#### Dark matter and exotic neutrino interactions in direct detection searches

Received: February
matter and exotic neutrino interactions in direct
Enrico Bertuzzo 0 1 2 4 5
Frank F. Deppisch 0 1 2 3 5
Suchita Kulkarni 0 1 2 5
Yuber F. Perez Gonzalez 0 1 2 4 5
Renata Zukanovich Funchal 0 1 2 4 5
London WC 0 1 2 5
E 0 1 2 5
BT 0 1 2 5
U.K. 0 1 2 5
E-mail: 0 1 2 5
0 1 2 5
Open Access 0 1 2 5
c The Authors. 0 1 2 5
0 Working within a simpli ed
1 Nikolsdorfer Gasse 18 , 1050 Wien , Austria
2 R. do Mata~o 1371, CEP. 05508-090, S~ao Paulo , Brazil
3 Department of Physics and Astronomy, University College London
4 Departamento de F sica Matematica, Instituto de F sica, Universidade de S~ao Paulo
5 nuclei. Using existing data
We investigate the e ect of new physics interacting with both Dark Matter (DM) and neutrinos at DM direct detection experiments. model formalism, we consider vector and scalar mediators to determine the scattering of DM as well as the modi ed scattering of solar neutrinos o from LUX as well as the expected sensitivity of LUX-ZEPLIN and DARWIN, we set limits on the couplings of the mediators to quarks, neutrinos and DM. Given the current limits, we also assess the true DM discovery potential of direct detection experiments under the presence of exotic neutrino interactions. In the case of a vector mediator, we show that the DM discovery reach of future experiments is a ected for DM masses m . 10 47 cm2. On the other hand, a scalar mediator will
cInstitut fur Hochenergiephysik; Osterreichische Akademie der Wissenschaften
1 Introduction The framework Vector mediator Scalar mediator
Introduction
Scattering at direct detection experiments
Neutrino and dark matter scattering
Recoil events induced by DM and neutrino scattering
Background free sensitivity in the presence of exotic neutrino interactions
Current and future limits on DM-neutrino interactions
Sensitivity to DM-nucleon scattering in presence of exotic neutrino
inThe Standard Model (SM) of particle physics, despite its enormous success in describing
experimental data, cannot explain DM observations. This has motivated a plethora of
Beyond the Standard Model (BSM) extensions. Despite intense searches, none of these
BSM extensions have been experimentally observed, leaving us with little knowledge of the
exact nature of DM.
The lack of an experimentally discovered theoretical framework that connects the SM
degrees of freedom with the DM sector has led to a huge activity in BSM model
building. Among various DM scenarios, the Weakly Interacting Massive Particle (WIMP) DM
remains the most attractive one, with several experiments actively searching for signs of
Within this paradigm, DM is a stable particle by virtue of a Z2 symmetry
under which it is odd. The WIMP interactions with the SM particles can be detected
via annihilation (at indirect detection experiments), production (at collider experiments)
and scattering (at direct detection experiments). If the WIMP idea is correct, the Earth
is subjected to a wind of DM particles that interact weakly with ordinary matter, thus
direct detection experiments form a crucial component in the experimental strategies to
At direct detection experiments, WIMP interactions are expected to induce nuclear
recoil events in the detector target material. These nuclear recoils can be in most detectors,
discriminated from the electron recoils produced by other incident particles. Depending
on the target material and the nature of DM | SM interactions, two di erent kind of DM
interactions can be probed: spin-dependent and spin-independent DM | nucleus
scattering. The current limits for spin-independent DM-nucleus interactions are considerably
more stringent, and the next generation of direct detection experiments will probe the
spin-independent interactions even further by lowering the energy threshold and increasing
A signal similar to DM scattering can also be produced by coherent neutrino scattering
nuclei (CNSN) in DM direct detection experiments [1{3], hence constituting a
background to the WIMP signal at these experiments. Unlike more conventional backgrounds
such as low energy electron recoil events or neutron scattering due to ambient
radioactivity and cosmic ray exposure, the CNSN background can not be reduced. The main
sources contributing to the neutrino background are the
uxes of solar and atmospheric
neutrinos [4], both fairly well measured in neutrino oscillation experiments [5, 6]. Within
the SM, CNSN originates from the exchange of a Z boson via neutral currents. Given
the minuscule SM cross-section
CNSN < 10 39 cm2 for neutrino energies < 10 MeV, and
the insensitivity of the existing DM detectors to this cross-section, CNSN events have yet
to be experimentally observed. The minimum DM | nucleus scattering cross-section at
which the neutrino background becomes unavoidable is termed the neutrino
oor [7]. In
fact, the neutrino oor limits the DM discovery potential of direct detection experiments,
so diminishing the uncertainties on the determination of solar and atmospheric neutrino
uxes as well as the direct measurement of CNSN is very important. Fortunately,
dedicated experiments are being developed to try to directly detect CNSN [8, 9] in the very
The absence of any WIMP signal at the existing direct detection experiments has
resulted in the need for next generation experiments. It is expected that these experiments
will eventually reach the sensitivity to measure solar (and perhaps atmospheric) neutrinos
from the neutrino
oor. It thus becomes important to analyse the capacity of these
experiments to discriminate between DM and neutrino scattering events. It has been shown
that a su ciently strong Non-Standard Interaction (NSI) contribution to the neutrino |
nucleus scattering can result in a signal at direct detection experiments [10{13]. Several
attempts have been made to discriminate between DM scattering and neutrino scattering
The cases considered so far involve the presence of BSM in either the neutrino scattering
or the DM sector. However, it is likely that a BSM mediator communicates with both the
neutrino and the DM sector, and the DM and a hidden sector may even be responsible
for the light neutrino mass generation [17]. In such cases, it is important to consider the
combined e ect of neutrino and DM scattering at direct detection experiments. In this
work we analyse quantitatively the e ect of the presence of BSM physics communicating
to both the neutrinos and the DM sector on the DM discovery potential at future direct
detection experiments.
The paper is organized as follows. In section 2 we de ne the simpli ed BSM models
we consider while section 3 is dedicated to calculational details of neutrino scattering and
DM scattering at direct detection experiments. Equipped with this machinery, in section 4,
we describe the statistical procedure used to derive constraints for the existing and future
experiments. We consider the impact of the BSM physics in the discovery potential of
direct detection experiments in section 5. Finally, we conclude in section 6.
The framework
Working within the framework of simpli ed models, we consider scenarios where the SM
is extended with one DM and one mediator eld. The DM particle is odd under a Z2
symmetry, while the mediator and the SM content is Z2 even. The symmetry forbids
the decay of DM to SM particles and leads to 2 ! 2 processes between SM and DM
sector which results in the relic density generation, as well as signals at (in)direct detection
To be concrete, we extend the SM sector by a Dirac DM fermion, , with mass m and
consider two distinct possibilities for the mediator. In our analysis we will only specify the
couplings which are relevant for CNSN and DM-nucleus scattering, namely, the couplings
of the mediator to quarks, neutrinos and DM. We will explicitly neglect mediator couplings
to charged leptons, and comment brie y on possible UV-complete models.
Vector mediator
In this scenario, we extend the SM by adding a Dirac fermion DM, , with mass m
a real vector boson, V , with mass mV . The relevant terms in the Lagrangian are:
where the currents are
Lvec = V (Jf + J ) +
f =
Af are the vector and axial-vector couplings of SM fermions to the vector
mediator V , while g
A de ne the vector and axial-vector couplings between the
mediator V and
. The Lagrangian contains both left-and right-handed currents, thus
implicitly assuming the presence of an extended neutrino sector either containing sterile
neutrinos or right-handed species. We will not go into the details of such an extended
neutrino sector, simply assuming the presence of such left-and right-handed currents and
dealing with their phenomenology.
Following the general philosophy of simpli ed DM models [18, 19], we write our e ective
theory after electroweak symmetry breaking (EWSB), assuming all the couplings to be
independent. This raises questions about possible constraints coming from embedding such
simpli ed models into a consistent UV-completion. The case of a U(1) gauge extension
has for example been studied in [20], where it has been shown that, depending on the
vector-axial nature of the couplings between the vector and the fermions (either DM or
SM particles), large regions of parameter space may be excluded.1 In our case we allow
1Even without considering the additional fermionic content which may be needed to make the model
the possibility of di erent couplings between the members of weak doublets, i.e. terms
with isospin breaking independent from the EWSB. As shown in [21], such a possibility
to be very small. Moreover, we expect a non-trivial contribution of the isospin breaking
sector to electroweak precision measurements, in particular to the T parameter. Since the
analysis is however highly model dependent, we will not pursue it here.
We brie y comment here on collider limits for the new neutral vector boson. For
mV < 209 GeV, limits from LEP I [22], analyzing the channel e+e
its mixing with the Z boson has to be < 10 3, implying the new gauge coupling to be
< 10 2. This limit can be evaded in the case of a U(1) gauge extension, if the new charges
, impose that
are not universal and the new boson does not couple (or couples very weakly) to muons or
by small U(1) charges in extensions involving extra scalar elds (See, for instance, eq. (2.5)
of ref. [23]). For mV > 209 GeV, there are also limits from LEP II [24], Tevatron [23] and
the LHC [25{27]. Since these limits depend on the fermion U(1) charges, they can be either
avoided or highly suppressed.
Scalar mediator
For a scalar mediator, we extend the SM by adding a Dirac fermion DM, , with mass m
and a real scalar boson, S, with mass mS. The relevant terms in the Lagrangian with the
associated currents are
Lsc = S @
The couplings gSf and gS de ne the interaction between the scalar and the SM and the
DM sectors, respectively. Similar to the vector mediator interactions, the presence of an
extended neutrino sector is assumed in the scalar mediator Lagrangian as well. Since in this
work we will focus on the spin-independent cross-section at direct detection experiments,
we consider only the possibility of a CP even real scalar mediator.
For a scalar singlet it is easier to imagine a (possibly partial) UV-completion. Take,
for example, the case of a singlet scalar eld S added to the SM, which admits a quartic
dimension 6 operators such as S2`LHeR are generated (with `L and eR being the SM
lepton doublets and singlets), which after spontaneous symmetry breaking and for energies
HS jHj2S2 and takes the vacuum expectation value (VEV) vS. Non local
= 21 arctan( HS vvS=(m2S
m2H )) and yf is the fermion Yukawa coupling. The coupling
with neutrinos can be arranged for example in the case of a neutrinophilic 2HDM [28, 29].
Typical values of gSf can be inferred from the speci c realization of the simpli ed model, but
in the remainder of this paper, we will remain agnostic about realistic UV-completions in
which the simpli ed models we consider can be embedded, focusing only on the information
that can be extracted from CNSN. We stress however that, depending upon the explicit
UVcompletion, other constraints apply and must be taken into account to assess the viability
of any model. For example, in generic BSM scenarios with a new mediator coupling to
fermions, the dijet and dilepton analyses at the LHC put important bounds, as has been
exempli ed in [30, 31]. In this paper we aim to concentrate only on the constraints arising
from direct detection experiments.
Scattering at direct detection experiments
Neutrino and dark matter scattering
Let us now remind the reader about the basics of CNSN. In the SM, coherent neutrino
nuclei is mediated by neutral currents. The recoil energy released by the
neutrino scattering can be measured in the form of heat, light or phonons. The di erential
cross-section in terms of the nuclear recoil energy ER reads [7]
= (QSVM)2F 2(ER) G2F mN
with the SM coupling factor
SM = N + (4s2W
Here, N and Z are the number of neutrons and protons in the target nucleus, respectively,
F (ER) the nuclear form factor, E the incident neutrino energy and mN the nucleus mass
we use the nuclear form factor [32]
F (ER) = 3 j1 (q(ER)rN ) exp
exchanged during the scattering, mn ' 932 MeV the nucleon mass, s
0:9 the nuclear
In the case of the vector model de ned in eq. (2.1), the di erential cross-section gets
modi ed by the additional V exchange. The total cross-section should be calculated as a
coherent sum of SM Z and vector V exchange, and reads
GV = 1 +
2 QV g
Here, the coupling factor QV of the exotic vector boson exchange is given by [33]
QV = (2Z + N )gVu + (2N + Z)gVd ;
and q2 =
2 mN ER is the square of the momentum transferred in the scattering process. To
obtain eq. (3.4), we assumed that the neutrino production in the sun is basically una ected
by the presence of NP, in such a way that only LH neutrinos hit the target. As expected,
the interference term proportional to gV
gA can give both constructive and destructive
interference; in particular, remembering that q2
negative, we have constructive interference for gV < gA. For a detailed discussion of the
interference e ects at direct detection using e ective theory formalism, see [34]. As a last
remark, let us notice that, due to the same Dirac structure of the SM and NP amplitudes,
the correction to the di erential cross-section amounts to an overall rescaling of the SM one.
For the simpli ed model with a scalar mediator de ned in eq. (2.3), the di erential
cross-section has a di erent form,
GS = jgSjQS
In this case, the modi ed di erential cross-section is not simply a rescaling of the SM
amplitude, but due to the di erent Dirac structure of the S
vertex with respect to the
SM vector interaction, it may in principle give rise to modi cation of the shape of the
distribution of events as a function of the recoil energy. However, as we will see, for all
practical purposes the impact of such modi cation is negligible.
Using the analysis presented in [33], the coupling factor for the scalar boson exchange
is given by
QS = Zmn 4
q=c;b;t mq 5
The form factors fTpq; fTnq capture the e ective low energy coupling of a scalar mediator to
a proton and neutron, respectively, for a quark avor q. For our numerical analysis we use
fT u = 0:0153, fTpd = 0:0191, fTnu = 0:011, fTnd = 0:0273 and fTp;sn = 0:0447, which are the
p
values found in micrOMEGAs [35]. A more recent determination of some of these form
factors can be found in refs. [36, 37], we have used this estimation to determine the e ect
of the form factors on our nal result (see section 5).
of purely SM interactions with no additional contributions from exotic interactions. For
the scalar case, the situation is much di erent. GS includes QS, a quantity dependent
on the target material. For LUX, QS
couplings, hence for jgSj
1362 gSq, considering universal quark-mediator
100 GeV, natural values of GS are
Turning now to DM, its scattering o the nucleus can give rise to either spin-independent
or spin-dependent interactions. In our analysis we will consider only the spin-independent
scattering,2 as the next generation experiments sensitive to this interaction will also be
sensitive to neutrino scattering events. The spin-independent di erential cross-section in
2For the mediators we consider here, the spin-dependent cross-section is in fact velocity suppressed by
v2, see for instance [38].
each of the two simpli ed models is given by
= F 2(ER) (gS )2Q2S
with the energy E of the incident DM particle and all other variables as previously de ned.
Recoil events induced by DM and neutrino scattering
Given the detector exposure, e ciency and target material, the above speci ed di erential
cross-sections can be converted into recoil event rates.
We rst look at the recoil event rate induced by neutrino scattering, where the di
erential recoil rate is given by
= N
=dER is the di erential
cross-section as computed in eqs. (3.4){(3.6) for the vector and scalar mediator models,
respectively. For our numerical analysis, we use the neutrino
uxes from [3]. Integrating
the recoil rate from the experimental threshold Eth up to 100 keV [7], one obtains the
number of neutrino events
Ev =
"(ER) dER ;
to be computed for either the scalar or the vector mediator models. Here, Eth is the
detector threshold energy and "(ER) is the detector e ciency function.
For the DM scattering o nuclei, the di erential recoil rate also depends on
astrophysical parameters such as the local DM density, the velocity distribution and it is given as
= N mN m
velocity, vmin(ER) is the minimum DM speed required to cause a nuclear recoil with energy
ER for an elastic collision and f (v) the DM velocity distribution in the Earth's frame of
reference. This distribution is in principle modulated in time due to the Earth's motion
around the Sun, but we ignore this e ect here as it is not relevant for our purposes. If the
detector has di erent target nuclides, one has to sum over all their weighed contributions
as, for instance, is done in ref. [39].
In what follows we will assume a Maxwell-Boltzmann distribution, given as
f (v) = <> Nesc (2
taken from [33].
eq. (3.12) as
In order to constrain only the DM-nucleon interaction cross-section
n at zero
momentum transfer, which is independent of the type of experiment, it is customary to write
= N 2 2n m
n =
Z 2 2N v2=mN d SI (ER = 0)
as a function of energy thresholds in the range 10 4 keV
102 keV, varied in
logarithmic steps. For each threshold we then compute the background-free exclusion
expression analogous to eq. (3.11), explicitly
Ev =
"(ER) dER :
Background free sensitivity in the presence of exotic neutrino interactions
The presence of CNSN at direct detection experiments highlights the existence of a
minimal DM - nucleon scattering cross-section below which CNSN events can not be avoided
and in this sense the direct detection experiments no longer remain background free. This
minimum cross-section is di erent for di erent experiments, depending on the detector
threshold, exposure and target material. Using the de nition given in eq. (3.15), it is
possible to represent the CNSN in the (m ;
n) plane introducing the so-called one neutrino
event contour line. This line essentially de nes the DM mass dependent threshold/exposure
pairs that optimise the background-free sensitivity estimate at each mass while having a
background of one neutrino event. The presence of additional mediators will modify this
minimum cross-section with respect to the SM and hence, modify the maximum reach of
an experiment. In this section, we show how the one neutrino event contour line changes
due to the additional vector and scalar mediators considered in eq. (3.4) and (3.6).
To compute the one neutrino event contour line we closely follow ref. [7]. Considering,
for instance, a ctitious Xe target experiment, we determine the exposure to detect a single
E (Eth) =
Ev = 1
V = 0.3
V = 2.3
V = 3.6
S = 29.2
S = 52.3
S = 82.8
detector. We show on the left (right) panel three examples for the vector (scalar) mediator. We also
show the SM one neutrino event contour line (in blue) for comparison. The red star is a point for
which we will show the energy spectrum. The green region is excluded by LUX at 90% of C.L. [41].
limits, de ned at 90% C.L. as the curve in which we obtain 2.3 DM events for the computed
n =
If we now take the lowest cross-section of all limits as a function of the DM mass,
we obtain the one neutrino event contour line, corresponding to the best background-free
sensitivity achievable for each DM mass for a one neutrino event exposure. Let us stress
that the one neutrino event contour line, as de ned in this section, is computed with a
100% detector e ciency. The e ect of a nite detector e ciency will be taken into account
in section 5 when we will compute how the new exotic neutrino interactions can a ect
the discovery potential of direct detection DM experiments. Comparing eq. (3.18) with
eqs. (3.12) and (3.15), we see that the simpli ed models introduced in section 2 can modify
the one neutrino event contour line. In fact, such modi cations have been studied in
speci c models with light new physics e.g. in [10]. We show in
gure 1 some examples
of a modi ed "one neutrino event contour line for our models,
xing the values of the
parameters GV and GS as speci ed in the legends. These parameters have been chosen to
be still allowed by current data, see sections 4 and 5. The left panel of the gure describes
changes in the one-neutrino event contour line in presence of a new vector mediator. As
will be explained below, it is possible to have cancellation between SM and exotic neutrino
For the vector case the one-neutrino event contour line is e ectively a rescaling of the SM
case. Figure 1 (right panel) on the other hand shows modi cation of the contour line for
a scalar mediator. Note that unlike in the vector scenario, the factor GS has a di erent
normalization. No signi cant change in the one-neutrino event contour line is expected in
the scalar case.
reduction of the CNSN cross session according to eqs. (3.19) and (3.20).
There are a few remarks we should make here. First, it is possible, in the context of the
vector mediator model, to cancel the SM contribution to CNSN and completely eliminate
the neutrino background. For mediator masses heavy enough to neglect the q2 dependence
of the cross-sections, this happens when, cf. with eq. (3.4),
A = QV
SM GF m2V =
where for the last equality we assume gVu = g
Vd = g
V is a numerical value that
depends only on the target nucleus. We show in table 1 the values of aV for various nuclei.
Second, in the case of the scalar scenario, it is possible to compensate for only part of
the SM contribution to the CNSN. Inspecting eqs. (3.1) and (3.6) we see that the positive
in an e ective increase of the cross-section. This is accomplished for
gS = QV
SM GF m2S =
where again aS is a numerical value that depends only on the target nucleus. Its value for
di erent nuclei are shown in table 1. We show in the right panel of gure 1 an example
Finally, we should note that the one neutrino event contour line only gives us a
preliminary estimate of the minimum cross-sections that can be reached by a DM direct detection
experiment. It is worth recalling that this estimate is a background-free sensitivity.
Interactions modifying both neutrino and DM sector physics will lead to a non-standard neutrino
CNSN background which should be taken into account. Furthermore, the compatibility of
the observed number of events should be tested against the sum of neutrino and DM events.
In this spirit, to answer the question what is the DM discovery potential of an experiment?
one has to compute the real neutrino
oor. This will be done in section 5, which will
include a more careful statistical analysis taking into account background uctuations and
the experimental e ciency.
Current and future limits on DM-neutrino interactions
When new physics interacts with the DM and neutrino sector, the limits from direct
detection experiments become sensitive to the sum of DM and neutrino scattering events. A
natural question to ask is the capacity of current experiments to constrain this sum. The
aim of this section is to assess these constraints and derive sensitivities for the next
generation of direct detection experiments. For the analysis of the current limits we consider the
results of the Large Underground Xenon (LUX) [41] experiment. This choice is based on
the fact that this experiment is at present the most sensitive one probing the m
region on which we focus. On the other hand, for the future perspectives we will consider
two Xe target based detectors: the one proposed by the LUX-ZonEd Proportional
scintillation in LIquid Noble gases (LUX-ZEPLIN) Collaboration [42] and the one proposed by
the DARk matter WImp search with liquid xenoN (DARWIN) Collaboration [43].
Current bounds. LUX is an experiment searching for WIMPs through a dual phase
Xe time projection chamber. We will consider its results after a 3:35
104 kg-days run
presented in 2016 [41], performed with an energy threshold of 1:1 keV. We also use the
e ciency function "(ER) reported in the same work.
In order to assess the constraining power of current LUX results for the two models
presented in eqs. (2.1){(2.3), we compute the total number of nuclear recoil events expected
at each detector as
parameter space.
Evtotal = Ev + Ev :
Using this total number of events, we compute a likelihood function constructed from a
Poisson distribution in order to use their data to limit the parameters of our models,
L(^jN ) = P (^jN ) =
where ^ indicates the set of parameters of each model, N the observed number of events, b
the expected background and (^) is the total number of events Evtotal. According to [14]
Maximizing the likelihood function we can obtain limits for the di erent planes of the
In the case of the vector model, we performed a scan of the parameter space in the
500 GeV, 710 GeV and 103 GeV.
while we always choose g
limits in gure 2 for
gV =m2V = 10 6 GeV 2,3 and
4 GeV 2 (right), which
2 = p
limit. In each case, we show the results for three values of the DM mass, m
= 10 GeV
(violet), 15 GeV (red) and 50 GeV (green). We see that we can clearly distinguish two
regions: for
2 = 10 6 GeV 2, when jgV
4 the DM contribution is the
dominant one (in particular, as jgV
at most the SM one), and sets jgV j < 2
gAj ! 0 the contribution to the neutrino
= 10 (50) GeV.
100 GeV, 315 GeV,
10--610 -8 -6 -4 -2 0 2 4 6 8 10
Λ-V2 = 10-6 GeV-2, Current Limit Λ-V2 = 4 π GeV-2, Current Limit
of the vector model. The coloured region can be excluded at 90% C.L. by current LUX data [44]
(continuous lines) and by the future LUX-ZEPLIN [42] (dashed lines) and DARWIN [43]
experiments (dotted lines). The plots are for m
for two di erent cases:
2 = 10 6 GeV 2 (left) and
2 = p
GeV 2 (right). For simplicity,
in the latter case we only show the DARWIN future sensitivity, since the LUX-ZEPLIN results are
qualitatively similar but a factor of
4-10 less sensitive.
2 =
= 10 (50) GeV and jgV
On the other hand, for larger values of jgV
gAj, the number of neutrino events rapidly
becomes dominant and no bound on the DM-mediator coupling can be set. For the extreme
4 GeV 2, one can set the limits jgV j < 4:3
Inspection of gure 2 shows two peculiar features: an asymmetry between the bounds
on positive and negative values of gV
gA, and the independence of these limits on the DM
mass. We see from eq. (3.4) that the asymmetry can be explained from the dependence of
ΛS-2 = 10-6 GeV-2, Current Limit ΛS-2 = 4 π GeV-2, Current Limit
di erent cases:
S 2 = 10 6 GeV 2 (left) and
S 2 = p
4 GeV 2 (right).
the scalar model. The coloured region can be excluded at 90% C.L. by current LUX data [44]
(continuous lines) and by the future LUX-ZEPLIN [42] (dashed lines) and DARWIN [43] experiments
(dotted lines). The plots are for m
the interference term on the sign of gV
gA. Such interference is positive for gV
explaining why the bounds on negative gV
gA are stronger. As for the independence of
A bounds from the DM mass, this can be understood from the fact that when
V becomes su ciently small we e ectively reach the gV ! 0 limit in which the DM mass
is not relevant.
Turning to the bounds that the current LUX results impose on the parameter space
of the scalar model, we varied the parameters in the ranges
2 =
Our results are presented in gure 3. On the top left (right) panel, xing
4 GeV 2), for m
(green). From these plots we see that LUX can limit jgS j < 4:5
= 10 (50) GeV if jgSj < 0:5, when
4 GeV 2, we get the bound jgS j < 1:3
2 = 10 6 GeV 2
. For the limiting case
= 10 (50) GeV
2 =
2 = 10 6 (= p
As gS ! 0, the contribution to the neutrino oor tends to the SM one, except for a
particular value of gS gSq, as discussed at the end of the previous section. In the opposite
limit, i.e. where the neutrino oor dominates, gS ! 0, the current limit is jgSj < 0:7 (jgSj <
. As in the vector case, we see that this bound
does not depend on the DM matter mass, for the same reasons explained above.
Future sensitivity.
To assess the future projected LUX-ZEPLIN sensitivity, we will
assume an energy threshold of 6 keV, a maximum recoil energy of 30 keV and a future
exposure of 15:34 t-years [42]. According to the same reference, we use a 50% e ciency for
the nuclear recoil. For DARWIN, we will consider an aggressive 200 t-years exposure, no
nite energy resolution but a 30% acceptance for nuclear-recoil events in the energy range
of 5{35 keV [43].
Let us now discuss the bounds that can be imposed on the parameter space of our
models in case the future experiments LUX-ZEPLIN and DARWIN will not detect any
signal. We scan the parameter space over the ranges of eqs. (4.3) and (4.4), obtaining the
exclusion at 90% C.L. The results are presented in the bottom panels of gure 2 ( gure 3)
for the vector (scalar) model.
In the region in which the DM events dominate, we see that LUX-ZEPLIN will be
able to improve the bound on jgV j and jgS j by a factor between 2 and 10 depending on the
DM mass, while another order of magnitude improvement can typically be reached with
DARWIN. However, we also see that, somehow contrary to expectations, the bounds on
the neutrino couplings are expected to be less stringent than the present ones. While the
e ect is not particularly relevant in the vector case, we can see that in the scalar case the
LUX-ZEPLIN sensitivity is expected to be about a factor of 4 worse than the current LUX
limit. This is due to the higher threshold of the experiment, that limits the number of
measurable solar neutrino events. As such, a larger jgS j is needed to produce a su ciently
large number of events, diminishing the constraining power of LUX-ZEPLIN. While in
principle this is also true for the DARWIN experiment, the e ect is compensated by the
aggressive expected exposure.
Sensitivity to DM-nucleon scattering in presence of exotic neutrino
In section 3, we computed the background-free sensitivity of direct detection experiments in
presence of exotic neutrino interactions. However, what is the true 3
discovery potential
given the exotic neutrino interactions background remains unanswered. In this section, we
perform a detailed statistical analysis, taking into account the estimated background and
observed number of events and comparing these against the DM and neutrino interaction
via a pro le likelihood analysis.
To assess the DM discovery potential of an experiment we calculate, as in ref. [45], the
minimum value of the scattering cross-section
n as a function of m
that can be probed
by an experiment. This de nes a discovery limiting curve that is the true neutrino
of the experiment. Above this curve the experiment has a 90% probability of observing a
DM detection. This is done by de ning a binned likelihood function [46, 47]
where we have a product of Poisson probability distribution functions (P) for each bin i
ux normalization, L( j ) [47]. The neutrino (Ev ) and DM (Ev ) number
of events were computed according to eqs. (3.11) and (3.16), respectively. For each
neuuxes from solar and atmospheric
neutrinos are denoted by
is a collection of the extra parameters (gVq;S, gV;S,
etc.) to be taken into account in the model under consideration. Since we will introduce
the discovery limit in the DM cross-section, note that we will keep the DM-mediator
coupling gV;S free. For this study, we considered only the contribution of the 8B and hep solar
and atmospheric neutrinos, due to the thresholds of the considered experiments. For a
xed DM mass, we can use eq. (5.1) to test the neutrino-only hypothesis H0 against the
neutrino+DM hypothesis H1 constructing the ratio
times, Z90, given by
where ^ and ^ n are the values of the uxes and DM cross-section that maximize the
each mass m
and cross-section
n we build a probability density function p(ZjH0) of the
test statistics under H0, the neutrino only hypothesis. This is performed by constructing
2 ln (0) [45{47]. Finally, we compute the signi cance that can be achieved 90% of the
p(ZjH0) dZ = 0:90 :
Therefore, the minimum value for the cross-section for which the experiment has 90%
probability of making a 3
DM discovery is de ned as the value of
n that corresponds
to Z90 = 3.
In gure 4 we can see the neutrino oor considering only the SM contribution to the
CNSN (dark blue) as well as the result for some illustrative cases, in the vector mediator
scenario, for the LUX-ZEPLIN experiment with two di erent energy thresholds. The case
V = 0.3
V = 2.3
V = 3.6
V = 0.3
V = 2.3
V = 3.6
coupling was obtained considering V 2 = 10 6 GeV2.
results are for the LUX-ZEPLIN experiment with two di erent energy thresholds: a very low one,
SM neutrino oor (dark blue) is shown, along with the most extreme case still allowed for the vector
2 = p
4 GeV 2. Above this curve a 3
can be achieved by the experiment, while below this curve it is di cult to discriminate
between a DM signal and a non-standard (vector mediated) contribution to the neutrino
with the opposite sign to the SM one, so it actually cancels some of the standard signal.
same phenomenon noticed in the literature: close to a DM mass of 6 GeV, the discovery
limit is substantially worsened because of the similarity of the spectra of 8B neutrinos and
the WIMP, see, for instance [45]. However, the minimum cross-section that can be probed
is di erent for each parameter GV , due to the contribution of the vector mediator. For the
limit according to the value of GV .
In gure 5 we can see the neutrino oor considering only the SM contribution to the
current limit on jgSj ( < 2 10 7) for
2 = p
CNSN (dark blue) as well as the result for some illustrative cases, in the scalar mediator
scenario, for the LUX-ZEPLIN experiment with two di erent energy thresholds. Here the
4 GeV 2. In the case of the lower threshold,
we see that the point where the discovery limit is highly a ected due to the 8B neutrinos
is displaced close to a mass of 7 GeV. This shift of the distribution is provoked by the
extra factor that appears in the scalar case with respect to the SM (see eq. (3.6)). For the
Therefore, we see that contrary to the vector case, the scalar contribution does not a ect
S = 58.4
S = 82.8
S = 58.4
S = 82.8
very much the discovery reach of the experiment as compared to the one limited by the
standard CNSN.
In gure 6 we show the behavior of the number of CNSN events as a function of the
energy threshold of the detector and for a detector e ciency varying from 40% to 60%.
of the LUX experiment for the vector and scalar mediator models, the number of neutrino
events for Eth
1 keV are basically the same and both about 10 times larger than the SM
contribution. However, for the choices Eth
0:1 keV (lower threshold) and Eth
(higher threshold) used in
gures 4 and 5, the number of CNSN events for the vector
model is about 4 times larger than that for the scalar model, explaining the di erence in
sensitivity for the vector and scalar models at those thresholds. We see again that the SM
and the vector mediator model number of CNSN events di er simply by a scale factor,
independent of the energy threshold, as expected from eq. (3.4). On the other hand, for
the scalar case there is a non-trivial behavior with respect to the SM due to the extra term
threshold low energy 8B neutrinos become accessible. However, the di erence between the
SM and the scalar mediator cross-sections diminishes more with lower Eth than it increases
with lower E so the number of CNSN events di ers only by a factor
3. For the higher
threshold only atmospheric neutrinos are available, both SM and scalar contributions are
expected to be of the same order as the extra scalar contribution is suppressed by E 2
also see that a detector e ciency between 40% to 60% does not a ect the above discussion
and consequently we do not expect the neutrino oors we have calculated in this section to
be very di erent had we chosen to use in our computation 40% or 60% e ciency instead
of the 50% we have used.
We have also performed an estimation of the e ect of the uncertainty on the form
factors fTp;qn on the results of our calculation and concluded that they can a ect the neutrino
V=3.6
S=82.8
threshold. In red we show the predictions for the SM and in blue (green) for the vector (scalar)
e ciency of 50%
corresponding to the red star in
gure 5, respectively. The di erent contributions are
shown separately: DM only (green), standard CNSN (black), non-standard CNSN (blue) as well as
the combined spectrum (red).
To exemplify the di culty in discriminating between an energy spectrum produced
by DM collisions from the modi ed neutrino
oor, in the two cases studied in this paper,
we show in
gure 7 examples of the energy spectrum for the points corresponding to
the red stars in
gure 4 (vector) and
gure 5 (scalar). We show explicitly the various
contributions: the recoil spectrum produced by DM events only (green), by the standard
CNSN (black), by the non-standard CNSN due either to the vector or scalar mediator
(blue). In red we show the combined spectrum. In both cases, one would be able to
discriminate the spectrum due to DM plus SM
events (orange curve) from only CNSN
events (black). However, if there is an extra contribution from non-standard interactions,
increasing the neutrino background (blue), one cannot discriminate anymore this situation
from the total spectrum which also contain DM events(red). Both points were chosen in a
region where solar neutrinos dominate the background and are only achievable for a very
low energy threshold. For the nominal threshold of the LUX-ZEPLIN experiment only the
vector scenario will a ect the sensitivity of the experiment for
do not present here our results for DARWIN as they are qualitative similar to those of
Conclusions
Coherent neutrino scattering o nuclei is bound to become an irreducible background for
the next generation of dark matter direct detection experiments, since the experimental
signature is very similar to DM scattering o
nuclei. In this work we have considered the
case in which new physics interacts with both DM and neutrinos. In this situation, it
becomes important to compute the neutrino oor while taking into account the contributions
from exotic neutrino interaction. This sets the true discovery limit for direct detection
experiments instead of a background-free sensitivity. For de nitiveness, we have focused
on two simpli ed models, one with a vector and one with a scalar mediator interacting with
the DM and the SM particles. We calculated the bounds on the parameter space of the two
simpli ed models imposed by the latest LUX data. These are presented in gures 2 and 3.
The most interesting case is, however, the one in which some signal could be detected
in a future DM direct detection experiments. In this case our models predict modi cations
to the standard neutrino
oor. The main result of our analysis is shown in
and 5, in which we show that it is possible to
nd points in the parameter space of the
models in which not only the number of events produced by DM and by the modi ed
CNSN are compatible, but in which also the spectra are very similar. This immediately
implies that the modi ed CNSN can mimic a DM signal above the standard neutrino oor,
challenging the interpretation of a DM discovery signal. We show that the problem is more
signi cant for experiments that can probe m
< 10 GeV or
n < 10 47 cm2. Although a
new scalar interaction will not, in practice, a ect the discovery reach of future experiments
such as LUX-ZEPLIN or DARWIN, a new vector interaction can mimic DM signals in a
region above the standard neutrino oor of those experiments, challenging any discovery
in this region.
It should be noted that the scenarios considered here lead to a variety of signatures
apart from a modi cation of the CNSN at direct detection experiments. First and foremost,
we did not account for any relic density constraints from DM annihilation. Throughout
the analysis we have assumed that the DM relic density is satis ed. Secondly, the DM
annihilation to neutrinos will generate signals at indirect detection experiments which
will lead to additional constraints on the parameter space.
Direct production of DM
particles at the LHC, constrained by monojet searches will also be an additional signature
of interest. Finally, exotic neutrino interactions themselves are constrained by several
neutrino experiments and should be taken into account for a more complete analysis.
Despite these possible extensions of the study, our analysis is new in the sense that
it considers for the rst time the combined e ect of exotic neutrino and DM interactions
at the direct detection experiments. We demonstrate the current limits on the combined
parameter space for the DM and neutrino couplings and nally demonstrate the reach of
direct detection experiments.
Acknowledgments
We are thankful to Achim Gutlein for several very useful discussions about neutrino oor
calculations. We also would like to thank Genevieve Belanger for helpful discussions. SK
wishes to thank USP for hospitality during her visit, where this work originated. SK is
supported by the `New Frontiers' program of the Austrian Academy of Sciences. This work
was supported by Fundac~ao de Amparo a Pesquisa do Estado de Sa~o Paulo (FAPESP) and
Conselho Nacional de Ci^encia e Tecnologia (CNPq). This project has received funding
from the European Union's Horizon 2020 research and innovation programme under the
Marie Sklodowska-Curie grant agreement No. 674896.
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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