Dark matter in the inert doublet model after the discovery of a Higgs-like boson at the LHC

A. Goudelis 1 B. Herrmann 1 O. Stal 0 Open Access 0 The Oskar Klein Centre, Department of Physics, Stockholm University , AlbaNova, SE-106 91 Stockholm, Sweden 1 LAPTh, Universite de Savoie , CNRS, 9 Chemin de Bellevue, B.P. 110, F-74941 Annecy-le-Vieux, France We examine the Inert Doublet Model in light of the discovery of a Higgs-like boson with a mass of roughly 126 GeV at the LHC. We evaluate one-loop corrections to the scalar masses and perform a numerical solution of the one-loop renormalization group equations. Demanding vacuum stability, perturbativity, and S-matrix unitarity, we compute the scale up to which the model can be extrapolated. From this we derive constraints on the model parameters in the presence of a 126 GeV Higgs boson. We perform an improved calculation of the dark matter relic density with the Higgs mass fixed to the measured value, taking into account the effects of three- and four-body final states resulting from off-shell production of gauge bosons in dark matter annihilation. Issues related to direct detection of dark matter are discussed, in particular the role of hadronic uncertainties. The predictions for the interesting decay mode h0 are presented for scenarios which fulfill all model constraints, and we discuss how a potential enhancement of this rate from the charged inert scalar is related to the properties of dark matter in this model. We also apply LHC limits on Higgs boson decays to invisible final states, which provide additional constraints on the mass of the dark matter candidate. Finally, we propose three benchmark points that capture different aspects of the relevant phenomenology. - The inert doublet model at tree level The inert doublet model beyond the tree level 3.1 One-loop corrections to the scalar masses 3.2 Renormalization group equations for the quartic couplings 1 Introduction 2 3 4 4.1 Theoretical constraints 4.2 Oblique parameters 4.3 Collider searches 4.4 Dark matter relic density 4.5 Dark matter direct detection Numerical analysis 5.1 Setup and strategy 5.2 Extrapolation scale 5.3 Dark matter 5.5 Benchmark scenarios 6 Summary A One-loop scalar masses B One-loop beta functions Introduction The Inert Doublet Model (IDM) is the simplest among the models with two Higgs doublets. In addition to the Standard Model (SM) particle content, it contains an extra doublet of complex scalar fields which couples to the SM scalar and gauge boson sector but not to the fermions. Moreover, it involves a discrete Z2 symmetry under which the new scalar doublet is odd and all the other particles are even, which makes that the new inert doublet particles can only appear in even number in interaction vertices. The IDM was first introduced more than three decades ago in studies of electroweak symmetry breaking (EWSB) [1]. Long after, it was proposed as a model that can provide a viable dark matter candidate according to the thermal relic picture [2, 3], since the neutral scalars contained in the new doublet can be seen as weakly interacting massive particles (WIMPs) and play the role of the dark matter (DM) in our universe. Due to its rich phenomenology for cosmology and particle physics, the IDM has received considerable attention [49]. Its DM candidate captures all the basic mechanisms through which the observed relic density can be generated in WIMP models [10]: The correct relic abundance [11] can be achieved by adjusting couplings, by approaching or taking distance from resonances, or by co-annihilating with another particle.1 Additionally, the IDM was advocated to allow for a heavier SM-like Higgs boson compatible with electroweak precision tests, mh0 & 200 GeV, without resorting to unnatural fine-tuning [3] (for recent work also considering this possibility, see, e.g., ref. [12]). The new states predicted by the IDM have been subjected to collider bounds [13], and they provide an interesting phenomenology for the Large Hadron Collider (LHC) [3, 1418]. While by now a heavy Higgs boson with SM couplings is experimentally ruled out [19, 20], the model still remains attractive due to its dark matter features. Furthermore, the IDM provides an interesting example of interplay between DM and Higgs physics, since the SM-like Higgs boson is one of the basic means of communication between the dark2 and visible sectors of the model. Hence, both the mass and the couplings of the SM-like Higgs boson are of crucial importance to assess whether the IDM can indeed explain the dark matter in the universe. With the recent announcement of the observation of a Higgs-like resonance with a mass of around 125126 GeV by the ATLAS and CMS collaborations [19, 20], as well as the supporting hints from the D and CDF experiments [21], it appears likely that the particle responsible for EWSB (or at least one of them) has been discovered. In this spirit, we find it timely and interesting to examine implications of this observation for the IDM. Apart from the obvious consequence that the number of free model parameters is reduced by one, other interesting features appear, as we shall describe in the present paper. Moreover, despite the attention that the IDM has received in the community, most studies rely on lowest order predictions only. An exception is the study beyond leading order that was performed in ref. [22]. This work is, however, limited to the interesting case of radiative electroweak symmetry breaking `a la Coleman-Weinberg, a scenario leading to rather extreme parameter values. Another exception is the very recent paper [23], where higher-order corrections to DM direct detection in the IDM are calculated. In the present work, we perform an analysis of the IDM parameter space assuming that the LHC is indeed observing a (SM-like) Higgs boson with a mass Mh0 126 GeV. In section 2, we introduce the model and the relevant notation. In section 3 we present one-loop corrections to the scalar masses in the IDM, and expressions for the one-loop renormalization group equations (RGEs) for the models quartic couplings, which are used to study vacuum stability, perturbativity, and unitarity constraints. Experimental constraints from collider, low-energy, and cosmological data are presented in section 4. The corresponding numerical analysis, which contains the main results of this work, is presented 1Coannihilation is absent, e.g., in the simpler singlet scalar model. 2This term is used in a slightly abusive way here, since the model does not contain what is usually dubbed a dark sector in the litterature. in section 5, where we perform extensive scans over the model parameter space. The implications for dark matter and the interesting Higgs decay into two photons are discussed in detail. Based on our analysis, we identify benchmark scenarios capturing general features of the parameter space. Finally, section 6 contains a summary of our results and the main conclusions. The inert doublet model at tree level The inert doublet model ( (...truncated)