Sterile neutrino portal to Dark Matter II: exact dark symmetry
Eur. Phys. J. C
Sterile neutrino portal to Dark Matter II: exact dark symmetry
0 Department of Physics and Astronomy, University of Sussex , Brighton BN1 9QH , UK
1 Departamento de Física Teórica and IFIC, Universidad de ValenciaCSIC, C/Catedrático José Beltrán , 2, 46980 Paterna , Spain
We analyze a simple extension of the standard model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group. Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sector and the SM particles, and generate masses for the active neutrinos via the seesaw mechanism. We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario. We also study the constraints from direct Dark Matter searches and the prospects for indirect detection via sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV.

Dark Matter and neutrino masses provide experimental
evidence for physics beyond the standard model (SM), and
finding a scenario where both phenomena are linked is an
exciting possibility. Another hint to a connection between these
two sectors comes from the standard mechanisms to
generate the Dark Matter relic abundance and neutrino masses, as
both seem to require new massive degrees of freedom, with
a thermal relic and righthanded neutrinos, respectively.
An obvious possibility would be for righthanded
neutrinos to constitute the Dark Matter of the Universe [1]. This
option is constrained to a specific region at the keV and small
mixing with active neutrinos in the minimal see saw model,
but in extended scenarios a larger parameter space is allowed,
for instance in the context of a gauged B − L symmetry [2,3].
a email:
b email:
c email:
Upcoming experiments may be able to exclude or establish
whether keV neutrinos are the origin of Dark Matter, see
e.g. [4].
In this paper we take a different approach, focusing on
the fact that heavy neutrinos can mediate between Dark
Matter and the SM. We propose a simple extension of the SM
with a new scalar and fermion, singlets under the SM gauge
group but charged under a dark sector symmetry group.
Sterile neutrinos, which are singlets under both groups, are able
to mediate the interactions between the dark sector and the
SM particles, as well as generate masses for the active
neutrinos via the seesaw mechanism. Therefore, the same
coupling that generates neutrino masses after electroweak
symmetry breaking, determines the Dark Matter phenomenology.
Indeed, Dark Matter annihilation to righthanded neutrinos
and subsequent decays to SM particles characterize the
computation of the relic abundance as well as indirect detection
probes, respectively.
This minimal setup has been studied in [5,6] for the case
of fermion Dark Matter, under the assumption that the sterile
neutrinos are pseudoDirac and heavier than the dark sector
particles. Our analysis differs from this previous work in that:
(1) we explore the region of parameter space where sterile
neutrinos are lighter than the dark sector, and therefore the
Dark Matter can annihilate into sterile neutrinos and (2) we
extend the analysis to the scalar Dark Matter case, which was
not considered before.
In a companion paper [7], we have explored an alternative
scenario with the dark sector charged under U (1)B−L , and
both papers provide two distinct possibilities for a sterile
neutrino portal to Dark Matter.
The paper is organized as follows. After presenting the
setup of our model in Sect. 2, we move onto the constraints
from Higgs decays and direct Dark Matter searches in Sect. 3.
We describe the calculation of the annihilation cross section
in Sect. 4 where we impose constraints from the relic
abundance of Dark Matter. These results are then linked to
indirect detection probes via sterile neutrinos decays to leptons
2 Exact dark symmetry
This portal is based upon the assumption that the dark sector
contains at least a scalar field φ and a fermion Ψ , which are
both singlets of the SM gauge group but charged under a
dark sector symmetry group, Gdark , so that the combination
Ψ φ is a singlet of this hidden symmetry. Independently of
the nature of the dark group, if all SM particles as well as
the sterile neutrinos are singlets of Gdark , the lighter of the
two dark particles turns out to be stable, and therefore it may
account for the Dark Matter density of the Universe.
SM
If this were the case then nothing would prevent a term
like
Lint = −(φΨ (λs + γ5λ p)N + φ† N (λs − γ5λ p)Ψ )
to appear, besides the standard Higgs portal term λH φ ( H † H )
(φ†φ) included in the scalar potential,
Lscalar = μ2H H † H − λH ( H † H )2 − μφ φ φ − λφ (φ†φ)2
2 †
α
Lν N = −(Yαa L L H N Ra + h.c.),
where α = e, μ, τ denotes lepton flavour and a = 1 . . . n,
being n the number of sterile neutrinos.
For simplicity we do not consider the possibility that the
scalar φ gets a vev, and we restrict the discussion to the
minimal matter content, although there could be more than one
set of dark fermions and scalars.
Another simplifying assumption made in this paper is that
the dark symmetry Gdark is a global symmetry at low
energies. We are therefore neglecting the possible
phenomenology of Gdark vector mediators, e.g., if the dark symmetry
were local there could also be kinetic mixing among the
dark gauge bosons and the SM ones, leading to further
SMdark particle interactions [8, 9]. The following discussion will
apply as well to this scenario, provided the kinetic
mixing is negligible. Nevertheless, the UV structure and
stability of Dark Matter depends on whether Gdark is a true
global symmetry or a gauge symmetry. Global symmetries
are sensitive to higherdimensional operators mediated by
quantum gravity effects [10], e.g. cΨ Ψ¯ H˜ †γ μ Dμ L /MPl or
c Fμν F μν /MPl , and could lead to disastrous decay of
Dark Matter unless cΨ, 1 [11–13].
Regarding the neutrino sector, light neutrino masses are
generated via TeV scale type I seesaw mechanism, which we
briefly review in the following. We denote να the active
neutrinos and Ns the sterile ones. After electroweak symmetry
breaking, the neutrino mass matrix in the basis (να , Ns ) is
given by
where m D = Y vH /√2 and Yαs are the Yukawa couplings.
The matrix Mν can be diagonalized by a unitary matrix
U , so that
where mν is the diagonal matrix with the three lightest
eigenvalues of Mν , of order m2D /m N , and M contains the heavier
ones, of order m N .
The mass eigenstates n = (νi , Nh ) are related to the active
and sterile neutrinos, (να , Ns ), by
U =
= U ∗
Usi = −[m−N1m TD UPMNS]si .
Ush = I ,
Notice that at this order the states Nh and Ns coincide, so we
identify them in the rest of this paper.
Neglecting the mixing between the CPeven scalars, the
Yukawa coupling of the SMlike Higgs field h to the neutrinos
can be written as [14]:
h
LY = − 2vH n¯ i [(mi + m j )Re(Ci j ) + i γ5(m j − mi )I m(Ci j )]n j ,
where the indices i, j refer to the light neutrinos νi for i, j =
1, 2, 3 and to Nh for i, j = 4, 5, 6, and the matrix C can be
written in terms of the mixing matrix U :
Ci j =
α=1
A variation of this scenario has been analyzed in [5, 6], where
the sterile neutrinos are assumed to be pseudoDirac and
Table 1 Explored parameter
space in the models
heavier than the dark sector particles, φ, Ψ . Thus, they can be
integrated out and generate at tree level the effective
dimension five operator
which after the SM Higgs doublet acquires a vev leads to
the interaction O(5) = (Ψ φ)νL vH /√2, involving a SM
lefthanded neutrino. This limit is in fact a (light) neutrino portal
to Dark Matter. Assuming that the fermion Ψ is the Dark
Matter, the model can accommodate current experimental
and observational constraints if Mψ is below ∼35 GeV, or it
is in a resonant region of the Higgs or Z boson, or the dark
scalar and dark fermion are almost degenerate.
Our analysis is complementary, since we focus on a
different region of the model parameter space: we assume that the
sterile neutrinos are lighter than the Dark Matter and
therefore the annihilation channel to N N is open. Furthermore,
we study both fermion and scalar Dark Matter. Although the
scalar Dark Matter case falls among the class of Higgs
portal models that have been extensively studied [15–34], it is
worth to explore whether the new annihilation channel into
N N allows one to obtain the observed relic density in regions
that are excluded in the standard Higgs portal framework.
In the following sections we describe the current
constraints on the above scenario and the results of our numerical
analysis, based on a Monte Carlo scan over the free
parameters (mΨ , mφ , m N , λs , λHφ ) in logarithmic scale, restricting
the values of the couplings and masses to the ranges
displayed in Table 1. We present the analytic results for
arbitrary Dark Matter—sterile neutrino couplings λs , λ p, but for
the numerical implementation we have chosen λ p = 0, since
as explained in Sect. 4, in this case strong constraints can
be set from indirect Dark Matter searches. We made use of
LanHep [35] and micrOMEGAs [36] in order to obtain the
correct relic abundance, Higgs decays and today’s
annihilation cross section. We calculate 106 points that match the
Planck constraint on the Dark Matter abundance at 3σ [37],
namely h2 = 0.1198 ± 0.0045.
3 Constraints from Higgs decays and direct Dark
Matter searches
The enlarged fermion and scalar sectors lead to new decays
of the Higgs boson, h, which can be constrained using the
BRinv =
ATLAS and CMS limits on the invisible Higgs decay
branching fraction:
being the SM Higgs width SM ≈ 4 MeV.
At tree level, there are two new Higgs decay channels:
when mφ < mh /2, the standard decay of the Higgs portal
scenarios, h → φφ is kinematically allowed, contributing to
the invisible Higgs decay width by
1 −
We show in Fig. 3 the upper limit on the Higgs portal
coupling λHφ derived from the experimental limit on the
invisible Higgs decay width in Eq. (12), as a function of the singlet
scalar mass, mφ .
Moreover, the Yukawa interaction term Y L H PR N also
leads to novel Higgs decay channels into neutrinos. The
corresponding decay width reads [14]:
(h → ni n j ) = 8πωmh λ1/2(m2h , mi2, m2j )
S 1 −
1 −
where λ(a, b, c) is the standard kinematic function, w =
1/n! for n identical final particles and the scalar and
pseudoscalar couplings are:
with Ci j defined in Eq. (10).
The largest branching ratio is for the decay into one light
and one heavy neutrino [38]:
The attainable values for the above branching fractions have
been analyzed in [38], for the case of two heavy
neutrinos, parameterizing the Yukawa couplings in terms of the
observed light neutrino masses and mixing angles, and a
complex orthogonal matrix. After imposing the relevant
constraints from neutrinoless double beta decay, lepton flavour
violating processes and direct searches of heavy neutrinos,
they find that branching ratios of h → νi Na larger than 10−2
are generally ruled out for heavy neutrino masses MN ≤ 100
GeV, and typically they are much smaller, due to the tiny
Yukawa couplings required to fit light neutrino masses with
sterile neutrinos at the electroweak scale. Therefore, the
contribution of such decay modes to the Higgs decay width is
negligible, and they do not alter the bounds discussed above.
At one loop, the d = 5 Higgs portal operator Ψ Ψ (H † H )
is generated (unless the coupling of the Dark Matter to the
dark scalar and sterile neutrinos is chiral, i.e., λs = λ p in
Eq. (1)) with a coefficient given by [6]:
Thus, when mΨ < mh /2 the invisible decay h → Ψ Ψ is
also allowed with partial decay width
1 −
Fig. 1 Left, right elastic cross
section diagrams for the scalar
and fermion Dark Matter cases,
respectively
and the current limit on the invisible Higgs decay
branching ratio only leads to an O(1) constrain on λHφ ,
depending on the values of the remaining free parameters, namely
λs , λ p, m N and mφ . Notice, however, that if mφ < mh /2, the
strong constraints from the invisible Higgs decay h → φφ
shown in Fig. 3 will apply as well.
Concerning the bounds from direct DM searches, they
also depend on which of the dark particles is lighter, and
therefore stable. In order to implement such bounds we shall
assume that the DM relic density is as determined by CMB
measurements, since this requirement is always fulfilled in
our scenario for both scalar and fermion DM, as we will see
in the next section.
If DM is the dark fermion, Ψ , it only interacts with the
SM quarks at oneloop level (see Fig. 1), via the induced
Higgs portal operator Ψ Ψ (H † H ) just discussed, and
therefore the bounds from direct detection are quite weak.
However, since the interaction to quarks is mediated through the
Higgs, the scattering will always be spin independent. We
refer the reader for the actual matrix elements to [39]. In
Fig. 2 we show the excluded region by the invisible Higgs
decay and current LUX [40,41] results (dark blue points),
as well as the expected excluded region by XENON1T [42]
(light blue) and LZ [43,44]+SuperCDMS [45] (purple).
Similar constraints can be set with the current results from the
PANDAX experiment [46].
Fig. 2 Constraints on the Higgs portal coupling for fermion DM
Fig. 3 Constraints on the Higgs portal coupling for scalar DM
However, if DM is the dark scalar φ, it interacts with the
SM quarks at tree level via the Higgs portal coupling, λH φ ,
and the null results from direct searches set strong limits
on this parameter. This is illustrated in Fig. 3, where we
show the allowed values of the Higgs portal coupling λH φ
as a function of the DM mass, mφ , derived from the
invisible Higgs decay width plus LUX bounds, as well as the
prospects from XENON1T and LZ+SuperCDMS. The dark
blue points in the usual Higgs portal scenario would be ruled
out, except for the upper limit, since the λH φ being too small
leads to a DM relic density larger than the one determined by
CMB measurements. In our scenario the alternative
annihilation channel into N N provides the correct relic density, but
the current constraints from LUX and Higgs invisible decay
width excludes them. We notice that for mφ 300 GeV the
usual Higgs portal model still provides the correct relic
abundance. However, we find that XENON1T can be sensitive to
such scenario for mφ < 2 TeV.
4 Dark Matter relic abundance
4.1 Thermal history
In order to discuss the thermal production of Dark Matter in
the early Universe we will first describe the thermal history
for both the scalar and fermion Dark Matter scenarios.
1. Fermion Dark Matter Ψ : At very early times φ, Ψ and N
are in thermal equilibrium with the standard model via
the Higgs portal coupling. The heavy dark particle
companion will decay at T mφ and the dark sector may
still be coupled to the standard model bath if the Yukawa
couplings of the sterile neutrinos are large enough. If
they are small, then the Ψ and N bath will decouple and
remain in thermal equilibrium but with a different
temperature.1 Then when the temperature of such a bath is
TD ∼ mΨ /20 the Dark Matter will be produced and
the sterile neutrinos will decay at TD m N . In order
to check whether the decoupling of the dark sector will
modify the production rate it is worth revisiting the
production mechanism, see [47] for a recent discussion of
decoupled dark sectors. Since the entropy is separately
conserved in both the visible and the dark sectors, the
standard relic abundance solution is modified
approximately by a factor geff /g where g measures the total
number of relativistic degrees of freedom in the SM bath
and geff = g + gD (TD / T )4 represents the effective
number of relativistic species. Given that the number of
degrees of freedom in the dark sector, gD is much smaller
than g and TD / T ∼ 1 then geff /g must be close to
one. Thus, a sizeable change in the couplings compared to
the case in which both sectors remain in thermal
equilibrium is not expected since furthermore χ h2 ∝ 1/λs4, p.
The only caveat to this argument occurs when mχ m N ,
because in that case the sterile neutrinos may have a larger
number density than the equilibrium one and in order to
generate the same amount of Dark Matter higher
couplings between χ and N will be needed. This scenario
has been recently studied by [48] for the precise model
proposed in this work. They found that in such region
one will need couplings a factor between 1 and 4 higher
depending on the Yukawa of the sterile neutrinos. Since
this change is mild, for our computations we will assume
that all species are equilibrium with the standard model.
2. Scalar Dark Matter φ: At very early times φ, Ψ and N
are in thermal equilibrium with the standard model via
the Higgs portal coupling. The heavy dark particle
companion will decay at T mΨ and the dark sector will
decouple from the standard model when the Dark Matter
freezes out at T ∼ mΨ /20 and the sterile neutrinos will
decouple and decay at T m N .
4.2 Relic abundance
In our scenario, the annihilation cross section into two sterile
neutrinos depends on the nature of the DM particle (scalar,
Dirac or Majorana fermion) and the type of coupling (scalar,
pseudoscalar). The relevant Feynman diagrams are shown in
Fig. 4. For example, let us assume righthanded neutrinos
are Majorana, and consider the two options of fermion and
scalar Dark Matter:
1 Yet, the actual value of the Yukawa couplings are not known.
The naive seesaw expectation is Y ∼ √mν m N /vH ∼ 4 ×
10−8√m N /(1 GeV) for mν ∼ 0.1 eV, but larger couplings are
consistent with neutrino masses, for instance in the context of inverse seesaw
scenarios.
Fig. 4 Relevant annihilation channels
Fig. 5 Allowed parameter
space of the mediator mass and
coupling in the scalar (left) and
fermion Dark Matter (right)
cases
1. Fermion Dark Matter Ψ : The cross section for fermionic Majorana Dark Matter and complex mediator φ reads
where α = λs2 − λ2p and β = λs2 + λ2p, rφ = mφ /mΨ ,
and rN Ψ = m N /mΨ .
One can obtain the case of a Dirac DM particle by in
Eq. (19) perform the exchange α ↔ β. Similarly, the
case of a real scalar can be obtained by setting λ p = 0 in
Eq. (19), which leads to α = β = λs2 in this expression.
2. Scalar Dark Matter φ: In the case of a real scalar Dark
Matter and Dirac mediator Ψ the cross section is as
follows:
where rΨ = mΨ /mφ and rN φ = m N /mφ .
To obtain the expression for a complex scalar, one can
multiply this equation by a factor 1/4. Similarly, to
consider a Majorana mediator one would multiply the
expression by a factor 4 and set λ p to zero, α = β.2
2 Note that our results agree with the expressions obtained in Ref. [49],
where both fermions were set to be Dirac particles.
An important observation is that there are situations where
the annihilation cross section at leading order in the relative
Dark Matter velocity, v, is proportional to the righthanded
neutrino mass. For example, the case of a Majorana Dark
Matter with chiral couplings, λs  = λ p (α = 0). In this
case when m N mφ , mΨ the cross section is effectively
pwave, which reduces the sensitivity of indirect detection
probes to these scenarios.
In the following we discuss two representative cases where
strong constraints can be set on the parameter space of the
sterile neutrino portal, namely cases where the cross section
is swave even for m N = 0. We choose two benchmark
scenarios, namely Majorana DM and real scalar DM with scalar
couplings α = β = λs2. In Fig. 5 we show the allowed
parameter space in the mass of the mediator versus
coupling, λs . Besides the perturbativity limits, the coupling λs
is constrained by the width of the mediator. In our approach,
the mediator particle is treated as a narrow resonance, i.e.
/m 1, which implies λs √8π . Taking into account
this limit, these plots show that the mass of the mediator must
be below m 1 TeV to satisfy 0.1m.
In the scalar Dark Matter case, annihilation into
righthanded neutrinos (Eq. (20)) is complemented via the Higgs
portal coupling λH φ into SM particles. Namely bb¯ for low
mass DM, and gauge bosons and Higgses for heavier DM
particles. These channels could, in principle, compete with
the annihilation into righthanded neutrinos, yet in Fig. 3 we
showed how couplings to SM are strongly constrained by
direct detection experiments (LUX) and LHC bounds on the
Fig. 6 Ratio between the cross section with standard model particles
in the final state and sterile neutrinos in the final state at v = 10−3 c,
as relevant for indirect detection searches. Currently, on the resonance
mφ mh /2 and for mφ > 150 GeV both cross sections are comparable.
However, XENON1T could set the annihilation cross section to
righthanded neutrinos to be dominant in the entire parameter space but for
the resonance
invisible width of the Higgs. We find that for mφ 100 GeV
the production cannot proceed via SM particles. As a result of
these bounds on the scalar portal, the relic abundance cannot
be satisfied in the standard scalar Dark Matter, which leads to
the conclusion that Higgs portal Dark Matter is not a viable
scenario for low dark matter masses. This is not the case here,
as our scalar has additional annihilation channels, via the
coupling to dark fermions. One can then find viable scenarios,
shown in Fig. 5, which satisfy the relic abundance and evade
direct detection constraints in all the Dark Matter mass range
from 1 GeV to 2 TeV.
Moreover, in the low Dark Matter mass region,
annihilations to righthanded neutrinos are dominant. This is shown
in Fig. 6, where we plot the ratio of annihilation cross
sections via the Higgs portal and to the righthanded neutrino
channel today, for relative Dark Matter velocity v = 10−3 c.
This ratio is very small, of the order or below 0.1% for low
mass, and up to 100% for mφ 300 GeV. When the dark
matter mass is low, the regions with larger ratios are
correlated with degeneracies in the dark sector, namely regions
where the dark fermion mediator and the scalar are close
in mass. This fact has implications in the ability of detecting
Dark Matter today, which we discuss in detail in the next
section. Notice that the ∼100% contributions to the Dark
Matter abundance currently allowed through SM interactions for
mφ 300 GeV, could be restricted by XENON1T to ∼10%
for most parameter space.3
3 The features in the low mass region of the plots are due to the
fact that the contributions to the SM are mediated by the Higgs
and there are several suppressions. When different channels become
Finally, in the fermion Dark Matter case, since the
coupling to the Higgs is generated at 1Loop, the contributions
to the annihilation cross section from the SM particles is only
nonnegligible in the resonant region mΨ mh /2.
5 Constraints from indirect searches and CMB
In this scenario the annihilation of Dark Matter (with mDM
100 GeV) into righthanded neutrinos is dominant, with the
heavy neutrinos decaying into SM particles via their mixing
with active neutrinos. Those decays can lead to significant
fluxes of gamma rays and neutrinos which can be probed
by experiments. In this section we consider the impact on
the model by limits from FermiLAT and H.E.S.S. on the
gammaray flux from dwarf spheroidal galaxies [50] and the
galactic center [51] respectively, as well as from studies of the
CMB [52] and IceCUBE analysis of neutrino fluxes [53–55].
To study the indirect detection signals in this model we
first need to understand how the heavy neutrino decays. If the
neutrino is light, m N < m W , N will mostly decay through
offshell Z and W . These threebody partial widths can be
read from Refs. [56, 57] and are listed in the appendix; here
we just quote the typical form it adopts:
where Uα N is the mixing matrix between the heavy and active
neutrinos. For heavier N , the twobody decays into massive
vector bosons or Higgs and fermions are open. In this case
the partial width scales as [14]:
See also the appendix for the detailed formulae.
The relative weight of the different lepton flavours to the
total width depends on the model for neutrino mass
generation. The large angle θ23 in the active neutrino mixing
matrix UPMNS suggests a similar decay rate of N into μ and
τ , while the one into e is largely unconstrained. In fact, the
measured mixing pattern (see for instance [58]) is close to
TriBimaximal, which leads to an exact μ − τ symmetry
[59]. In our case, if we assume that the largest active
neutrino mass is generated by only one of the sterile neutrinos,
m3 ≈ α (Yα N vH )2/m N and the mixing angles are given
by Uα N ∼ Yα N vH /m N . Then tan θ23 ∼ YμN /Yτ N ∼ 1 and
Yμ2N + Yτ2N ∼ 0.15 imply that UeN
Fig. 7 Annihilation cross
section today and lines of
exclusion of decays to leptons
from FermiLAT from dwarf
galaxies and H.E.S.S. from the
galactic center, for the cases of
scalar (left) and fermionic
(right) Dark Matter
A detailed study of the indirect detection signatures of our
scenario is beyond the scope of this work, since DM does
not decay directly to SM particles, as is usually assumed in
most analyses. Therefore we just estimate here the expected
constraints using current analysis, taking into account that in
general the cascade decays lead to a softer energy spectrum
of the final SM particles than in the standard twobody decay.
In Fig. 7 we present the results of such an estimate exercise in
the case of decays to leptons, where limits from Refs. [50,51]
have been naively rescaled as mDM → mDM/2. We find that
decays of the righthanded neutrinos resulting in tauleptons,
e.g. from N → τ qq or N → ντ +τ −, are potentially the
most sensitive modes. Indeed, if these decays were dominant
one could obtain a limit from indirect detection on the Dark
Matter mass of O(100) GeV for both fermion and scalar
Dark Matter. One could also use the production of quarks
from offshell W and Z to set bounds on the model.
Note that indirect detection signals in this case (i.e., m N <
mW ) have been studied in [61], showing that it could be
possible to explain the galactic center gammaray excess revealed
by various studies of the FermiLAT data in 1–4 GeV gamma
rays. Indeed, assuming that DM particles annihilate into two
sterile neutrinos lighter than the W boson, they find that m N
in the range 10–60 GeV can explain the observed spectrum,
while the fitted annihilation cross section σ v is (0.5–5)
×10−26cm3/s, roughly compatible with the WIMP
annihilation cross section σ v decouple ∼ (2 − 3) × 10−26cm3/s,
when the Dark Matter particles decouple. More precisely,
the best fit points are around m N ∼ 30 GeV and mDM ∼ 45
GeV, which are within the ranges we have found compatible
with all current experimental constraints in our model.
Finally, let us mention other sources of indirect constraints
for this model. Measurements of the cosmic microwave
background (CMB) anisotropies are also sensitive to Dark Matter
annihilation during the cosmic dark ages, because the
injection of ionizing particles will increase the residual ionization
fraction, broadening the last scattering surface and
modifying the anisotropies. Under the assumption that the power
deposited to the gas is directly proportional to that injected
at the same redshift, with some efficiency factor feff ,
constraints can be placed on the combination feff σ v /mDM,
for different SM annihilation channels in s wave. Again, the
available calculations of feff assume that DM annihilates
directly to a pair of SM particles [52], and thus they are not
directly applicable to our model, but we can roughly estimate
the expected impact of such limits in the allowed parameter
space assuming as before that the constraints will be
similar for cascade decays, appropriately rescaled for mDM/2.
Under these circumstances, we find these limits are weaker
than the ones from FermiLAT discussed above.
Besides signatures from gamma rays, in the N N
annihilation channel also light neutrinos are copiously produced,
which could generate an observable flux from dense regions
of Dark Matter. IceCUBE has set constraints on the Dark
Matter annihilation cross section to neutrinos by measuring
the flux from nearby Galaxies and Clusters [53], the Galactic
Halo [54] and the Galactic Center [55]. However, currently
these probes lie three orders of magnitude above the model
prediction, and thus cannot place a constrain on our model.
Dark Matter particles in the galactic halo can also scatter
elastically with a nucleus and become trapped in the
gravitational well of astronomical objects like the Sun, eventually
thermalize and concentrate at the core of the object. Then they
may annihilate into SM particles, in particular neutrinos that
can be detected by neutrino experiments such as IceCUBE
or SuperKamiokande. In our scenario the limits from direct
searches are tighter than such indirect probes, since the
interaction of Dark Matter to quarks is spin independent.
6 Conclusions and outlook
In this paper we have analyzed in detail a simple scenario
of a dark sector composed of a scalar and a fermion, both
singlets under the SM gauge group but charged under a dark
symmetry group. This sector is linked to the origin of neutrino
masses via couplings to the sterile neutrinos, which are able
to mediate between the dark sector and the SM.
This scenario has been studied in Refs. [5, 6], considering
just the case of fermionic Dark Matter and for sterile
neutrinos heavier than the dark sector, with the result that current
experimental and observational constraints (electroweak
precision limits, Dark Matter relic abundance, direct and
indirect detection constraints), can be accommodated only for
mDM 35 GeV, or in the resonances, mDM mh , m Z ,
unless the dark scalar or dark fermion are almost degenerate.
We have extended these previous studies in two ways: we
explore the phenomenology of this type of models when the
sterile neutrinos are lighter than the dark sector, so that the
Dark Matter annihilation channel into N N is kinematically
allowed, and we consider both, fermionic and scalar Dark
Matter in this context. We have performed for the first time
an exhaustive numerical analysis of this alternative region
of the model parameter space, and after imposing all the
relevant constraints from direct detection and collider probes,
we find that it is possible to obtain the observed Dark Matter
relic abundance in the whole mass range explored, mDM ∈
[1 GeV, 2 TeV], both for scalar and fermion Dark Matter.
We find that the scalar case is an interesting extension of
the Higgs portal. Indeed, in the usual portal the constraints
on the Higgs invisible decay and Dark Matter nucleon cross
section rule out the possibility of the scalar as the main
component of Dark Matter for mφ 100 GeV. But in our
scenario, annihilation can occur via the neutrino portal which
is dominant, i.e. more than 90%, in most of the parameter
space. On the other hand, in the case of a fermion Dark
Matter, the contribution to the quark–Dark Matter scattering and
Higgs invisible width decay is at one loop and the Higgs
portal coupling is only mildly constrained.
Finally we explore the indirect detection characteristics of
this model, determined by the decays of the righthanded
neutrinos into SM bosons and leptons. We consider constraints
from FermiLAT and find that those could be sensitive to
Dark Matter up to the electroweak scale, mDM 100 GeV
independently of whether the Dark Matter particle is a scalar
of a fermion. However, a more detailed analysis of these
constraints need to be done, as we performed a naive scaling on
constraints of Dark Matter decays to two SM particles. In our
scenario, the more complex decays of righthanded
neutrinos would lead to less energetic SM probes. Finally, we also
comment on the possibility of this channel to be responsible
of the gammaray galactic excess at few GeV.
Acknowledgements We thank Olga Mena, Sergio Palomares Ruiz,
Roberto Ruiz de Austri, Jordi Salvadó, A. Vincent and J. Wudka for
illuminating discussions, and Concha GonzálezGarcía for comments
on the manuscript. ME thanks Antonia Abenza for inspiring and
encouraging conversations. This work has been partially supported by the
European Unions Horizon 2020 research and innovation programme
under the Marie SklodowskaCurie Grant Agreements Nos. 674896
and 690575, by the Spanish MINECO under Grants FPA201457816P
and SEV20140398, and by Generalitat Valenciana Grant
PROMETEO/2014/050. ME is supported by Spanish Grant FPU13/03111 of
MECD. NR acknowledges the support from the Munich Institute for
Astro and Particle Physics (MIAPP) of the DFG cluster of excellence
“Origin and Structure of the Universe”. The work of VS is supported
by the Science Technology and Facilities Council (STFC) under Grant
Number ST/J000477/1.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://creativecomm
ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit
to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Funded by SCOAP3.
Appendix: Sterile neutrino decay widths
Here we summarize the sterile neutrino decay modes,
relevant for indirect Dark Matter searches.
If the sterile neutrino is lighter than the W boson, it will
decay through offshell h, Z , W bosons to three fermions.
Since the decay via a virtual h is further suppressed by the
small Yukawa couplings of the SM fermions, it is a very
good approximation to consider only the processes mediated
by virtual W, Z , whose partial widths read [56]:
+3 f (w) − 2ae g(z, w)]
where C N N is defined in Eq. (10),
a f , b f are the left and right neutral current couplings of the
fermions ( f = q, ), the variables z, w are given by
z = (m N /m Z )2,
w = (m N /m W )2,
and the functions f (z), f (w, 0) and g(z, w) can be found in
[57].
For larger values of m N , twobody decays to SM particles
are open, and the corresponding widths read [14]:
In the above expressions, we have assumed that N is a
Majorana fermion. If it is Dirac, then the decay channel
N → W − + is forbidden and the decay widths into Z / h, ν
are D (N → Z / h ν ) = M (N → Z / h ν )/2.
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