Advances in High Energy Physics

Volume 2016 (2016), Article ID 8278375, 9 pages

http://dx.doi.org/10.1155/2016/8278375

## Constraints to Dark Matter from Inert Higgs Doublet Model

Instituto de Física, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile

Received 19 November 2015; Revised 25 January 2016; Accepted 28 January 2016

Academic Editor: Michal Kreps

Copyright © 2016 Marco Aurelio Díaz et al. 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 study the Inert Higgs Doublet Model and its inert scalar Higgs as the only source for dark matter. It is found that three mass regions of the inert scalar Higgs can give the correct dark matter relic density. The low mass region (between 3 and 50 GeV) is ruled out. New direct dark matter detection experiments will probe the intermediate (between 60 and 100 GeV) and high (heavier than 550 GeV) mass regions. Collider experiments are advised to search for decay in the two jets plus missing energy channel.

#### 1. Introduction

Astrophysical observations provide strong evidence for the existence of dark matter (DM) [1] and its abundance in the current phase of the Universe [2]. According to the newest results from Planck collaboration, there is 74% approximately of matter which is not directly visible but is observed due to its gravitational effects on visible matter. Additional evidence for the existence of DM comes from study of the rotation curves of spiral galaxies [3], the analysis of the bullet cluster [4], and the study of baryon acoustic oscillations [5]. One of the most common hypotheses used to explain these phenomena is to postulate the existence of weakly interacting massive particles (WIMPs) [6].

In order to explain DM, we study a simple extension of the Standard Model (SM), called the Inert Higgs Doublet Model (IHDM). This model, which was originally proposed for studies on electroweak (EW) symmetry breaking [7], introduces an additional doublet and a discrete symmetry. These two characteristics of the model modify the SM phenomenology, but there are some regions of the parameter space which predict only small deviations from the SM. Nevertheless, one of the most attractive characteristics of the IHDM is the presence of a stable neutral particle which can be a DM candidate.

In this work the IHDM is revisited, considering various restrictions, focusing our analysis on the zones of the parameter space which reproduce the correct DM relic density according to the newest measurements [8, 9]. In this context, three not connected mass regimes for the lightest inert particle are found. These regimes are also analyzed using LHC observables like branching ratios to invisible particles and a specific SM-like Higgs boson decay mode. Additionally, we study some inert decays modes. Finally, we use a direct detection approach to rule out one of the mass regimes. It is further shown that this regime can also be ruled out by constraints from collider physics [10].

This paper is organized as follows. After a short introduction in Section 1 the model is introduced in Section 2 by formulating the associated potential and constraints of the model, and by exploring the parameter space and its characteristics in Section 3. In Section 4 the behavior of the model is presented from a collider physics perspective, studying the modifications of the SM and its implications for the IHDM. In Section 5 the results of this study are complemented by an analysis from the dark matter perspective. Finally, in Section 6 we remark on the most important conclusions of our work.

#### 2. The Inert Higgs Doublet Model

Consider an extension of Standard Model (SM), which contains two Higgs doublets and a discrete symmetry [7] ( and ). All fields of the SM are invariants under the discrete symmetry, and is completely analogous to the SM Higgs doublet.

The most general renormalizable invariant Higgs potential that also preserves the discrete symmetry iswhere , , are given byThe parameters and are intrinsically real, and will be assumed to be real [11]. After Spontaneous Symmetry Breaking, the vacuum expectation values of the Higgs doublets arewhere is forced by the discrete symmetry and GeV. Expanding the fields around those vacua, we definewhere and are the neutral and charged Goldstone bosons and is the SM-like Higgs boson. The fields in the second doublet belong to the so-called* dark* or* inert* sector. They are the scalar and pseudoscalar , both neutral, and the charged scalar . As in the SM, the parameter is related to by the tree-level tadpole condition . The masses of physical states [12, 13] arewithAs independent and free parameters we take the masses , , and at tree-level and the couplings and . The SM-like Higgs boson mass is fixed now thanks to the measurement GeV [14, 15].

The constraints we initially impose include vacuum stability at tree-level, where constraints on the couplings and mass terms appear [16–18]; perturbation () [19, 20] and unitarity [21], where we impose that the scalar potential is unitary and that several scattering processes between scalar and gauge bosons are bounded; electroweak precision tests through the , , and parameters [22] applied to the IHDM [21, 23], with values given bywith a correlation coefficient of [24]; and collider constraints [16, 25–27], where we satisfy lower bonds on the Higgs boson masses.

The DM particle must be neutral. In our analysis we assume it is the boson; thus and , which due to (5) translates to

We do not consider as the DM candidate because it is analogous to consider as the DM candidate defining instead of .

#### 3. IHDM Parameter Space

We randomly scan the parameter space of the IHDM, taking into account all the constraints mentioned in the previous section. Additionally, we compute some astrophysical properties of the model using the micrOMEGAs software [28]. We consider masses satisfying 1 GeV 1 TeV, where . In addition, we consider cosmological measurements: the DM relic density is a property related to its abundance in the current phase of the Universe. This quantity is well measured by WMAP [29] and Planck [30] experiments. Following [31] to combine both measurements we obtain

In Figure 1 the coupling is shown as a function of the Higgs boson mass varying (, , , , and ). We work with the hypothesis that the light inert Higgs boson is providing the complete DM density given in (9). The color code is as follows: red points (dark gray) produce a relic density above the limit given in (9); blue points (black) produce a relic density within the region; green points (light gray) produce a relic density below the limit. Regarding the points that satisfy the relic density we see three clear regions [12, 32], one for low ( GeV), another one for medium ( GeV), and finally one for high values of ( GeV). The explanation for the gap is related to annihilation processes and it will be given later. At GeV the IHDM can no longer be compatible with vacuum existence and stability [33, 34].