being a Dirac fermion and $\chi^{c}$ its charge-conjugation field. In this
case, $\chi$ has the same quantum numbers as the right-handed neutrino and
therefore its stability is not automatic. An ad hoc $\mathbb{Z}_{2}$ symmetry
under which $\chi$ is odd must be imposed by hand. We include this case in our
study for the sake of completeness. In model II, the dark matter carries
lepton number $+2/3$ and is stabilized by a $\mathbb{Z}_{3}$ symmetry. In this
case, $\chi$ must be a complex scalar. Model III slightly goes beyond the
minimality and contains two components of dark matter, $\chi_{1},\chi_{2}$,
which carry lepton numbers $\mathtt{q}-2$ and $\mathtt{q}$ respectively. We
will assume $\chi_{1},\chi_{2}$ are Dirac fermions. For generic values of
$\mathtt{q}$ their couplings to SM particles are forbidden, thus the lighter
of the two (assumed to be $\chi_{1}$) can be the dark matter candidate. In
this case, the stabilization symmetry is a $U(1)$.

It is worth pointing out that the $\mathbb{Z}_{2}$, $\mathbb{Z}_{3}$ and
$U(1)$ symmetries in the above models (with the exception of model IB) and the
stability of dark matter are the natural consequences of the assumed $B-L$
conservation. The $B-L$ quantum number assignment forbids any renormalizable
interaction for the dark matter candidate to decay into standard model
particles. For example, the $\mathbb{Z}_{2}$ symmetry in model IA is the
analogue of $R$-parity in $B-L$ conserving supersymmetric theories (where
$\chi$ is like a right-handed sneutrino).

The above models will serve as the benchmarks for our study. In the following,
we will first derive the favored regions of parameter space in each model that
give the correct dark matter relic density via the thermal freeze out
mechanism. Afterwards, we investigate the prospects of using the DUNE near
detector(s) to test these well-motivated thermal targets.

##  III Dark matter thermal relic density

We consider the thermal relic abundance of dark matter described in the above
models. The relevant annihilation processes are in depicted in Fig. 1, where
the dark matter freezes out by annihilating directly to SM neutrinos via an
off-shell mediator $\phi$. We will focus sub-GeV dark matter and mediator mass
scales, which makes them kinematically accessible in neutrino experiments.
Throughout this study, we assume the mediator $\phi$ to be heavier than the
dark matter $\chi$ or $\chi_{1,2}$.222If $m_{\chi}>m_{\phi}$, the freeze-out
of $\chi$ could occur through the annihilation into $\phi$’s instead of
neutrinos. The subsequent decay $\phi\to\nu_{\alpha}\nu_{\beta}$ is allowed to
happen on a much longer time scale. In such a secluded scenario, there is no
direct connection between the $\phi-\nu$ coupling $\lambda$, which could be
probed at DUNE (this work), and the thermal relic abundance of dark matter
$\chi$. For this reason, we will restrict ourselves to the heavier mediator
case ($m_{\phi}>m_{\chi}$). The annihilation cross sections are thus
proportional to the square of $\lambda_{\alpha\beta}$ couplings which, as we
show later on, could manifest themselves at DUNE.

Figure 1: Annihilation channels for dark matter to freeze out in model IA
(upper left), IB (upper right), II (lower left) and III (lower right). Time
flows from left to right. Arrows represent the direction of lepton number
flows.

Figure 2:  Expected reach of mono-neutrino search at DUNE versus the theory
landscape of neutrinophilic dark matter with thermal relic density: Model IA:
solid (dashed) red curve corresponds to $y_{IA}/m_{\phi}=\lambda_{\mu\mu}$
($y_{IA}/m_{\phi}=1.0$); Model IB: solid (dashed) blue curve corresponds to
$y_{IB}=\lambda_{\mu\mu}$ ($y_{IB}=1.0$); Model II: solid (dashed) yellow
curve corresponds to $y_{II}=\lambda_{\mu\mu}$ ($y_{II}=1.0$); Model III:
solid (dashed) green curve corresponds to $y_{III}=\lambda_{\mu\mu}$
($y_{III}=1.0$) and $\Delta=0.2$. We assume $m_{\chi}=m_{\phi}/10$ for all the
curves. Also shown are the present and future experimental constraints. The
gray shaded regions are already ruled out by the charged kaon semi-leptonic
decays (upper-left region), the Higgs boson invisible decay (large
$\lambda_{\mu\mu}$ region) and the CMB (small $m_{\phi}$ region) measurements,
as will be discussed in section V. The solid and dot-dashed thick black curves
show the DUNE mono-neutrino reach with and without taking into account of
charge identification, as will be discussed in detail in section IV.

In each model, the dark matter annihilation cross section is calculated in the
low relative velocity $v_{\rm rel}$ limit, keeping the leading term in the
$v_{\rm rel}$ expansion.

Model IA: For scalar $\chi$, the annihilation is $S$-wave,

$\sigma v_{\rm
rel}(\chi\chi\to\nu_{\alpha}\nu_{\beta})=\frac{|\lambda_{\alpha\beta}y_{IA}|^{2}}{8\pi(4m_{\chi}^{2}-m_{\phi}^{2})^{2}(1+\delta_{\alpha\beta})}\
.$ (3)

Model IB: For fermionic $\chi$, the annihilation is $P$-wave,

$\sigma v_{\rm
rel}(\chi\chi\to\nu_{\alpha}\nu_{\beta})=\frac{|\lambda_{\alpha\beta}y_{IB}|^{2}m_{\chi}^{2}v_{\rm
rel}^{2}}{16\pi(4m_{\chi}^{2}-m_{\phi}^{2})^{2}(1+\delta_{\alpha\beta})}\ .$
(4)

For the dark matter relic density, we follow the semi-analytical approach in
Refs. Griest and Seckel (1991); Kolb and Turner (1990),

$\begin{split}\Omega_{\rm DM}h^{2}&=\frac{2.1\times 10^{9}\,{\rm
GeV}^{-1}\sqrt{g_{*}}(n+1)x_{f}^{n+1}}{g_{*S}M_{pl}\sigma_{0}}\ ,\\\
x_{f}&\simeq\log\frac{0.038g_{\chi}c(c+2)M_{pl}m_{\chi}\sigma_{0}}{\sqrt{g_{*}}}\
,\end{split}$ (5)

where $g_{\chi}=2$. For $S$-wave annihilation, $n=0$ and $\sigma_{0}=\sigma
v_{\rm rel}$; while for $P$-wave annihilation, $n=1$ and
$\sigma_{0}=6\sigma/v_{\rm rel}$. We set $c(c+2)=n+1$ following the
prescription in Ref. Kolb and Turner (1990). $\Omega_{\rm DM}h^{2}$ includes
contributions from both $\chi$ and $\chi^{*}$ ($\chi^{c}$).

Model II: The dark matter in this model freezes out via semi-annihilation
D’Eramo and Thaler (2010),

$\sigma v_{\rm
rel}(\chi\chi\to\chi^{*}\nu_{\alpha}\nu_{\beta})=\frac{|\lambda_{\alpha\beta}y_{II}|^{2}}{2048\pi^{3}m_{\chi}^{2}(1+\delta_{\alpha\beta})}\int_{0}^{1}dz\frac{z\sqrt{(1-z)(9-z)}}{(m_{\phi}^{2}/m_{\chi}^{2}-z)^{2}}\
.$ (6)

This integral can be performed analytically, but we will not show the lengthy
full result except for the large $m_{\phi}$ limit,

$\sigma v_{\rm
rel}(\chi\chi\to\chi^{*}\nu_{\alpha}\nu_{\beta})\simeq\frac{(57-80\ln
2)|\lambda_{\alpha\beta}y_{II}|^{2}m_{\chi}^{2}}{4096\pi^{3}m_{\phi}^{4}(1+\delta_{\alpha\beta})}\
.$ (7)

This is an $S$-wave semi-annihilation. The dark matter relic density can be
calculated by generalizing Eq. (5), only with the change $c(c+2)\to c(c+1)$.
However, we still set $c(c+1)=n+1$ in the relic density calculation.

Model III: In this model, the way to freeze out dark matter in early universe
is via coannihilation of $\chi_{1},\chi_{2}$, whose cross section is

$\sigma v_{\rm
rel}(\chi_{1}\bar{\chi}_{2}\to\nu_{\alpha}\nu_{\beta})=\frac{|\lambda_{\alpha\beta}y_{III}|^{2}m_{\chi_{1}}^{2}(2+\Delta)^{2}v_{\rm
rel}^{2}}{64\pi[m_{\chi_{1}}^{2}(2+\Delta)^{2}-m_{\phi}^{2}]^{2}(1+\delta_{\alpha\beta})}\
,$ (8)

where $\Delta\equiv(m_{2}-m_{1})/m_{1}$. Like model IB, this is again a
$P$-wave annihilation. The dark matter relic density in this case can be
calculated using Eq. (5) but with the replacement Griest and Seckel (1991)

$\begin{split}g_{\chi}&\to g_{\rm
eff}=g_{\chi}\left[1+(1+\Delta)^{3/2}e^{-x_{f}\Delta}\right]\ ,\\\
\sigma_{0}&\to\frac{6\sigma}{v_{\rm rel}}\times
2(1+\Delta)^{3/2}e^{-x_{f}\Delta}\ .\end{split}$ (9)

Fig. 2 shows parameter space where the dark matter in the above models can
obtain the observed relic density. For each model, we choose two benchmark
values of the $\chi$-$\phi$ coupling, democratic and hierarchical. Namely,
$\phi$ having similar branching ratios decaying into $\chi$’s or $\nu$’s, and
$\phi$ mainly decaying into $\chi$’s, respectively. For model IA, the solid
(dashed) curve corresponds to $y_{IA}/m_{\phi}=\lambda_{\mu\mu}$
($y_{IA}/m_{\phi}=1$). For models IB, II and III, the solid curves stand for
the case where $\phi$ couples with equal strength to dark matter and neutrinos
($y_{\bullet}=\lambda_{\mu\mu}$ where $\bullet=IB,II,III$), whereas the dashed
curves stand for the case of hierarchical couplings with $y_{\bullet}=1$. In
model III, we set the $\chi_{1}$-$\chi_{2}$ mass difference to be
$\Delta=0.2$. We also set $m_{\chi}=m_{\phi}/10$. These benchmark parameters
are chosen in order to give an idea of the range of thermal dark matter
targets for experimental searches – the main focus of the upcoming sections.

##  IV Mono-neutrino at DUNE near detectors

In this section, we propose the mono-neutrino channel as the new signal from
$\phi$ as the mediator to dark matter with a sub-GeV mass, and explore the
exciting opportunity of probing it at accelerator neutrino experiments, in
particular the near-future DUNE experiment. Such a signal is commonly
predicted by the above benchmark models. We consider neutrino near detectors
which are located near the fixed-target collisions and see the most intense
flux of neutrinos. Because the accelerator neutrinos are predominantly made of
the muon flavor at production, and charged muons are easiest to identify
experimentally, we will focus on the $\lambda_{\mu\mu}$ coupling of $\phi$.

###  IV.1 The mono-neutrino signal and background

First, imagine an accelerator neutrino experiment whose beam is running in the
neutrino mode, the key process of interest to us is

$\nu_{\mu}+N\to\mu^{+}+N^{\prime}+\phi^{*}$ (10)

as depicted in Fig. 3, where an on-shell $\phi^{*}$ particle is radiated off
the initial state muon neutrino before it undergoes the SM CC weak
interaction. Such neutrino beamstrahlung process has been proposed in Berryman
et al. (2018). In the models considered in this work, the $\phi^{*}$ particle
will subsequently decay into dark matter or neutrinos and appear as missing
energy. Because $\phi^{*}$ takes away two units of lepton number, a $\mu^{+}$
particle is created in (10), accompanied with a momentum transfer to the
target nucleus, leading to nuclear activities (labelled by $N^{\prime}$). We
will restrict our study to those events where the final state $N^{\prime}$
remains as a nucleon, as additional hadronic activity (e.g., deeply-inelastic
scattering events) tends to bring more uncertainties to the final state
momentum measurement. If the neutrino detector in which the above process
occurs is able to identify the outgoing muon and the recoiling nucleon, and
measure their energy and momenta precisely, it will discover an imbalance
among the final state momenta of these visible particles in the directions
orthogonal to the incoming neutrino beam. The missing transverse momentum,
defined as

$\cancel{p}_{T}\equiv\left|\sum_{i=\mathrm{visible}}\left(\vec{p}_{T}\right)_{i}\right|\
,$ (11)

could serve as the smoking gun for neutrinophilic dark matter through the
$\phi$ portal. This is the mono-neutrino signal we shall explore in detail.

The main backgrounds for such signal are the SM charged current quasi-elastic
(CCQE) events,

$\displaystyle\nu_{\mu}+N\to\mu^{-}+N^{\prime}$ (12)
$\displaystyle\bar{\nu}_{\mu}+N\to\mu^{+}+N^{\prime}$ (13)

There are no invisible final state particles in these processes. However, with
a realistic detector, the uncertainties in the final state momentum
reconstruction (more uncertain on the nucleon side) could result in a nonzero
$\cancel{p}_{T}$ measurement, in which case they fake the mono-neutrino
signal.

Although we are considering a neutrino beam in the above example, there is
always an anti-neutrino contamination in the beam thus the process in (13)
also needs to be taken into account. Given that the antineutrino flux is only
a few percent of that of neutrinos, the rate for (13) is subdominant to (12).
However, because (13) produces a muon with the same sign as that in our signal
process (10), it contributes as a more irreducible background even for
detectors with a charge identification capability.

Figure 3: Neutrino beamstrahlung process that appears as a mono-neutrino event
at DUNE. The $\phi$ particle is radiated off the incoming neutrino when a CC
process occurs, followed by its invisible decay into dark matter or neutrinos.
Time flows from left to right. Arrows represent the direction of lepton number
flow.

Another potential background worth worrying about arises from the neutral
current process

$\displaystyle\nu+N\to\nu+N^{\prime}+\pi^{\pm}$ (14)

with the final state $\pi^{\pm}$ misidentified as a charged muon. In this
case, such a process can fake our mono-neutrino signal because the final-state
neutrino takes away a missing transverse momentum. The number of these events
at the DUNE near detector is expected to be around half the number of CCQE
events Acciarri et al. (2015). There are, however, several useful handles for
reducing this contribution.

First, such a process dominantly proceeds via an intermediate $\Delta$-baryon
resonance, whose contribution can be efficiently suppressed with a cut on the
$N^{\prime}\pi^{\pm}$ invariant mass vetoing the window around $\Delta$ mass.
Second, the discrimination between the $\pi^{\pm}$ and $\mu^{\pm}$ tracks is
possible using the $dE/dx$ observable Marshall  (especially in a gaseous argon
detector as discussed below). Third, because $\pi^{\pm}$ interacts strongly,
it tends to shower more, producing a number of ancillary tracks as it travels
through the liquid argon Asaadi . Fourth, the charged pion once produced could
either get absorbed by an argon nucleus, or decay weakly into $\mu^{\pm}$. The
former possibility allows (14) to fake our signal, while the latter features a
track with a kink (when $\pi^{\pm}$ and $\mu^{\pm}$ travel in different
directions), which is relatively easy to identify. The ratio of these two
possibilities is in principle calculable. Therefore, measuring the rate of the
tracks with kinks will help to have control of the background from absorbed
pions. Last but not the least, the Michel electrons from $\mu^{\pm}$ decay
could serve as an important handle on identifying our signal process, which is
absent in the $\pi^{\pm}$ decay. For all the above considerations, we decide
to neglect the $\nu_{\mu}N\to\nu_{\mu}N^{\prime}\pi^{\pm}$ background process
in the following simulations and sensitivity estimates.

Atmospheric neutrinos with CC interactions could, in principle, fake our
desired signal as well, since the incoming neutrino direction is unknown.
However, the rate of atmospheric neutrino events at the DUNE near detector is
expected to be small (less than 10 per year), and additionally, timing
information with the DUNE beam spills would allow these events to be further
reduced, since our desired signal arrives in time with the neutrino beam.

###  IV.2 Features of mono-neutrino events at DUNE near detectors

Clearly, in order to suppress the background discussed above, the most useful
neutrino detectors need to have excellent energy/momentum resolution and
charge discrimination of final state leptons. This leads us to consider the
future DUNE near detector setup, which according to the present plans Bross ;
Marshall , includes a liquid argon (LAr) time projection chamber (TPC)
Sinclair , a high-pressure gaseous argon (HPg) TPC Martin-Albo (2017); Mohayai
, a 3D projection scintillator tracker McGrew , as well as the DUNE PRISM
concept of designing movable detectors Vilela . Among them, of the most
interest to this study are the LAr and HPg TPCs, which will be placed
downstream the neutrino beam from the fixed target collision hall. A schematic
plot of the detector setup is shown by Fig. 4. For a mono-neutrino process
initiated in the LAr TPC, the final state muon and nuclear recoil leave
distinct tracks, based on which their energies and momenta could be measured
Acciarri et al. (2015). If the muon is energetic enough to travel into the HPg
TPC, the sign of its charge can be easily identified using a magnetic field,
in together with its energy and momentum. Although the LAr TPC will not be
magnetized, it still retains certain charge identification ability by
utilizing the Michel electron from muon decay, which will be discussed in more
detail below.

Figure 4: A schematic plot of the DUNE near detector setup, with liquid and
magnetized gaseous argon detectors located downstream the neutrino beam.

Our goal here is to estimate the reach of these DUNE near detectors in search
for the mono-neutrino signal. We will focus on the processes initiated in the
LAr TPC rather than the HPg one because the former has a much higher target
mass. Based on the expected neutrino beam flux provided in Acciarri et al.
(2015) and an effective LAr target mass equal to 75 ton Bross , the SM CCQE
background is estimated to occur about 20 million times every year Acciarri et
al. (2015). To derive the final state phase space distributions for the signal
and background, we simulate the corresponding processes at nucleon level using
MadGraph Alwall et al. (2011), assuming $N=p,N^{\prime}=n$ in (10) and (13)
and $N=n,N^{\prime}=p$ in (12). We impose an energy smearing of $40\%/\sqrt{E\
[\rm GeV]}$ for the final state neutron, $20\%/\sqrt{E\ [\rm GeV]}$ for
proton, and $3\%/\sqrt{E\ [\rm GeV]}$ for muon, on event by event basis. These
smearings account for the errors in final state momentum reconstructions
Acciarri et al. (2015). We first generate the events for fixed neutrino energy
and then convolve them with the incoming neutrino beam energy spectrum.

Fig. 5 (left) shows the resulting $\cancel{p}_{T}$ distributions for our
signal and background, using events with fully contained muons produced and
then stopping inside the LAr TPC (with $E_{\mu}<1\,$GeV).333Typically, a muon
produced with energy larger than 1 GeV will eventually leave the LAr TPC
instead of stopping NGLES et al. . Hereafter, we use $E_{\mu}=1$ GeV as the
boundary between full contained muons within the LAr and the through-going
muons that reach the GAr. Based on the near detector design Mohayai , the
fraction of through-going muons that miss the GAr detector is neglected to a
good approximation. The solid (dashed) curves correspond to the DUNE beam
running in the neutrino (antineutrino) mode. The neutrino mode has a
relatively higher background because of its higher CC cross section (by a
factor of 3). For the signal, the red (blue) curves correspond to
$m_{\phi}=500\,{\rm MeV}$ (1 GeV) with the coupling parameter
$\lambda_{\mu\mu}=1$ fixed. Clearly, barring the uncertainties in the
energy/momentum reconstruction, the signal events extend to much higher
$\cancel{p}_{T}$ bins than the background. The kinematic region with
$\cancel{p}_{T}\gtrsim 0.5$ GeV is expected to be almost background free given
the time scale of the DUNE experiment ($\sim 10$ years) thus serves as the
main signal region for hunting the mono-neutrino signal.

Figure 5: Expected number of events per year at the DUNE Near Detector that
are identified as signal events in neutrino mode (solid lines) and
antineutrino mode (dashed lines). See text and Tables 1 and 2 for explanation
of signal. We show events for fully contained muons ($E_{\mu}<1$ GeV), and in
the right panel, we further restrict to events with reconstructed neutrino
energy $E_{\nu}^{\mathrm{reco}}<1.5$ GeV to highlight the difference in signal
and background distributions as a function of this variable. For the mono-
neutrino process of interest, red (blue) lines assume $m_{\phi}=500$ MeV ($1$
GeV) and $\lambda_{\mu\mu}=1$. Distributions take into account the factors
regarding Michel electron tagging discussed in the text.

In addition, Ref. Berryman et al. (2018) has pointed out that another
observable, $E_{\nu}^{\mathrm{reco}}$, defined as the neutrino energy inferred
by assuming $2\to 2$ scattering (where a neutrino with energy
$E_{\nu}^{\mathrm{reco}}$ strikes a nucleon at rest), can be useful for
further signal-background differentiation. It was found that, for the SM
background, $E_{\nu}^{\mathrm{reco}}$ peaks around 4 GeV, whereas for our
signal, $E_{\nu}^{\mathrm{reco}}$ is typically less than 1–2 GeV, mainly
because the radiated $\phi$ carries away a significant fraction of the
injected energy. In Fig. 5 (right), we have further imposed a
$E_{\nu}^{\mathrm{reco}}<1.5\,$GeV cut in the event selection.

Even more excitingly, on top of the above kinematic handles***Another
potentially useful kinematical cut is the invariant mass of the incoming
neutrino, which can be inferred by assuming the target nucleon to be at rest
and from the reconstructed final state momenta. Ideally, it vanishes for the
background processes, but not for our signal if $\phi$ is radiated from the
initial state with a nonzero transverse momentum. In practice, we find that
the role of such a cut is already played by the $\cancel{p}_{T}$ cut.
($\cancel{p}_{T}$ and $E_{\nu}^{\mathrm{reco}}$), the DUNE detectors will also
be able to discriminate the signs of final state muons. The highly energetic
muons ($E_{\mu}>1\,$GeV) will travel though the LAr and reach the magnetized
HPg TPC (as shown by the yellow track “c” in Fig. 4). We simply assume 100%
charge discrimination efficiency in this case Mohayai . The less energetic
muons ($E_{\mu}<1\,$GeV) will mostly stop inside the LAr and become fully
contained. A $\mu^{+}$ always decays after stopping, giving rise to a Michel
electron which can be tagged together with the stopped muon track (as shown by
the yellow track “a” in Fig. 4). In contrast, a $\mu^{-}$ is first captured by
the argon nucleus into a muonic atom, and quickly settles down to the ground
state Vulpescu (1999). Afterwards, it has $\sim 25\%$ probability of decaying,
producing a Michel electron, and $\sim 75\%$ probability of being further
captured by the nucleus through weak interaction, converting into a muon
neutrino, without producing Michel electron (as shown by the yellow track “b”
in Fig. 4). These features can be used to further enhance the signal to
background ratio. For example, in the signal process (10), a $\mu^{+}$ is
produced which always decays into a Michel electron. For fully contained muon
events, we can suppress the dominant background (12) by a factor of 0.25 by
requiring the presence of a Michel electron. On the other hand, with an
antineutrino beam, the dominant signal arises via the charge-conjugate process
to (10) and a $\mu^{-}$ is produced. In this case, we could suppress the
dominant background (the charge conjugation of (12) which creates a $\mu^{+}$)
almost completely by by vetoing events containing a Michel electron at the end
of the stopped muon track, at the price of suppressing the signal by a factor
of $0.75$ at the same time. Recently, the MicroBooNE and ArgoNeuT experiments
have demonstrated the ability of measuring Michel electrons and MeV scale
physics in their LAr TPCs Acciarri et al. (2017); Caratelli (2017); Acciarri
et al. (2018). A similar capability is expected at the DUNE near detector as
well.

To better understand the signal and background event distributions in the
different $\cancel{p}_{T}$ and $E_{\nu}^{\mathrm{reco}}$ kinematic regions, as
well as the impact of the charge identification discussed above, we divide the
generated events into several categories, as shown in the following Tables 1
and 2, assuming the DUNE beam running in the neutrino and antineutrino mode,
respectively. For each mode, we first divide the events into two cases with
fully contained muons in LAr TPC (with $E_{\mu}<1$ GeV) and through-going
muons that reach the HPg TPC (with $E_{\mu}>1$ GeV). For each case, we further
divide the events into two subsets with $E_{\nu}^{\mathrm{reco}}>(<)1.5$ GeV.
In each $E_{\mu}$ and $E_{\nu}^{\mathrm{reco}}$ window, we further select
events by applying the corresponding charge identifications. For events with
muons fully contained in the LAr TPC, we require the presence (absence) of
Michel electron near the end of the muon track, for the neutrino
(antineutrino) beam mode. The resulting penalty factors for the signal and
background are given in unit of percentage in the square brackets. The HPg TPC
is assume to veto all background events containing opposite-sign muons to
those in the signal.

$\nu$ Mode: $\mu^{+}$ Michel/Gas-tagged | $E_{\mu}<1$ GeV |  $E_{\nu}^{\mathrm{reco}}<1.5$ GeV | $E_{\mu}>1$ GeV |  $E_{\nu}^{\mathrm{reco.}}<1.5$ GeV
---|---|---|---|---
$E_{\nu}^{\mathrm{reco.}}\geq 1.5$ GeV |  $E_{\nu}^{\mathrm{reco}}\geq 1.5$ GeV
Signal: $\nu_{\mu}p\to\phi\mu^{+}n$ | Michel $e^{+}$ [100%] | $6.10\times 10^{3}\ (1.53\times 10^{3})$ | Tagged $\mu^{+}$ [100%] | $2.60\times 10^{3}\ (660.4)$
$423.4\ (59.9)$ | $2.32\times 10^{3}\ (516.4)$
Background: $\nu_{\mu}n\to\mu^{-}p$ | Michel $e^{-}$ [25%] | $3.71\times 10^{5}$ | Tagged $\mu^{-}$ [0%] | $5.27\times 10^{5}$
$1.23\times 10^{6}$ | $1.55\times 10^{7}$
Background: $\overline{\nu}_{\mu}p\to\mu^{+}n$ | Michel $e^{+}$ [100%] | $4.33\times 10^{4}$ | Tagged $\mu^{+}$ [100%] | $3.41\times 10^{4}$
$2.28\times 10^{4}$ | $6.30\times 10^{5}$
Table 1: Number of expected signal and background events per year at the DUNE near detector, assumed to contain 75 ton of liquid argon, with the beam running in the neutrino mode. We divide the events into four kinematical categories with $E_{\mu}<(>)1$ GeV and $E_{\nu}^{\mathrm{reco}}>(<)1.5$ GeV. For charge identification, we require the presence of Michel electrons from fully contained muons inside the LAr TPC or tagged $\mu^{+}$ inside the HPg TPC. The resulting penalty factors for the signal and background are given in unit of percentage in the square brackets. We show the number of signal events for $\phi$ emission assuming $\lambda_{\mu\mu}=1$ and $m_{\phi}=500$ MeV ($m_{\phi}=1$ GeV in the parentheses). $\bar{\nu}$ Mode: $\mu^{-}$ No Michel/Gas-tagged | $E_{\mu}<1$ GeV |  $E_{\nu}^{\mathrm{reco}}<1.5$ GeV | $E_{\mu}\geq 1$ GeV |  $E_{\nu}^{\mathrm{reco.}}<1.5$ GeV
---|---|---|---|---
$E_{\nu}^{\mathrm{reco.}}\geq 1.5$ GeV |  $E_{\nu}^{\mathrm{reco}}\geq 1.5$ GeV
Signal: $\bar{\nu}_{\mu}n\to\phi\mu^{-}p$ | Nuclear captured [75%] | $3.30\times 10^{3}(486.2)$ | Tagged $\mu^{-}$ [100%] | $1.46\times 10^{3}(216.7)$
$409.5(40.8)$ | $1.67\times 10^{3}(222.3)$
Background: $\overline{\nu}_{\mu}p\to\mu^{+}n$ | Michel $e^{+}$ [0%] | $5.38\times 10^{5}$ | Tagged $\mu^{+}$ [0%] | $6.30\times 10^{5}$
$4.43\times 10^{5}$ | $6.18\times 10^{6}$
Background: $\nu_{\mu}n\to\mu^{-}p$ | Nuclear captured [75%] | $6.34\times 10^{4}$ | Tagged $\mu^{-}$ [100%] | $3.30\times 10^{4}$
$1.95\times 10^{5}$ | $1.94\times 10^{6}$
Table 2: Similar to Table 1 but with the DUNE beam running in the antineutrino
mode. For charge identification, we require the absence of any Michel electron
for fully contained muons inside the LAr TPC or tagged $\mu^{-}$ inside the
HPg TPC in this case.

From these tables, there is important information one could learn about the
features of the signal and background. First, the dominant background category
contains through-going muons that reach the HPg TPC. Among them, the opposite-
sign muon background (compared to the signal) can be vetoed with a magnetic
field. Second, the majority of signal events have fully contained muons in the
LAr TPC. The number of background events can be suppressed by an order of
magnitude by focusing on these fully contained muons. Furthermore, we find
that the background can be suppressed by another order of magnitude by
requiring the presence/absence of a Michel electron from muon decay together
with a $E_{\nu}^{\mathrm{reco}}<1.5$ GeV cut. In contrast, these event
selection criteria only hurt the number of signal events by an order one
factor.

###  IV.3 Expected DUNE reach

Here we assess the prospects of using the DUNE near detectors to explore the
mono-neutrino signal, and their implications for the neutrinophilic dark
matter models presented in section II. In order to fully take advantage of the
differences between the signal and background as found above, we perform a
log-likelihood comparison between the two using a Poisson distribution

$-2\ln{\mathcal{L}}=-2\sum_{C,T}\sum_{i=1}^{24}\sum_{j=1}^{20}\left(-\lambda_{ij}+\mu_{ij}\ln{\lambda_{ij}}-\ln{\mu_{ij}!}\right),$
(15)

where $\mu_{ij}$ ($\lambda_{ij}$) is the number of background (signal +
background) events 444The difference between $\lambda_{ij}$ and $\mu_{ij}$ –
the number of signal events in a bin – is proportional to
$\lambda_{\mu\mu}^{2}$. in the $i$th bin of $\cancel{p}_{T}$ and $j$th bin of
$E^{\mathrm{reco}}_{\nu}$. We assume ten years of data collection (equal time
in neutrino and antineutrino modes) and bins of $125$ MeV in $\cancel{p}_{T}$
between $0$ and $3$ GeV (24 total) and bins of $500$ MeV in
$E_{\nu}^{\mathrm{reco}}$ between $0$ and $10$ GeV (20 total).

We perform the following two analyses. The first one involves both fully
contained ($C$) events within the LAr TPC and the ones with through-going
events ($T$) muons that could reach the HPg TPC. We take into account the
charge identification efficiency factors discussed above. The second analysis
involves only the $C$-type events, and to be conservative, in this case we
explore the impact of having no charge identification, meaning no
discrimination between captured $\mu^{-}$ and those that produce a Michel
electron/positron after stopping. This amounts to the factors in brackets in
Tables 1 and 2 all being $100\%$ – an increase in background by a factor of
$\sim 4$ in neutrino mode and a factor of a few in antineutrino mode.

In Fig. 2, the black curves show the 90% confidence level reach in the
$\lambda_{\mu\mu}$ versus $m_{\phi}$ parameter space (corresponding to
$-2\Delta(\ln{\mathcal{L}})=4.6$ for two parameters) by using the DUNE near
detector to look for the proposed mono-neutrino signal for 10 years. The solid
(dot-dashed) curve corresponds to using both $C$ and $T$ (just $C$) events. As
explained earlier, the colored curves represent the parameter space for
neutrinophilic dark matter which obtains the correct thermal relic abundance
via the annihilation into neutrinos. Clearly, a sizable portion of these
regions of interest can be covered. Including the $T$-type events and enabling
the charge identification capability of detectors allows the sensitivity in
$\lambda_{\mu\mu}$ to be enhanced by a factor of $\sim 2$.

In our discussions so far, we have sticked the $\phi$, $\chi$ mass relation to
be $m_{\phi}=10m_{\chi}$. To present our results for generalized mass
relations, In the left panel of Fig. 6, we show the parameter space of thermal
targets versus the DUNE reach assuming $m_{\phi}=3m_{\chi}$. In this case,
most of the relic density curves for the neutrinophilic dark matter models
discussed in Section II move downwards slightly, compared Fig. 2 (shown again
in the right panel). Clearly, the DUNE is still able to cover a substantial
portion of the parameter space of interest. On the other hand, if we increase
the $m_{\phi}/m_{\chi}$ mass ratio, the correct dark matter relic density will
call for larger couplings and the DUNE reach will get better.

Figure 6: Left: Same as Fig. 2 but assuming a mass relation
$m_{\phi}=3m_{\chi}$. Right: a reproduction of Fig. 2 for comparison.

##  V Other constraints

In this section, we comment on other existing constraints on the benchmark
models under consideration.

###  V.1 Precision Measurements in the Standard Model

There are relevant existing constraints on the $\phi$ couplings from precision
measurements in the SM, as shown by the gray regions in Fig. 2. The leading
ones are the charged meson ($\mathfrak{m}=\pi,K,D$) decays and the Higgs boson
invisible decays. In particular, the semi-leptonic decay of charged kaon,
$K^{-}\to\ell^{-}+\bar{\nu}_{\ell}$, is helicity suppressed by the mass of the
charged lepton $\ell$, which will no longer be the case if a $\phi$ particle
is radiated off the final state neutrino Barger et al. (1982); Laha et al.
(2014). The three-body decay meson rate for
$\mathfrak{m}^{-}\to\ell+\nu_{\ell}+\phi$ has been calculated in Ref. Berryman
et al. (2018), which is valid when $m_{\phi}<m_{\mathfrak{m}}-m_{\ell}$. In
this work, we extend the result to the $m_{\phi}>m_{\mathfrak{m}}-m_{\ell}$
region and calculate the four-body decay rate
$\mathfrak{m}^{-}\to\ell^{-}+\nu_{\ell}+\bar{\nu}+\bar{\nu}$ via an off-shell
$\phi$ in Appendix A. The kaon decay constraint excludes the gray shaded
region in the upper-left corner of Figs. 2 and 6.

The effective operator in Eq. (1) also leads to a new Higgs boson decay mode,
$h\to\phi\nu\nu$. The upper bound on the Higgs invisible decay width from the
LHC translates into an upper limit on $\lambda_{\mu\mu}$ Berryman et al.
(2018), shown by the gray shaded region near the top of Figs. 2 and 6. The
$\phi$ radiation also modifies the $W/Z$ boson decay widths which lead to
weaker constraints than the ones discussed above.

###  V.2 Lower Bound on Thermal Dark Matter Mass from CMB

For the dark matter to obtain its relic density via the thermal freeze out
mechanism, there is a generic lower bound on its mass from the CMB measurement
of the effective number of relativistic degrees of freedom, $\Delta
N_{\mathrm{eff}}$ Aghanim et al. (2018). If the dark matter is too light, the
transfer of entropy into its annihilation product will increase $\Delta
N_{\mathrm{eff}}$; this leads to a lower bound on dark matter mass around 4
MeV Nollett and Steigman (2015); Escudero (2018). We include this lower bound,
translated into a lower bound on $m_{\phi}$ depending on the $\phi$-$\chi$
mass ratio, in our main results in Figs. 2 and 6. Recently, it has been argued
that if dark matter enters thermal equilibrium with neutrinos after the BBN,
the CMB constraint can be relaxed Berlin and Blinov (2018). However, the dark-
matter-neutrino coupling for this to occur must be very small, and cannot lead
to a large enough mono-neutrino rate at DUNE.

###  V.3 Constraint on Dark Matter Self Interaction

The $\phi$ exchange can also give rise to dark matter self interactions among
the dark matter particles, whose cross section is bounded from above from the
observation of the bullet cluster Randall et al. (2008),
${\sigma_{\chi\chi\to\chi\chi}}/{m_{\chi}}\lesssim 1.25\,{\rm cm^{2}}/{\rm
g}\simeq 4.6\times 10^{3}\,{\rm GeV}^{-3}$. Here we discuss the implication of
this constraint in each model.

Model IA: For each $\chi$ particle, there are two ways for it to self
interact, $\chi\chi\to\chi\chi$ via $s$-channel $\phi$ exchange, and
$\chi\bar{\chi}\to\chi\bar{\chi}$ via $t$-channel $\phi$ exchange. In the
large $m_{\phi}$ limit, the two cross sections are comparable to each other,

$\sigma_{\chi\chi\to\chi\chi}=\frac{1}{2}\sigma_{\chi\bar{\chi}\to\chi\bar{\chi}}=\frac{y_{IA}^{4}}{128\pi
m_{\chi}^{2}m_{\phi}^{4}}\ .$ (16)

Model IB: The channels for $\chi$ to self interact are like model IA. The
cross sections in this case are

$\sigma_{\chi\chi\to\chi\chi}=\frac{y_{IB}^{4}m_{\chi}^{2}v_{\rm
rel}^{4}}{128\pi m_{\phi}^{4}}\ ,\ \ \
\sigma_{\chi\bar{\chi}\to\chi\bar{\chi}}=\frac{y_{IB}^{4}m_{\chi}^{2}}{4\pi
m_{\phi}^{4}}\ .$ (17)

Interestingly, the $\chi\chi\to\chi\chi$ process (via $s$-channel $\phi$
exchange) is highly suppressed at low velocities, which is the case for dark
matter on cluster scales ($v_{\rm rel}\sim 0.03c$). This implies that if the
dark matter relic abundance is asymmetric today, made of only $\chi$ or
$\bar{\chi}$ particles, its self interaction constraint is more relaxed.

Model II, III: In these two models, the dark matter self interactions occur at
one loop level. The cross section in model II is

$\sigma_{\chi\chi\to\chi\chi}\sim\sigma_{\chi\bar{\chi}\to\chi\bar{\chi}}\simeq\frac{1}{64\pi
m_{\chi}^{2}}\left[\frac{y_{II}^{2}}{16\pi^{2}}\left(\ln\frac{\mu^{2}}{m_{\phi}^{2}}-\frac{m_{\chi}^{2}}{m_{\phi}^{2}-m_{\chi}^{2}}\ln\frac{m_{\phi}^{2}}{m_{\chi}^{2}}\right)\right]^{2}\
,$ (18)

where the logarithmic divergence indicates that the $|\chi|^{4}$ coupling is
renormalized by the $\chi^{3}\phi$ coupling at one-loop level, and the $\chi$
self interaction is not calculable. In practice, we get rid of the cutoff
scale dependence by assuming the bare $|\chi|^{4}$ coupling vanishes at the
scale $\mu=m_{\phi}$. We estimate the cross sections in model III as

$\sigma_{\chi_{1}{\chi}_{1}\to\chi_{1}{\chi}_{1}}\sim\sigma_{\chi_{1}\bar{\chi}_{1}\to\chi_{1}\bar{\chi}_{1}}\simeq\frac{y_{III}^{8}m_{\chi}^{2}}{16\pi
m_{\phi}^{4}}\left(\frac{1}{16\pi^{2}}\right)^{2}\ .$ (19)

In each model, we explore the implications of self interaction constraint,
$\sigma/m_{\chi}\lesssim 1.25$ cm2/g, on its parameter space. To present the
results, we fix $m_{\chi}=m_{\phi}/10$ and consider the same $\phi$-$\chi$
couplings as used in Fig. 2. For model IA, with $y_{IA}/m_{\phi}=1$, small
enough self interaction requires $m_{\phi}\gtrsim 106$ MeV. For the other
models, with $y_{\bullet}=1$ ($\bullet=IB,II,III$), we derive lower bounds
$m_{\phi}\gtrsim 12$ MeV, $6$ MeV, $0.2$ MeV, respectively. These lower
bounds, when translated into bounds on $m_{\chi}$, are comparable to those
from the CMB discussed in the previous subsection. On the other hand, assuming
$y_{IA}/m_{\phi}=\lambda_{\mu\mu}$ or $y_{\bullet}=\lambda_{\mu\mu}$ in the
other models, the self interaction constraints on the parameter space are much
weaker than the other existing bounds.

Because we have assumed the force carrier $\phi$ to be heavier than the dark
matter in this work, the above self interaction strength can be safely
suppressed in the large $m_{\phi}$ limit. Within the parameter space of
interest to this study, we find it safe to conclude that the dark matter self
interaction constraint is always satisfied. In the complementary regime,
making $\phi$ lighter than the dark matter could result in resonant
enhancements to the self interaction cross section at low dark matter
velocities Buckley and Fox (2010); Tulin et al. (2013) and the constraint from
clusters is typically much more severe. On the other hand, it is possible to
accommodate a self-interacting dark matter candidate in this case Rajaraman
and Smolinsky (2018); Tulin and Yu (2018).

###  V.4 IceCube and High-energy Cosmic Neutrinos Interacting with Dark Matter

In the models we consider, the $\phi$ exchange gives rise to neutrino self
interactions as well as neutrino-dark-matter interactions. The observation of
very high energy cosmic neutrinos at IceCube constrains these interactions
because they have to survive traveling through the ambient cosmic neutrino and
dark matter backgrounds before reaching the earth Ng and Beacom (2014); Cherry
et al. (2014). Moreover, the coincidence in the recent observations of high
energy neutrinos and gamma rays indicates the distance of the source, allowing
one to use their relative flux to limit the high energy neutrino free
streaming length Kelly and Machado (2018). We examine this constraint and find
that, for dark matter and $\phi$ heavier than MeV scale, the focus of this
work, the IceCube constraint is weaker than other existing ones.

##  VI Summary and Outlook

In this work, we present the mono-neutrino process as a new signal and
powerful probe of neutrinophilic dark matter candidates, that can be searched
for at neutrino experiments. The main idea is to consider the radiation of
light invisible particle(s) off the neutrino beam when a charge-current weak
process occurs for neutrino to get detected. This leads to a missing
transverse momentum in the final states with respect to the incoming neutrino
beam direction, which is a clean signal with low standard model background.

We focus on a class of models where a complex scalar $\phi$ with lepton number
$-2$ interacts with standard model neutrinos via the $(LH)^{2}\phi$ operator.
This way, the Higgs condensate, by breaking the $SU(2)_{L}$ gauge invariance,
allows $\phi$ to couple exclusively to neutrinos. We discuss several options
for $\phi$ to be the portal to dark matter, where the latter is a standard
model singlet and is stabilized due to various global symmetries,
$\mathbb{Z}_{2}$, $\mathbb{Z}_{3}$ and $U(1)$. We derive the model parameter
space that allows the dark matter to obtain the correct thermal relic
abundance by annihilating into neutrinos through $\phi$. The results serve as
well motivated targets for the mono-neutrino search proposed here. Moreover,
the radiation of $\phi$ from the neutrino beam carries away two units of
lepton number. Thus, it also leads to “wrong sign” charged lepton production –
another striking signal that accompanies the missing transvers momentum.

We investigate the feasibility and prospects of using the DUNE near detectors
to hunt for the above signals, including the liquid argon TPC, for final state
tracking and momentum reconstruction, and a prospective magnetized gaseous
argon TPC, which is good at lepton charge identification. We estimate the
standard model background based on a simplified nucleon level simulation with
a final momentum smearing. Based on our analysis, we find it is well motivated
and feasible for the DUNE, as a multipurpose experiment, to efficiently probe
the presently allowed parameter space of neutrinophilic thermal dark matter.
Our result could be further improved in the future with more precise modeling
of nuclear recoils (see Friedland and Li (2018) for a recent discussion on
this topic) as well as realistic detector simulations. The search strategy
discussed here is applicable to other neutrino experiments such as the short
baseline neutrino program at Fermilab.

Although our discussion of the mono-neutrino signal has focused on the
coupling of $\phi$ to muon neutrinos, we hope it could inspire future
considerations on other neutrino flavors by exploring a broader range of
neutrino sources and detectors.

###### Acknowledgements.

We thank Jeffrey Berryman, Zackaria Chacko, André de Gouvêa, Roni Harnik,
Joshua Isaacson, Chris Marshall and Hai-Bo Yu for useful discussions. This
manuscript has been authored by Fermi Research Alliance, LLC under Contract
No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science,
Office of High Energy Physics. The work of Y.Z. is also supported by the DoE
under contract number DE-SC0007859. Y.Z. acknowledges a travel support from
the Colegio De Fisica Fundamental E Interdisciplinaria De Las Americas (COFI).

##  Appendix A Four Body Charged Meson Decay Through Off-shell Mediator $\phi$

Here we discuss the four-body final state of a meson decay,
$\mathfrak{m^{+}}\to\ell^{+}\overline{\nu}\phi^{*},$ $\phi^{*}\to\nu\nu$
(where $\phi^{*}$ denotes that the $\phi$ is off-shell and can even be heavier
than the meson $\mathfrak{m}$ in this case) and its charge-conjugate.
Following the four-body phase space developed in Ref. Anastasiou et al. (2004)
for massless final-state particles and extended to include one massive
particle (in our case, $\ell$) in Ref. Asatrian et al. (2012), we can write
the width of this process as

$\Gamma_{\mathfrak{m^{\pm}}\to\ell^{\pm}\nu\nu\overline{\nu}}=\frac{\lambda_{\alpha\beta}^{4}G_{F}^{2}f_{\mathfrak{m}}^{2}m_{\mathfrak{m}}^{5}}{2^{10}\pi^{6}}\int
g(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})d^{5}\vec{\lambda}\ ,$ (20)

where $G_{F}$ is the Fermi weak coupling; $f_{\mathfrak{m}}$ is the decay
constant of meson $\mathfrak{m}$; $m_{\mathfrak{m}}$, $m_{\phi}$, and
$m_{\ell}$ are the masses of $\mathfrak{m}$, the mononeutrino $\phi$, and
charged lepton $\ell$, respectively, and
$g(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})$ is a function of the
parameters $\lambda_{i}$, $i=1,\dots,5$. The integration over
$d^{5}\vec{\lambda}$ ranges over $\lambda_{i}=0$ to $\lambda_{i}=1$ for all
$i$. We write $g(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})$ as

$\begin{split}g(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})&=\frac{(1-\lambda_{2})^{2}\lambda_{2}m_{\mathfrak{m}}^{2}(1-\sqrt{x_{1}})^{4}s_{\lambda_{1}}}{4\sqrt{\lambda_{5}(1-\lambda_{5})}\left(\lambda_{1}(1-\lambda_{2})\lambda_{4}m_{\mathfrak{m}}^{2}m_{\phi}^{2}\left(f_{\Gamma}^{2}-2(1-\sqrt{x_{1}})^{2}\right)+\lambda_{1}^{2}(1-\lambda_{2})^{2}\lambda_{4}^{2}m_{\mathfrak{m}}^{4}(1-\sqrt{x_{1}})^{4}+m_{\phi}^{4}\right)}\\\
&\times\left[(\lambda_{1}-1)(2\lambda_{3}-1)s_{\lambda_{1}}\left(\lambda_{1}(1-\sqrt{x_{1}})^{2}+x_{1}-1\right)+\rule{0.0pt}{14.22636pt}\right.\\\
&\left.\sqrt{\lambda_{1}-1}\left((2\lambda_{3}-1)(1+\sqrt{x_{1}})\sqrt{\lambda_{1}^{2}-2\lambda_{1}(1+x_{1})+(1-x_{1})^{2}}+\lambda_{1}^{2}(\sqrt{x_{1}}-1)^{3}+\lambda_{1}(1+\sqrt{\lambda_{1}})\right)\right]\
,\end{split}$ (21)

where
$s_{\lambda_{1}}\equiv\sqrt{\lambda_{1}+(\lambda_{1}-1)x_{1}-2(1+\lambda_{1})\sqrt{x_{1}}-1}$.
The integrals over $\lambda_{3}$ and $\lambda_{5}$ are straightforward, and we
arrive at $h(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})\equiv\int
g(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})d\lambda_{3}d\lambda_{5}$,

$h(\vec{\lambda};m_{\mathfrak{m}},m_{\phi},m_{\ell})=\frac{\pi
m_{\mathfrak{m}}^{2}\lambda_{1}\lambda_{2}(1-\lambda_{2})^{2}(1-\sqrt{x_{1}})^{4}(1+\sqrt{x_{1}}+\lambda_{1}(\sqrt{x_{1}}-1)^{3})s_{\lambda_{1}}}{4\left(\lambda_{1}(1-\lambda_{2})\lambda_{4}(f_{\Gamma}^{2}-2(1-\sqrt{x_{1}})^{2})m_{\mathfrak{m}}^{2}m_{\phi}^{2}+\lambda_{1}^{2}(1-\lambda_{2})^{2}\lambda_{4}^{2}(1-\sqrt{x_{1}})^{4}m_{\mathfrak{m}}^{4}+m_{\phi}^{4}\right)}\
.$ (22)

For large $m_{\phi}\gg m_{\mathfrak{m}}$, this decay width can be solved
analytically. Keeping terms to $\mathcal{O}(m_{\mu}/m_{\mathfrak{m}})$, we
have the result:

$\Gamma_{\mathfrak{m^{\pm}}\to\ell^{\pm}\nu\nu\overline{\nu}}=\frac{\lambda_{\alpha\beta}^{4}G_{F}^{2}f_{\mathfrak{m}}^{2}m_{\mathfrak{m}}^{6}(m_{\mathfrak{m}}+4m_{\mu})}{2^{16}3^{2}\pi^{5}m_{\phi}^{4}}\
.$ (23)

## References

  * Acciarri et al. (2016a) R. Acciarri et al. (DUNE), “Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE),” (2016a), eprint 1601.05471.
  * Acciarri et al. (2015) R. Acciarri et al. (DUNE), “Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE),” (2015), eprint 1512.06148.
  * Acciarri et al. (2016b) R. Acciarri et al. (DUNE), “Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE),” (2016b), eprint 1601.02984.
  * Jungman et al. (1996) G. Jungman, M. Kamionkowski, and K. Griest, “Supersymmetric dark matter,” Phys. Rept. 267, 195 (1996), eprint hep-ph/9506380.
  * Bertone et al. (2005) G. Bertone, D. Hooper, and J. Silk, “Particle dark matter: Evidence, candidates and constraints,” Phys. Rept. 405, 279 (2005), eprint hep-ph/0404175.
  * Goodman and Witten (1985) M. W. Goodman and E. Witten, “Detectability of Certain Dark Matter Candidates,” Phys. Rev. D31, 3059 (1985), [,325(1984)].
  * Agashe et al. (2014) K. Agashe, Y. Cui, L. Necib, and J. Thaler, “(In)direct Detection of Boosted Dark Matter,” JCAP 1410, 062 (2014), eprint 1405.7370.
  * Chatterjee et al. (2018) A. Chatterjee, A. De Roeck, D. Kim, Z. G. Moghaddam, J.-C. Park, S. Shin, L. H. Whitehead, and J. Yu, “Searching for boosted dark matter at ProtoDUNE,” Phys. Rev. D98, 075027 (2018), eprint 1803.03264.
  * Bringmann and Pospelov (2018) T. Bringmann and M. Pospelov, “Novel direct detection constraints on light dark matter,” (2018), eprint 1810.10543.
  * Ema et al. (2018) Y. Ema, F. Sala, and R. Sato, “Light Dark Matter at Neutrino Experiments,” (2018), eprint 1811.00520.
  * Batell et al. (2009) B. Batell, M. Pospelov, and A. Ritz, “Exploring Portals to a Hidden Sector Through Fixed Targets,” Phys. Rev. D80, 095024 (2009), eprint 0906.5614.
  * Coloma et al. (2016) P. Coloma, B. A. Dobrescu, C. Frugiuele, and R. Harnik, “Dark matter beams at LBNF,” JHEP 04, 047 (2016), eprint 1512.03852.
  * Aguilar-Arevalo et al. (2017) A. A. Aguilar-Arevalo et al. (MiniBooNE), “Dark Matter Search in a Proton Beam Dump with MiniBooNE,” Phys. Rev. Lett. 118, 221803 (2017), eprint 1702.02688.
  * Aguilar-Arevalo et al. (2018) A. A. Aguilar-Arevalo et al. (MiniBooNE DM), “Dark Matter Search in Nucleon, Pion, and Electron Channels from a Proton Beam Dump with MiniBooNE,” (2018), eprint 1807.06137.
  * de Gouvêa et al. (2018) A. de Gouvêa, P. J. Fox, R. Harnik, K. J. Kelly, and Y. Zhang, “Dark Tridents at Off-Axis Liquid Argon Neutrino Detectors,” (2018), eprint 1809.06388.
  * Grossman et al. (2017) Y. Grossman, R. Harnik, O. Telem, and Y. Zhang, “Self-Destructing Dark Matter,” (2017), eprint 1712.00455.
  * Serra et al. (2010) P. Serra, F. Zalamea, A. Cooray, G. Mangano, and A. Melchiorri, “Constraints on neutrino – dark matter interactions from cosmic microwave background and large scale structure data,” Phys. Rev. D81, 043507 (2010), eprint 0911.4411.
  * Wilkinson et al. (2014) R. J. Wilkinson, C. Boehm, and J. Lesgourgues, “Constraining Dark Matter-Neutrino Interactions using the CMB and Large-Scale Structure,” JCAP 1405, 011 (2014), eprint 1401.7597.
  * Di Valentino et al. (2018) E. Di Valentino, C. Bøehm, E. Hivon, and F. R. Bouchet, “Reducing the $H_{0}$ and $\sigma_{8}$ tensions with Dark Matter-neutrino interactions,” Phys. Rev. D97, 043513 (2018), eprint 1710.02559.
  * Mangano et al. (2006) G. Mangano, A. Melchiorri, P. Serra, A. Cooray, and M. Kamionkowski, “Cosmological bounds on dark matter-neutrino interactions,” Phys. Rev. D74, 043517 (2006), eprint astro-ph/0606190.
  * Hannestad et al. (2014) S. Hannestad, R. S. Hansen, and T. Tram, “How Self-Interactions can Reconcile Sterile Neutrinos with Cosmology,” Phys. Rev. Lett. 112, 031802 (2014), eprint 1310.5926.
  * Dasgupta and Kopp (2014) B. Dasgupta and J. Kopp, “Cosmologically Safe eV-Scale Sterile Neutrinos and Improved Dark Matter Structure,” Phys. Rev. Lett. 112, 031803 (2014), eprint 1310.6337.
  * Bringmann et al. (2014) T. Bringmann, J. Hasenkamp, and J. Kersten, “Tight bonds between sterile neutrinos and dark matter,” JCAP 1407, 042 (2014), eprint 1312.4947.
  * Cherry et al. (2014) J. F. Cherry, A. Friedland, and I. M. Shoemaker, “Neutrino Portal Dark Matter: From Dwarf Galaxies to IceCube,” (2014), eprint 1411.1071.
  * Bertoni et al. (2015) B. Bertoni, S. Ipek, D. McKeen, and A. E. Nelson, “Constraints and consequences of reducing small scale structure via large dark matter-neutrino interactions,” JHEP 04, 170 (2015), eprint 1412.3113.
  * Binder et al. (2016) T. Binder, L. Covi, A. Kamada, H. Murayama, T. Takahashi, and N. Yoshida, “Matter Power Spectrum in Hidden Neutrino Interacting Dark Matter Models: A Closer Look at the Collision Term,” JCAP 1611, 043 (2016), eprint 1602.07624.
  * Davoudiasl et al. (2018) H. Davoudiasl, G. Mohlabeng, and M. Sullivan, “Galactic Dark Matter Population as the Source of Neutrino Masses,” Phys. Rev. D98, 021301 (2018), eprint 1803.00012.
  * Desai et al. (2004) S. Desai et al. (Super-Kamiokande), “Search for dark matter WIMPs using upward through-going muons in Super-Kamiokande,” Phys. Rev. D70, 083523 (2004), [Erratum: Phys. Rev.D70,109901(2004)], eprint hep-ex/0404025.
  * Choi et al. (2015) K. Choi et al. (Super-Kamiokande), “Search for neutrinos from annihilation of captured low-mass dark matter particles in the Sun by Super-Kamiokande,” Phys. Rev. Lett. 114, 141301 (2015), eprint 1503.04858.
  * Aartsen et al. (2015) M. G. Aartsen et al. (IceCube), “Search for Dark Matter Annihilation in the Galactic Center with IceCube-79,” Eur. Phys. J. C75, 492 (2015), eprint 1505.07259.
  * Adrian-Martinez et al. (2015) S. Adrian-Martinez et al. (ANTARES), “Search of Dark Matter Annihilation in the Galactic Centre using the ANTARES Neutrino Telescope,” JCAP 1510, 068 (2015), eprint 1505.04866.
  * Srednicki et al. (1987) M. Srednicki, K. A. Olive, and J. Silk, “High-Energy Neutrinos from the Sun and Cold Dark Matter,” Nucl. Phys. B279, 804 (1987).
  * Zentner (2009) A. R. Zentner, “High-Energy Neutrinos From Dark Matter Particle Self-Capture Within the Sun,” Phys. Rev. D80, 063501 (2009), eprint 0907.3448.
  * Chen and Zhang (2011) S.-L. Chen and Y. Zhang, “Isospin-Violating Dark Matter and Neutrinos From the Sun,” Phys. Rev. D84, 031301 (2011), eprint 1106.4044.
  * Gao et al. (2011) Y. Gao, J. Kumar, and D. Marfatia, “Isospin-Violating Dark Matter in the Sun,” Phys. Lett. B704, 534 (2011), eprint 1108.0518.
  * Batell et al. (2018) B. Batell, T. Han, and B. Shams Es Haghi, “Indirect Detection of Neutrino Portal Dark Matter,” Phys. Rev. D97, 095020 (2018), eprint 1704.08708.
  * Olivares-Del Campo et al. (2018) A. Olivares-Del Campo, C. Bœhm, S. Palomares-Ruiz, and S. Pascoli, “Dark matter-neutrino interactions through the lens of their cosmological implications,” Phys. Rev. D97, 075039 (2018), eprint 1711.05283.
  * Berryman et al. (2017) J. M. Berryman, A. de Gouvêa, K. J. Kelly, and Y. Zhang, “Dark Matter and Neutrino Mass from the Smallest Non-Abelian Chiral Dark Sector,” Phys. Rev. D96, 075010 (2017), eprint 1706.02722.
  * McKeen and Raj (2018) D. McKeen and N. Raj, “Monochromatic dark neutrinos and boosted dark matter in noble liquid direct detection,” (2018), eprint 1812.05102.
  * Ng and Beacom (2014) K. C. Y. Ng and J. F. Beacom, “Cosmic neutrino cascades from secret neutrino interactions,” Phys. Rev. D90, 065035 (2014), [Erratum: Phys. Rev.D90,no.8,089904(2014)], eprint 1404.2288.
  * Cherry et al. (2016) J. F. Cherry, A. Friedland, and I. M. Shoemaker, “Short-baseline neutrino oscillations, Planck, and IceCube,” (2016), eprint 1605.06506.
  * Argüelles et al. (2016) C. Argüelles, A. Kheirandish, and A. C. Vincent, “Constraining Dark Matter Neutrino Interaction with High Energy Neutrinos,” PoS ICHEP2016, 512 (2016), eprint 1612.08472.
  * Capozzi et al. (2017) F. Capozzi, I. M. Shoemaker, and L. Vecchi, “Solar Neutrinos as a Probe of Dark Matter-Neutrino Interactions,” JCAP 1707, 021 (2017), eprint 1702.08464.
  * Kelly and Machado (2018) K. J. Kelly and P. A. N. Machado, “Multimessenger Astronomy and New Neutrino Physics,” JCAP 1810, 048 (2018), eprint 1808.02889.
  * Berlin (2016) A. Berlin, “Neutrino Oscillations as a Probe of Light Scalar Dark Matter,” Phys. Rev. Lett. 117, 231801 (2016), eprint 1608.01307.
  * Krnjaic et al. (2018) G. Krnjaic, P. A. N. Machado, and L. Necib, “Distorted neutrino oscillations from time varying cosmic fields,” Phys. Rev. D97, 075017 (2018), eprint 1705.06740.
  * Brdar et al. (2018) V. Brdar, J. Kopp, J. Liu, P. Prass, and X.-P. Wang, “Fuzzy dark matter and nonstandard neutrino interactions,” Phys. Rev. D97, 043001 (2018), eprint 1705.09455.
  * Hu et al. (2000) W. Hu, R. Barkana, and A. Gruzinov, “Cold and fuzzy dark matter,” Phys. Rev. Lett. 85, 1158 (2000), eprint astro-ph/0003365.
  * Hui et al. (2017) L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, “Ultralight scalars as cosmological dark matter,” Phys. Rev. D95, 043541 (2017), eprint 1610.08297.
  * Davoudiasl and Murphy (2017) H. Davoudiasl and C. W. Murphy, “Fuzzy Dark Matter from Infrared Confining Dynamics,” Phys. Rev. Lett. 118, 141801 (2017), eprint 1701.01136.
  * Abercrombie et al. (2015) D. Abercrombie et al., “Dark Matter Benchmark Models for Early LHC Run-2 Searches: Report of the ATLAS/CMS Dark Matter Forum,” (2015), eprint 1507.00966.
  * Gelmini and Roncadelli (1981) G. B. Gelmini and M. Roncadelli, “Left-Handed Neutrino Mass Scale and Spontaneously Broken Lepton Number,” Phys. Lett. 99B, 411 (1981).
  * Barger et al. (1982) V. D. Barger, W.-Y. Keung, and S. Pakvasa, “Majoron Emission by Neutrinos,” Phys. Rev. D25, 907 (1982).
  * Berryman et al. (2018) J. M. Berryman, A. De Gouvêa, K. J. Kelly, and Y. Zhang, “Lepton-Number-Charged Scalars and Neutrino Beamstrahlung,” Phys. Rev. D97, 075030 (2018), eprint 1802.00009.
  * Aghanim et al. (2018) N. Aghanim et al. (Planck), “Planck 2018 results. VI. Cosmological parameters,” (2018), eprint 1807.06209.
  * Griest and Seckel (1991) K. Griest and D. Seckel, “Three exceptions in the calculation of relic abundances,” Phys. Rev. D43, 3191 (1991).
  * Kolb and Turner (1990) E. W. Kolb and M. S. Turner, “The Early Universe,” Front. Phys. 69, 1 (1990).
  * D’Eramo and Thaler (2010) F. D’Eramo and J. Thaler, “Semi-annihilation of Dark Matter,” JHEP 06, 109 (2010), eprint 1003.5912.
  * (59) C. Marshall, “https://indico.fnal.gov/event/18430/session/0/contribution/1/material/slides/0.pdf,”.
  * (60) J. Asaadi, “https://web.fnal.gov/organization/theory/JETP/2016/Asaadi_LArIAT_WC.pdf,”.
  * (61) A. Bross, “https://indico.fnal.gov/event/18430/session/0/contribution/0/material/slides/0.pdf,”.
  * (62) J. Sinclair, “https://indico.fnal.gov/event/18430/session/1/contribution/36/material/slides/0.pdf,”.
  * Martin-Albo (2017) J. Martin-Albo (DUNE), “A pressurized argon gas TPC as DUNE near detector,” J. Phys. Conf. Ser. 888, 012154 (2017), eprint 1610.07803.
  * (64) T. A. Mohayai, “https://indico.fnal.gov/event/18430/session/1/contribution/27/material/slides/0.pdf,”.
  * (65) C. McGrew, “https://indico.fnal.gov/event/18430/session/1/contribution/44/material/slides/0.pdf,”.
  * (66) C. Vilela, “https://indico.fnal.gov/event/18430/session/2/contribution/35/material/slides/0.pdf,”.
  * Alwall et al. (2011) J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, “MadGraph 5 : Going Beyond,” JHEP 06, 128 (2011), eprint 1106.0522.
  * (68) K. NGLES, T. JUNK, and A. MARCHIONNI, “https://indico.fnal.gov/event/14933/contribution/10/material/paper/0.pdf,”.
  * Vulpescu (1999) B. Vulpescu, Ph.D. thesis, Karlsruhe U., EKP (1999).
  * Acciarri et al. (2017) R. Acciarri et al. (MicroBooNE), “Michel Electron Reconstruction Using Cosmic-Ray Data from the MicroBooNE LArTPC,” JINST 12, P09014 (2017), eprint 1704.02927.
  * Caratelli (2017) D. Caratelli (MicroBooNE), “Michel Electron Reconstruction Using the MicroBooNE LArTPC Cosmic Data,” J. Phys. Conf. Ser. 888, 012185 (2017).
  * Acciarri et al. (2018) R. Acciarri et al. (ArgoNeuT), “Demonstration of MeV-Scale Physics in Liquid Argon Time Projection Chambers Using ArgoNeuT,” (2018), eprint 1810.06502.
  * Laha et al. (2014) R. Laha, B. Dasgupta, and J. F. Beacom, “Constraints on New Neutrino Interactions via Light Abelian Vector Bosons,” Phys. Rev. D89, 093025 (2014), eprint 1304.3460.
  * Nollett and Steigman (2015) K. M. Nollett and G. Steigman, “BBN And The CMB Constrain Neutrino Coupled Light WIMPs,” Phys. Rev. D91, 083505 (2015), eprint 1411.6005.
  * Escudero (2018) M. Escudero, “Neutrino Decoupling Beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and precise $N_{\rm eff}$ evaluation,” (2018), eprint 1812.05605.
  * Berlin and Blinov (2018) A. Berlin and N. Blinov, “Thermal Dark Matter Below an MeV,” Phys. Rev. Lett. 120, 021801 (2018), eprint 1706.07046.
  * Randall et al. (2008) S. W. Randall, M. Markevitch, D. Clowe, A. H. Gonzalez, and M. Bradac, “Constraints on the Self-Interaction Cross-Section of Dark Matter from Numerical Simulations of the Merging Galaxy Cluster 1E 0657-56,” Astrophys. J. 679, 1173 (2008), eprint 0704.0261.
  * Buckley and Fox (2010) M. R. Buckley and P. J. Fox, “Dark Matter Self-Interactions and Light Force Carriers,” Phys. Rev. D81, 083522 (2010), eprint 0911.3898.
  * Tulin et al. (2013) S. Tulin, H.-B. Yu, and K. M. Zurek, “Resonant Dark Forces and Small Scale Structure,” Phys. Rev. Lett. 110, 111301 (2013), eprint 1210.0900.
  * Rajaraman and Smolinsky (2018) A. Rajaraman and J. Smolinsky, “Self-Interacting Dark Matter Through the Majoron Portal,” (2018), eprint 1811.06619.
  * Tulin and Yu (2018) S. Tulin and H.-B. Yu, “Dark Matter Self-interactions and Small Scale Structure,” Phys. Rept. 730, 1 (2018), eprint 1705.02358.
  * Friedland and Li (2018) A. Friedland and S. W. Li, “Understanding the energy resolution of liquid argon neutrino detectors,” (2018), eprint 1811.06159.
  * Anastasiou et al. (2004) C. Anastasiou, K. Melnikov, and F. Petriello, “A new method for real radiation at NNLO,” Phys. Rev. D69, 076010 (2004), eprint hep-ph/0311311.
  * Asatrian et al. (2012) H. M. Asatrian, A. Hovhannisyan, and A. Yeghiazaryan, “The phase space analysis for three and four massive particles in final states,” Phys. Rev. D86, 114023 (2012), eprint 1210.7939.