Advances in High Energy Physics

Volume 2018, Article ID 4809682, 11 pages

https://doi.org/10.1155/2018/4809682

## Neutrino Mass and the Higgs Portal Dark Matter in the ESSFSM

Correspondence should be addressed to Najimuddin Khan; moc.liamg@321.scisyhpnahk

Received 20 November 2017; Accepted 8 February 2018; Published 13 March 2018

Academic Editor: Farinaldo Queiroz

Copyright © 2018 Najimuddin Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We extend the standard model with three right-handed singlet neutrinos and a real singlet scalar. We impose two and symmetries. We explain the tiny neutrino mass-squared differences with two - and -even right-handed neutrinos using type I seesaw mechanism. The -odd fermion and the -odd scalar can both serve as viable dark matter candidates. We identify new regions in the parameter space which are consistent with relic density of the dark matter from recent direct search experiments LUX-2016 and XENON1T-2017 and LHC data.

#### 1. Introduction

The found Higgs boson at the Large Hadron Collider (LHC) [1–3] completes the search for the particle content of the standard model (SM). The hierarchy problem related to the Higgs boson mass has motivated a plethora of models such as supersymmetry, and extra dimensions in which the fine-tuning is reconsidered. However, an inevitable consequence of these models is that the new physics should lie close to the TeV scale. Nonobservations [4] of any new physics from the collider experiments imply that the Higgs hierarchy issue is reverting back to being an unsolved open problem.

In addition, the SM is unable to explain some physical phenomena in nature such as the existence of massive neutrinos, the presence of dark matter (DM), the observed matter-antimatter asymmetry, and so forth. In the SM, by construction, the neutrinos are massless as it does not include right-handed neutrinos. However, from the neutrino oscillation experiments, we got convinced that at least two neutrinos have nonzero mass. The neutrino oscillation experiments have given information about the mass-squared differences between neutrino mass eigenstates. However the individual value of the masses is not yet known. It has been seen that the sum of the three neutrino masses is less than 0.1 eV [5–7] which is consistent with the cosmological measurements. Individual masses and the basic nature of neutrinos, that is, whether they are Dirac or Majorana particles, are still an open question.

As neutrino masses are very tiny compared to the other fermion masses, it is believed that the mechanism behind neutrino mass generation is different from the other fermions. The other fermions are obtained mass through the Higgs mechanism. The most popular natural explanation of small neutrino masses is the seesaw mechanism. There are broadly three classes of such models, namely, type I, type II, and type III seesaw models requiring involvement of right-handed neutrinos, a triplet scalar with hypercharge and hyperchargeless triplet fermions, respectively. The minimal scenario in this respect is the canonical type I seesaw mechanism, in which the SM is extended by a right-handed Majorana neutrinos [8–14]. The TeV-scale seesaw mechanism has been discussed in [15–17]. Including extra scalar fields, it has been studied in [18–21].

Various kinds of astrophysical observations, such as anomalies in the galactic rotation curves, gravitational lensing effects in the Bullet cluster, and excess gamma rays (The excess gamma rays from the galactic centers may come from other sources like pulsars.) from the galactic centers, have indicated the existence of DM in the Universe. The cosmological measurements of tiny anisotropies in Cosmic Microwave Background Radiation (CMBR) by the WMAP and Planck Collaboration [5] suggest that the Universe is made of dark energy, dark matter, and ordinary matter.

Astrophysical and cosmological data can tell us about the total amount/density of the DM of the Universe. There is still no consensus on what it is composed of and the properties are still unknown. The possibilities of different kinds of baryonic or nonbaryonic DM candidates have been discussed in [22]. The weakly interacting massive particles (WIMPs) are the best viable DM candidates. No evidence of the WIMP has been found from the direct detection experiments such as XENON100 [23], LUX [24, 25], and XENON1T [26]. As these DM-nucleon scattering experiments still have not found any signature in the detector, these experiments have ruled out low mass (10–50 GeV) regions in the parameter space of a - and Higgs -portal DM. Recent LUX-2016 [25] data has also excluded the mass range 65–550 GeV of a -portal fermionic (it depends on the mixing angle between Higgs and singlet scalar) DM model [27] and scalar DM models [27–29]. It indicates that we may need the multicomponent DM particles to explain the experimental data. We may detect these DMs in the more efficient detector in the future experiments. Multicomponent DM model is needed [30] to explain the Galactic Center gamma ray excess [31] and the colliding galaxy cluster [32–34] simultaneously. Multicomponent DM models have been considered in [35, 36] in various models which also include neutrino, Axion, and supersymmetric particles. Various models with two WIMP candidates could lead to typical signatures at different mass scale and have been studied in [37–58].

We add three right-handed singlet fermions and a singlet scalar to the SM. We also impose two and symmetries. All SM and the first two fermion fields are even under these and transformations. The Dirac mass terms can be formed using these fermions and the SM neutrinos. We use type I seesaw mechanism to explain the tiny neutrino mass-squared differences and the mixing angles which are observed by the neutrino oscillation experiments. The third -odd fermion and -odd scalar both can serve as viable DM particles in this work. Moreover, the requisite rate of annihilation is ensured by postulating some and preserving dimension-four and dimension-five operators for the scalar and fermion particles, respectively. The four-point interaction term of the extra fermions and scalar can be obtained from other five-dimensional operators [59]. The interaction term of the third fermion and the scalar allows a larger region of the parameter space than what we would have had with a single DM particle (either fermion or scalar) alone. This interplay brings an enriched DM phenomenology compared to the other models having fermion or scalar DM particle. The region of DM masses 65–550 GeV of a fermionic or scalar Higgs portal DM model is excluded from the present LUX experimental data. In this model, we show that the region with masses 50–550 GeV up to 300 TeV is still allowed by the direct search experiments. Hence, we feel a desirable feature of our model for future study.

The plan of the paper is as follows. In Section 2, we present the theoretical framework of our extended singlet scalar fermionic standard model (ESSFSM). We also discuss the diagonalization procedure to get the neutrino mass matrix and the relic density calculation of two dark matter particles. We show the detailed constraints on this model in Section 3. We present our numerical results and show the allowed region in the parameter spaces from the neutrino mass and mixing angle, relic density, and direct detection in Section 4. Finally, we conclude in Section 5.

#### 2. Theoretical Framework of the Model

In this section, we give a description of our model. We add three right-handed neutrinos and a scalar to the SM Lagrangian. These extra particles are singlet under transformation. We impose two and symmetries such that the SM fields and first two right-handed neutrinos are even under these and transformations. The third right-handed neutrino is odd (even) under () transformation whereas the scalar field is even (odd) under () transformation. The quantum numbers of the SM fields and extra right-handed neutrinos and scalar fields are summarized in Table 1. The -even neutrinos are free to mix with the usual SM neutrinos and therefore generate the neutrino masses through type I seesaw mechanism. These symmetries prohibited the coupling of an odd number of the third fermion and/or the scalar particle to the SM particles. The part of Lagrangian that is invariant under transformation is given bywhere summation over is implied, with denoting generation indices for the right-handed fermions. stands for the charge conjugation. The mutual interaction terms of the SM Higgs, left-handed leptons, the extra scalar, and fermions are given by is the SM Higgs doublet, , where and are the Goldstone bosons, and is the SM Higgs. stands for charge conjugate of . with and being the left-handed lepton doublet. does not assume the third index as the third fermion is odd under -symmetry. The indices ; hence the second term in (2) generates the mixing mass term between two - and -even neutrinos. After electroweak (EW) symmetry breaking, the fourth term, that is, the dimension-five operator also gives an additional mixing mass term. The Higgs to extra neutrinos couplings are also generated from the dimension-five operators (fourth and fifth term in (2)). This will lead to the Higgs boson decay into these extra neutrons. As the - and -even neutrinos are considered to be very heavy, the partial decay width of the Higgs to these neutrinos is zero. As we are allowing these dimension-five operators in the Lagrangian, for completeness, we also add the other dimension-five operators and , which in turn give more room in the parameter space to maneuver. In this work, we focus on the dominant dimension-five operators related to the neutrino and Higgs portal dark matter physics, that is, those involving at least one Higgs and neglecting other possible operators which are allowed by the SM gauge and symmetries. ’s are the cut-off scales for the new physics. In our calculation, we assume . , , , and are dimensionless coupling parameters. The cut-off scale and and the Yukawa couplings are important to explain the neutrino oscillation observables, whereas , , , and could change the masses and coupling strength of DM particles to the Higgs. In addition, these could alter the self-annihilation interaction probability of the heavier DM particles into the lighter DM particles. Hence, these parameters play a crucial role to calculate the relic density of the DM particles and . The masses of the DM particles are given byand the coupling strength of the DM candidates with the Higgs can be written as