Inert Higgs Doublet Dark Matter in Type-II Seesaw

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Nuclear Physics B Proceedings Supplement 00 (2014) 1–3

Nuclear Physics B Proceedings Supplement

Inert Higgs Doublet Dark Matter in Type-II Seesaw

Chuan-Hung Chen and Takaaki Nomura

Department of Physics, National Cheng-Kung University, Tainan 701, Taiwan

Abstract

Weakly interacting massive particle (WIMP) as a dark matter (DM) candidate is further inspired by recent AMS- 02 data, which confirm the excess of positron fraction observed earlier by PAMELA and Fermi-LAT experiments.

Additionally, the excess of positron+electron flux is still significant in the measurement of Fermi-LAT. For solving the problem of massive neutrinos and observed excess of cosmic-ray by DM annihilation, we study the model with an inert Higgs doublet (IHD) in the framework of type-II seesaw mechanism by imposing aZ2symmetry on the IHD, where the lightest particle of IHD is the DM candidate while the neutrino masses origin from the Higgs triplet in type-II seesaw model. We calculate the cosmic-ray production in our model and find that if leptonic triplet decays are dominant, the observed excess of positron/electron flux could be explained well in normal ordered neutrino mass spectrum, when the constraints of DM relic density and comic-ray antiproton spectrum are taken into account.

Keywords: Dark Matter, Inert Higgs doublet, Type-II seesaw, Cosmic Ray

1. Introduction

There are two strong indication of the existence of new physics: one is the observation of neutrino oscilla- tions leading to massive neutrinos [1], and another one is the astrophysical evidence of dark matter(DM). The potential DM signals have been observed by the indi- rect detection such that the results measured by AMS- 02 [3] have confirmed the excess of positron fraction which was observed earlier by PAMELA [4] and Fermi- LAT [5] experiments(recently AMS-02 published new results [7, 8]). Motivated by these issues, we consider the model accommodating neutrino mass and DM [9].

We addZ2symmetry in the Standard Model(SM) where all SM particles are even under the Z2. We then introduce new Higgs doublet and Higgs triplet which are Z2 odd and even respectively. TheZ2 odd doublet cor- responds to the inert Higgs doublet(IHD) providing a DM candidate [10, 11], and Higgs triplet leads neutrino mass via Type-II seesaw mechanism [12]. In this study, we investigate new interactions in the model and search for the paramter region which can explain excess of the cosmic-ray as well as DM relic density.

2. Inert Higgs doublet with type-II seesaw

We extend the SM introducing discreteZ₂symmetry, scalar SU(2) doublet Φwith hypercharge Y = 1, and scalar SU(2) triplet∆with hyperchargeY =2. The SM particles and∆are allZ2 even andΦisZ2 odd. Thus the lightest particle from inert doubletΦis stable and can be DM candidate when it is neutral. The triplet ∆ have Yukawa interaction with lepton doublets, and provide neutrino mass after electroweak symmetry break- ing, known as Type-II seesaw mechanism.

The new gauge interactions, new Yukawa couplings and scalar potential are written such that

L_NP=(DµΦ)^†D^µΦ +(Dµ∆)^†D^µ∆

−

"

1

2L^TChiσ2∆PLL+h.c.

#

−V(H,Φ,∆), (1)

where we have suppressed the flavor indices in Yukawa sector,hdenotes the 3×3 Yukawa matrix, P_L =(1− γ5)/2,L^T =(ν_`, `) is the lepton doublet,σ2is the second Pauli matrix andC =iγ0γ2. The new scalar fields are

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written as

Φ = H⁺ (S +iA)/√

2

! ,

∆ = δ⁺/√

2 δ⁺⁺

(v_∆+δ⁰+iη⁰)/√

2 −δ⁺/√ 2

!

, (2)

wherev_∆ is the VEV of triplet andS is our DM candidate. As in the Type-II seesaw models, the value of v_∆is constrained by theρ-parameter which is given by, at tree level, ρ ' (1+2v²_∆/v²₀)/(1+4v²_∆/v²₀) . Taking the current precision measurement forρ-parameter to be ρ=1.0004⁺_−0.0004^0.0003[1], we getv_∆<3.4 GeV when 2σer- rors is taken into account. The value of triplet VEV de- termines the decay pattern of triplet Higgs bosons where they decay into dilepton(diboson) modes forv_∆ ( )10⁻⁴ GeV. In our analysis, we assume triplet Higgs bosons decays 100% into leptons.

The neutrino mass matrices are obtained such that h = (√

2/v_∆)U^∗_PMNSm^dia_ν U_PMNS^† , where m^dia_ν = diag(m₁,m₂,m₃), m_is are the physical masses of neutrinos andU_PMNSis the PMNS matrix. We have several possible mass pattern of neutrinos such as normal ordering(NO) (m1 <m2 <m3), inverted ordering(IO) (m3 <

m2 <m1), and quasi-degeneracy(QD)(m1 ∼m2 ∼m3).

In this proceeding, we show results for NO case which is most promising to reproduce the observed data.

Finally we discuss parameter setting in our analysis.

The interactions which we consider are four-point couplings of two-Φs and two-∆s, and three-point couplings of two-Φand one-∆. The former includes two coupling constantsχA andχB, while the latter is determined by massive couplingµ₂. We thus take these parameters as input in following analysis. Furthermore, we assume negligible coupling between SM Higgs and inert doublet. For simplifying our numerical analysis, we adopt following mass relations

mS =mA−1 GeV,mH^±=mA,

mδ^±±=mδ^±=m_δ0≡mδ=500 GeV. (3) where mXs are the masses of particle X. Note that the first two relations, requiring degenerate inert Higgs masses, suppress the gauge interactions of inert Higgs for heavy mass region. For more detailed discussion of the model, see the Ref. [9].

3. Relic Density and Cosmic-Ray fluxes

In this section, we discuss the relic density and cosmic ray fluxes from DM annihilation in our model. The processes of our interest are DM annihilation into triplet

Figure 1: The allowed region in scenario-Ia,c and scenario-II when Ωh²is satisfied. Left panel denotes the correlation betweenmS and χ_A(χ_B) in scheme Ia(c). The Schemes Iaand Ichave the same results, and the results of scheme Ibis also similar.

Higgs bosons which further decays into leptons. In our analysis, we consider scenarios I and II where the former is s-channel dominant and latter is t-channel dominant. These scenarios depend on the parameter sets {mS, χA, χB} and {mS, µ2} respectively. For scenario- I, we further consider three cases as follows : (Ia) χ_A χ_B ≈ 0, (Ib)χ_A = χ_B and (Ic)χ_A ≈ 0 χ_B. We first constrain the parameters so that the observed relic density of DM is explained. We then estimate the cosmic-ray fluxes of anti-proton, positrons and elec- trons. Usually we need boost factor(BF) to enhance current DM annihilation cross section to explain the excess of cosmic-rays. We introduce BF as a parameter and it is constrained by anti-proton flux data.

The relic density of DM S is determined by the thermally-averaged cross sections of (co)annihilation processes. For numerical calculations, we use micrOMEGAs [13] to estimate the relic density by im- plementing our model. The relic density of S is re- quired to satisfy 90% CL(confidence level) range of observed value such as 0.1159 ≤ Ωh² ≤ 0.1215 [14].

For scenario-I, we consider three cases based on rela- tive magnitude ofχAandχB. We then find that theO(1) value ofχA,B can explain the observed relic density for DM mass of order TeV. For scenario II, we find that the parameterµ2should be same order as DM massmS to provide right relic density.

The BF can not be arbitrary and we need to investigate the limit by the observed value. Our model provides anti-proton flux from DM annihilation intoWW andZZvia gauge interaction. UsingmicrOMEGAs, we estimate the flux taking into account the galactic prop- agation of charged particles and solar modulation, and compare with the experimental data [15, 16] to obtain the limit of BF. As a result we estimated upper limit of BF as {30,500,1800,4500}for DM mass of{1,2,3,4}

TeV respectively.

We then investigate the influence of DM annihilation on the positron/electron flux taking into account limit of BF. We then need to know the background contribution of primary and secondary positrons. In

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Figure 2: The positron+electron spectrum for normal ordered neutrino masses, where we have usedmS =3000 GeV and boost factorBF= 1500. The thick solid line is the cosmic-ray background. In the figure, we quote the data of PAMELA [6] and Fermi-LAT [19].

Figure 3: The positron fraction, where the settings are same as electron-positron flux of Fig. 2. In the figure, we quote the data of PAMELA [4], Fermi-LAT [5] and AMS02 [3].

our numerical calculation, we apply the following fit- ting functions for primary (secondary) cosmic ray fluxes Φ^prim(sec) given in Refs. [17, 18], where unit of flux is [GeV⁻¹cm⁻²s⁻¹sr⁻¹]. The total electron and positron fluxes are thus given byΦe⁻ =κΦ^prim_e⁻ +Φ^sec_e⁻ +Φ^DM_e⁻ ,and Φe⁺ = Φ^sec_e+ + Φ^DM_e+ whereΦ^DM_e−(+)is the electron(positron) flux from DM annihilations. Note that the normaliza- tion of the primary electron flux is parametrized by the parameterκwhere we takeκ=0.78 in our analysis.

We calculateE³(Φe⁺ + Φe⁻) andΦe⁺/(Φe⁺+ Φe⁻) as functions of energy in the normal ordering case for each scenarios discussed above. The Figs. 2 and 3 show the results formS =3000 GeV andBF=1500 as reference values. The solid, dotted, dashed and dash-dotted lines in turn denote the scenarios-Ia, -Ib, -Icand -II respectively, and the thick solid line is the cosmic-ray background. We find that the contributions of scenario-I_cand scenario-II are much smaller than data due to small ratio of charged triplet Higgs mode in annihilation processes, while scenario-I_aand -I_bcan give fluxes reproducing the observed value closely. The case of other mass pattern of neutrinos and analysis of neutrino flux are discussed in Ref. [9].

4. Summary and discussions

We proposed the model which have inert Higgs doublet and Higgs triplet. The IHD provides the dark matter candidate. The Higgs triplet gives neutrino masses via triplet VEV: Type-II seesaw mechanism. We investi- gated the parameter region where new interaction of the model is dominant. Especially, we search for the possi- bility to accommodate relic density of the DM, neutrino masses, observed excess of positron/electron flux and positron fraction.

Acknowledgments: This work is supported by the National Science Council of R.O.C. under Grant

#: NSC-100-2112-M-006-014-MY3 (CHC) and NSC- 102-2811-M-006-035 (TN). We also thank the National Center for Theoretical Sciences (NCTS) for supporting the useful facilities.

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