UNIFYING ASYMMETRIC INERT FERMION DOUBLET DARK MATTER AND LEPTOGENESIS WITH NEUTRINO MASS

# Unifying Asymmetric Inert Fermion Doublet Dark Matter and Leptogenesis With Neutrino Mass

NARENDRA SAHU

UNIFYING ASYMMETRIC INERT FERMION DOUBLET DARK MATTER AND LEPTOGENESIS WITH NEUTRINO MASS

Department of Physics, Indian Institute of Technology Hyderabad

Yeddumailaram 502205, AP, India

We propose a scalar Triplet extension of the standard model (SM) to unify the origin of neutrino mass with the visible and dark matter component of the Universe. We assume that the scalar triplet is super heavy, so that its CP-violating out-of-equilibrium decay in the early Universe not only produce asymmetric dark matter which is the neutral component of an additional vector like fermion doublet, but also give rise to lepton asymmetry. The latter gets converted to observed baryon asymmetry via B+L violating sphaleron processes. Below electroweak phase transition the scalar triplet acquires a vacuum expectation value and give rise to sub-eV Majorana masses to three flavors of active neutrinos. Thus an unification of the origin of neutrino mass, lepton asymmetry and asymmetric dark matter is achieved within a scalar triplet extension of the SM.

## 1 Introduction

Strong evidence from galaxy rotation curve, gravitational lensing and large scale structure implies that there exist invisible matter whose relic abundance, , is well measured by the WMAP satellite . This invisible matter is usually called dark matter (DM) and interacts gravitationally as the above evidences imply. However, it does not have any electromagnetic interaction with the visible matter. But DM can have weak interaction as many direct, indirect and collider experiments are currently exploring it.

The existing evidence of DM imply that it should be massive, electrically neutral and is stable on cosmological time scales. However, such a particle is absent in the SM particle spectrum and therefore led to many theories in the physics beyond SM scenarios. Another issue concerning SM is the origin of tiny amount of visible matter in the Universe which is in the form of baryons with , that could be arising from a baryon asymmetry , as established by WMAP combined with the big-bang nucleosynthesis (BBN) measurements. Moreover, the tiny masses of three active neutrinos required by the oscillation experiments are not explained within the SM framework.

The fact that could be a hint that both sectors share a common origin and the present relic density of DM is also generated by an asymmetry . In this talk we present an economic model where the asymmetric DM and baryonic matter densities can be generated simultaneously in the early Universe (above electroweak phase transition) and Majorana masses of three flavours of active neutrinos at late epochs (below electroweak phase transition) from a common source. We extend the SM by introducing two scalar triplets and . We also add a vector like fermion doublet and impose a discrete symmetry under which is odd while rest of the fields are even. As a result the neutral component of becomes a candidate of DM. The CP-violating out-of-equilibrium decays: , where is the lepton doublet, and then induce the asymmetries simultaneously in visible and DM sectors. The lepton asymmetry is then transferred to a baryon asymmetry through the B+L violating sphaleron transitions while the asymmetry in the DM sector remains intact as the B+L current of vector like fermion doublet is anomaly free. In the low energy effective theory the induced vacuum expectation value (vev) of the same scalar triplet gives rise to sub-eV Majorana masses, as required by oscillations experiments, to the three active neutrinos through the lepton number violating interaction , where is the SM Higgs.

## 2 The Scalar Triplet Model with Inelastic Dark Matter

In addition to the vector-like lepton doublet , we have two scalar triplets . In our convention the scalar triplet is defined as , with hypercharge . Since the hypercharge of is 2, it can have bilinear couplings to Higgs doublet as well as to the lepton doublets and . The scalar potential involving (from here onwards we drop the subscripts for the two scalar triplets and refer to them loosely as ) and can be written as follows:

 V(Δ,H) = M2ΔΔ†Δ+λΔ2(Δ†Δ)2−M2HH†H+λH2(H†H)2+λΔHH†HΔ†Δ (1) + 1√2[μHΔ†HH+h.c.].

Below electroweak phase transition the scalar triplet acquires an induced vacuum expectation value (vev):

 ⟨Δ⟩=−fHv2√2MΔ, (2)

where = 246 GeV. The value of is upper bounded to be around 1 GeV in order not to spoil the SM prediction: . The bi-linear couplings of leptons and Higgs to are given by:

 −L⊃1√2[fHMΔΔ†HH+(fL)α,βΔLαLβ+fψΔψψ+h.c.], (3)

where and . The above Lagrangian satisfy a discrete symmetry under which is odd, while rest of the fields are even. As a result the neutral component of , i.e. behaves as a candidate of DM. When acquires a vev, the coupling gives Majorana masses to three flavors of active neutrinos as:

 (Mν)αβ=√2fαβ⟨Δ⟩=−fL,αβfHv2MΔ. (4)

Taking GeV and and we get (eV), which is compatible with the observed neutrino oscillation data. Moreover, the coupling also give a Majorana mass to given by

 m=√2fψ⟨Δ⟩=fψfHv2MΔ. (5)

Therefore the Dirac spinor can be written as sum of two Majorana spinors and . The Lagrangian for the DM mass becomes:

 −LDMmass = MD[¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(ψDM)L(ψDM)R+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(ψDM)R(ψDM)L] (6) +m[¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(ψDM)cL(ψDM)L+¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯(ψDM)cR(ψDM)R].

This implies there is a mass matrix for the DM in the basis . By diagonalising it two mass eigenstates and arise, with masses and . The small mass splitting between the two mass eigen states: led to the property of DM to be inelastic type. From the direct search experiments this is required to be keV. We will come back to this issue while discussing inelastic scattering of DM with nucleons.

## 3 Simultaneous generation of visible and DM asymmetries

We assume that the scalar triplets and are super heavy. So that the CP-violating out-of-equilibrium decay of the lightest one, say , in the early Universe can generate asymmetries simultaneously in visible and DM sectors. From Eq. (3) we see that the scalar triplets can decay in three channels: , and . Moreover, these couplings are complex. Therefore, CP violation can arise from the interference of tree level and self-energy correction diagrams as shown in the figure (1). From these diagrams we see that to generate a net CP asymmetry at least two scalar triplets and are required. As a result the interaction of and is described by a complex mass matrix instead of a single mass term as mentioned in (1). The diagonalisation of the flavour basis spanned by () gives rise to two mass eigenstates with masses and . The complex conjugate of are given by . Unlike the flavor eigenstates and , the mass eigenstates and are not CP eigenstates and hence their decay can give rise to CP asymmetry. Assuming a mass hierarchy in the mass eigenstates of the triplets, the final asymmetry arises by the decay of lightest triplet and . The CP asymmetries are estimated to be:

 ϵL= (7) ϵDM= (8)

where

 Γ1=M18π(|f1H|2+|f1ψ|2+|f1L|2), (9)

is the total decay rate of the lightest triplet. When fails to compete with the Hubble expansion scale of the Universe, decays away and produces asymmetries in either sectors. As a result the yield factors are given by:

 YL≡ nLs=ϵLXζηL, (10) YDM≡ nψs=ϵDMXζηDM, (11)

where , is the entropy density and , are the efficiency factors, which take into account the depletion of asymmetries due to the number violating processes involving , and . At a temperature above EW phase transition a part of the lepton asymmetry gets converted to the baryon asymmetry via the sphaleron processes. As a result the baryon asymmetry is . From (11) we get the DM to baryon ratio:

 ΩDMΩB=10.55mDMmpϵDMϵLηDMηL, (12)

where GeV is the proton mass. From this equation it is clear that the criteria can be satisfied by adjusting the ratio of CP-violation: and the ratio of efficiency factors: . The details of numerical analysis can be found in refs..

## 4 Inelastic Inert Fermion Doublet DM and Direct Searches

We now comment on the implications of our model for DM search. As already mentioned, the coupling between and provides a small Majorana mass to . In the mass basis, has an off diagonal coupling with the boson, preventing it to be excluded by direct detection searches. If the mass splitting is of the order of several keV, the DM actually has enough energy to scatter off nuclei and to go into its excited state , which is the definition of inelastic scattering .

The state of art for inelastic inert fermion doublet DM is given in figure 2 in the -plane, where the cross-section is fixed by the model, while the Majorana mass is allowed to vary in a reasonable range of values, in order for the scattering to occur. A Majorana mass of the order of 100 keV accounts for the DAMA  annual modulated signal (shaded region), while a much wider range accounts for the event excess seen in CRESST  (blue non filled region). However those regions are severely constrained by XENON100  and KIMS . KIMS is very constraining being a scintillator with Iodine crystals as DAMA. Our DM candidate can explain simultaneously the DAMA and CRESST detection, with a marginal compatibility at with XENON100 and KIMS, for a mass range that goes from 45 GeV up to GeV. If we give up the DAMA explanation, then it could account for the CRESST excess up to masses of the order of GeV.

In summary we present a scalar triplet extension of the SM where the decay of triplet in the early Universe produces visible and DM, while its induced vev give rise to Majorana masses to three flavours of active neutrinos in the late universe.

## Acknowledgments

I would like to thank Rabindra N. Mohapatra and Chira Arina for useful discussions.

## References

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