#### Dark matter physics in neutrino specific two Higgs doublet model

Received: December
matter physics in neutrino specific two Higgs
0 Open Access , c The Authors
1 85 Hoegiro , Dongdaemun-gu, Seoul 02455 , Republic of Korea
2 School of Physics, Korea Institute for Advanced Study
Although the seesaw mechanism is a natural explanation for the small neutrino masses, there are cases when the Majorana mass terms for the right-handed neutrinos are not allowed due to symmetry. In that case, if neutrino-specific Higgs doublet is introduced, neutrinos become Dirac particles and their small masses can be explained by its small VEV. We show that the same symmetry, which we assume a global U(1)X , can also be used to explain the stability of dark matter. In our model, a new singlet scalar breaks the global symmetry spontaneously down to a discrete Z2 symmetry. The dark matter particle, lightest Z2-odd fermion, is stabilized. We discuss the phenomenology of dark matter: relic density, direct detection, and indirect detection. We find that the relic density can be explained by a novel Goldstone boson channel or by resonance channel. In the most region of parameter space considered, the direct detections is suppressed well below the current experimental bound. Our model can be further tested in indirect detection experiments such as FermiLAT gamma ray searches or neutrinoless double beta decay experiments. ArXiv ePrint: 1611.09145
Beyond Standard Model; Cosmology of Theories beyond the SM; Global
1 Introduction The model Dark matter physics 3.1
Direct detection
3.3 Indirect detection 4 Conclusions and discussions
Introduction
A natural scenario to explain the sub-eV neutrino masses is type-I seesaw mechanism in
which very heavy standard model (SM) singlet right-handed neutrinos are introduced. In
this case the light-neutrinos become Majorana particles and the scenario can be tested at
neutrinoless double beta decay experiments.
A more straightforward way for the generation of neutrino masses in parallel with the
generation of quark or charged lepton masses is just to introduce right-handed neutrinos
to get Dirac neutrino masses with the assumption of lepton number conservation to forbid
the Majorana mass terms of the right-handed neutrinos. The problem in this case is
coupling is of order 1. To give Dirac masses to neutrinos, while avoiding this large hierarchy
the small neutrino masses are explained by the small VEV of a second Higgs doublet
(v1 = √
authors in ref. [1] introduced global U(1) symmetry, U(1)X , which is softly broken to forbid
Majorana mass terms of the right-handed neutrinos. In their model, all the SM fermions
except neutrinos obtain masses via Yukawa interactions with the SM-like Higgs doublet,
the small VEV is obtained by seesaw-like formulas
v1 =
1 eV can be obtained by m12 ∼ O(100) keV.
model the global symmetry, U(1)X , is spontaneously broken down to discrete Z2 symmetry
by VEV of a new singlet scalar, S. The remnant Z2 symmetry makes the dark matter
candidate stable. The resulting Goldstone boson provides a new annihilation channel for
the DM relic density. It is feebly coupled to the SM particles due to tiny v1, avoiding
experimental constraints. We also study the DM direct detection and indirect detection.
They are typically well below the current experimental sensitivity.
The paper is organized as follows. In section 2, we introduce our model. In section 3,
we study DM phenomenology in our model: relic abundance, direct and indirect detection
of the DM. In section 4, we conclude.
The model
In this section, we introduce our model which is an extension of the model given in ref. [1].
The scalar field contents and new fermions are summarized in table. 1 where we also show
the charge assignments under global U(1)X symmetry. We can write U(1)X -invariant as
well as the SM-gauge invariant scalar potential, Yukawa interactions for the leptons and
new fields as
L ⊃ −yiej L¯iΦ2eRj − yiνj L¯i Φ˜1νRj + h.c,
L ⊃ ψ¯iγμ∂μψ − mψψ¯ψ − 2
much smaller than electroweak scale to obtain tiny neutrino mass [1, 2]. In addition, a
Z2 odd particle while other particles including those in SM sector are even under the Z2,
Here we note that a global symmetry is considered to be broken by quantum effect
at Planck scale, Mpl. In such a case we would have a Planck suppressed effective
opernot suppressed by very small dimensionless coupling. This instability could be avoided
assuming our global U(1)X is a subgroup of some gauge symmetry broken at scale higher
we just assume our DM candidate is stabilized by the Z2 from U(1)X . On the other hand,
the breaking of the global U(1)X at Planck scale does not affect neutrino mass since such
The scalar fields can be written by
Φ1 = √12 (v1 + h1 + ia1)
, Φ2 = √12 (v2 + h2 + ia2)
since aS becomes physical Goldstone boson as shown below. The VEVs of the scalar fields
−2m121v1 + 2λ1v13 + v1(λ1SvS2 + λ3v22 + λ4v22) −
−2m222v2 + 2λ2v23 + v2(λ2SvS2 + λ3v12 + λ4v12) −
−2m2SSvS + 2λSvS3 + vS(λ1Sv12 + λ2Sv22) −
√2µv 2vS = 0,
√2µv 1vS = 0,
√2µv 1v2 = 0.
the same order with µ :
√2µv 2vS
v1 ≃ λ1SvS2 + (λ3 + λ4)v22 − 2m211 .
Yukawa coupling Y ν is O(1)[O(10−6)(∼ me/v2)].
We note, however, that small µ (≪ v)
to additional U(1) under which only the S field is charged while all the others are neutral.
Here we consider masses and mass eigenstate of the scalar sector by analyzing the
scalar potential with v1 ∼ µ ≪ {v2, vS}.
Pseudo-scalar. Mass matrix for pseudo-scalars is given, in the basis of (a1, a2, aS), by
−vS −v2
−v2 v1
less Nambu-Goldstone (NG) boson which is absorbed by Z boson. The mass of A is given by
m2A =
µ (v12v22 + v12vS2 + v22vS2)
√2v1v2vS
≃ √2v1
Note that the existence of physical Goldstone boson a does not lead to serious problems in
particle physics or cosmology since it does not couple to SM particles directly except to SM
Higgs. Invisible decay width of Z-boson strongly constrains the Z → Hia decay.1 Since
heavier than the Z-boson mass to evade the problem [7]. In our model, a can couple also
Our model can also contribute about 0.39 to the effective number of neutrino species
discrepancy between Hubble Space Telescope [9] and Plank [11] in the measurement of
Hubble constant. Since the mechanism is almost the same with that detailed in [4] we do
M H2± =
− 2 (
imately G±, the NG boson absorbed by W ± boson. We obtain the charged Higgs mass as
m2H± =
(v12 + v22)(√2µv S − λ4v1v2)
CP-even scalar. In the case of CP-even scalar, all three components are physical, and
M H2 = (λ3 + λ4)v1v2 − √
≃
√2v1
1Hi(i = 1, 2, 3) are neutral scalars defined below.
scale and the mixings between h1 and other components are negligibly small while the h2
are given by
m2H2,H3 =
m−2222−mm223233 ,
m222 + m323 ∓
(m222 − m233)2 + 4m423 ,
L ⊃ ψ¯′iγμ∂μψ′ − mψψ¯′ψ′ − 2vS
a pair of self-charge-conjugate fields;
− = √−i
2The numerical analyses on the Higgs decays are performed using the program HDECAY, see refs. [12, 13].
Then mass eigenstates are obtained as
Higgs doublet sector which is consistent with current SM Higgs analysis [17]. In addition,
we take into account constraint from h → aa decay which is induced by interaction term
and we require upper limit of the branching ratio as BR(h → aa) < 0.23 based on constraint
of invisible decay of SM Higgs [18–20]. The phenomenology of two Higgs doublet sector
and constraints are discussed in refs. [1, 21, 22] in detail. We thus focus on DM physics in
the following analysis.
which satisfy Majorana conditions ψ±c = ψ
± and have mass eigenvalues
mass eigenstates is given by
− 2 2
L ⊃ 2
1 X ψ¯α [iγμ∂μ − m±] ψα − 4vS
Dark matter physics
In this section, we discuss DM physics such as relic density, direct detection and indirect
− which is stable due to
Z2 symmetry as a remnant of the global U(1)X symmetry. Interactions relevant to DM
physics are obtained from the kinetic term of S, terms in eq. (2.1), and (2.20):
L ⊃ − 2√2 ρ(ψ¯+ψ+ − ψ¯−ψ−) − 4vS
ρ∂μa∂μa − µ 1S ρ φ1+φ1− + (h12 + a12)
terms of mass eigenstates via eq. (2.17). In the following analysis, we consider four different
scenarios for the coupling constants: (I) f ≤
f as figure 1-(A) [4, 23–25] and aa via process in figure 1-(B). In the scenario (II), final
− − → H3 → H3H3
mode in figure 1-(B) is added. In the scenarios (III) and (IV), a DM pair dominantly
and (D), and aa channel in figure 1-(B) which contributes to both scenarios. Note that, µ 2S
into account Higgs portal interaction [26–32] with the mixing effect for scenario (III).
√4π and µ 1S,2S,SS ≪ 0.1 GeV, (II) f ≤
Relic density
We estimate the thermal relic density of DM numerically using micrOMEGAs 4.3.1 [33] to
solve the Boltzmann equation by implementing relevant interactions inducing the DM pair
annihilation processes. Then we search for parameter sets which satisfy the approximate
region for the relic density [34]
In numerical calculations random parameter sets are prepared in the following parameter
ranges for each scenario:
For all scenario :
− ∈ [50, 1100] GeV,
mH3 ∈ [30, 2200],
vS = 1000 GeV,
scenario (I) : f ∈ [0.1, √4π], µ 1S = µ 2S = µ SS = 10−3 GeV,
mH1 = mH± = mA ∈ [70, mψ] GeV,
In figure 2, we show parameter points which explain the observed relic density of DM for
scenario (I) where red and blue points correspond to the case of (a) m
− + m+ > mH3 > m
relic density with f < √4π since only ψ ψ
− > mH3 . We find that the case of mH3 > m
− + m+ cannot provide observed
± → aa channel is allowed. In the case (a),
H3a is enhanced near threshold mH3 ≃ m
− + m+ due to the t-channel propagator of ψ
− → H3H3, aa, shown in figure 1-(A),(B). The
resonance dominance in the case (a).
We find that the allowed parameter points for scenario (II) is similar to scenario (I)
− → H3 → H3H3 is subdominant. The allowed
− > mH3 while
most of µ SS region can be allowed. Since the result is similar to that of scenario (I) we
omit the plot for scenario (II).
The allowed parameter points for scenario (III) and (IV) are given in figure 3 in
− as
can be seen from figure 1-(C) and (D) can explain the relic density since resonant
enhance10% is required. For the resonant region, wide range of µ 2S(1S) is allowed as shown in left
plots of figure 3. For scenario (III), parameter space with large value of µ 2S is constrained
Higgs. In addition, larger resonant enhancement is required to obtain sufficient
annihilation cross section. In scenario (IV), also dependence on the value of mH1 is small unless it
is not very close to that of m .
Direct detection
Here we discuss direct detection of DM in our model focusing on our scenario (III) since
by the SM Higgs exchanging process via mixing effect in scalar sector in our model, which
is calculated in non-relativistic limit. We obtain the following effective Lagrangian by
integrating out h and H3;
Leff =
2√2v
m2h − m2H3
where the effective coupling constant fN is obtained by
Here we replace the heavy quark contribution by the gluon contributions such that [30]
Leff =
2√2v
m2h − m2H3
− −
fN =
X fqN =
hN |q¯q|N i.
fqN =
mN q=c,b,t
mass respectively, and the sum is over all quark flavors. The effective Lagrangian can be
which is obtained by calculating the triangle diagram. The trace of the stress energy tensor
is written as follows by considering the scale anomaly;
Combining eqs. (3.11) and (3.12), we obtain
fqN =
9 1 −
fN =
m2h − m2H3
nucleon and DM. For simplicity, we estimate DM-neutron scattering cross section since
of neutron [36]. The figure 4 shows the DM-nucleon scattering cross section for the allowed
parameter sets in scenario (III); for other scenarios the cross section is negligibly small
constraint from LUX [37] (few parameter space is excluded), and some parameter sets
would be tested in future direct detection experiments [38].
Indirect detection
Here we discuss possibility of indirect detection in our model. The thermally averaged
cross section in current Universe is estimated with micrOMEGAs 4.3.1 applying allowed
parameter sets. The figure 5 shows the cross section for scenario (I) and scenarios (III,IV)
in left and right panel respectively; the scenario (II) provide same feature as scenario (I)
and the corresponding plot is omitted here.
For scenario (I), colors of points correspond to that of in figure 2. We find that the
cross section is suppressed since the amplitude of the process decreases as momentum of
− → H3H3 does not change much while that for
− is required in
the latter case and the current cross section can be much different from that in freeze out
era; the case of mH3 ≃ (.)2m
mH3 & 2m
amplitude decreases as DM momentum. The H3 further decays into hh and SM particles
current constraint by LUX [37] and future prospect by XENON 1t [38].
ScenarioHIII, IVL
sets which provides observed relic density. In the left plot, colors of points correspond to that in
figure 2. In the right plot, red and blue points correspond to scenario (III) and (IV) respectively.
pattern of H3 and detailed analysis is beyond the scope of this paper. The scenario (II)
provide same result as scenario (I) since annihilation processes are almost same.
For scenario (III) and (IV), the s-channel processes with µ 2S and µ 1S can be also
− − →
µ 2S from mixing with H3 and SM Higgs. Note that due to resonant enhancement the
cross section can be ∼ 10−27cm2/s for the processe ψ−ψ
− → H3 → {H1H1, AA, H+H−}
such as Fermi-LAT [39] since H± decay into charged leptons. The decays of {H1, A, H±}
also provide neutrino flux, which is much smaller than current constraint by High energy
neutrino search such as IceCube [40, 41], and It would be tested in future observation.
Conclusions and discussions
We have studied a dark matter model in which neutrinos get Dirac masses. The global
U(1)X symmetry forbids the Majorana mass terms of the right-handed neutrinos, thereby
allowing the Dirac masses for the neutrinos. The same symmetry, broken down to a discrete
Z2 symmetry, guarantees the stability of a dark matter candidate which is a hidden sector
fermion charged under the global U(1)X . The spontaneous symmetry breaking of U(1)X
occurs due to VEV, vS, of a hidden sector scalar S whose pseudo-scalar component becomes
Goldstone boson, providing a new channel to the DM annihilations.
S, SM Higgs and S, and scalar doublet for neutrinos and S, respectively. In scenario (I),
In scenarios (I) and (II), depending on the DM mass, coupling f & 0.05 can explain
the current DM relic abundance. In scenarios (III) and (IV), the DM relic density can be
accommodated near the resonance, 2m
− ≈ mH3 , where the DM annihilation cross section
Only scenario (III) has tree-level contribution to the direct detection via dark-scalar
mixing with the SM Higgs boson. Even in this case the direct detection cross section is
marginal or well below the current LUX bound due to small mixing as observed at the LHC.
We also investigated the implications of our model on the indirect detection of DM.
− → {aH3, H3H3}, are suppressed because the
− → aa can be sizable due to
Breit-Wigner enhancement. However, aa channel can not be detected by the observation.
In scenario (III), the cross section for hh channel is suppressed due to constraint from H3
and SM mixing. On the other hand, In scenario (IV), with resonant enhancement the
when scalar bosons decay into charged fermions.
Acknowledgments
This work is supported in part by National Research Foundation of Korea (NRF) Research
Grant NRF-2015R1A2A1A05001869 (SB).
Open Access.
This article is distributed under the terms of the Creative Commons
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any medium, provided the original author(s) and source are credited.
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