Dark matter with two inert doublets plus one Higgs doublet

Venus Keus 0 1 2 3 5 6 7 8 Stephen F. King 0 1 3 5 8 Stefano Moretti 0 1 2 3 5 8 Dorota Sokolowska 0 1 3 4 8 Egham Hill 0 1 3 8 Egham TW 0 1 3 8 EX 0 1 3 8 U.K. 0 1 3 8 E-mail: 0 1 3 8 0 1 3 8 Open Access 0 1 3 8 c The Authors. 0 1 3 8 0 Chilton , Didcot, Oxon OX11 0QX, U.K 1 Highfield campus, University Road , Southampton, SO17 1BJ, U.K 2 Particle Physics Department, Rutherford Appleton Laboratory 3 Gustaf Hallstromin katu 2, FIN-00014 University of Helsinki , Finland 4 University of Warsaw, Faculty of Physics 5 School of Physics and Astronomy, University of Southampton 6 Department of Physics, Royal Holloway, University of London 7 Department of Physics and Helsinki Institute of Physics 8 Pasteura 5 , 02-093 Warsaw , Poland Following the discovery of a Higgs boson, there has been renewed interest in the general 2-Higgs-Doublet Model (2HDM). A model with One Inert Doublet plus One Higgs Doublet (I(1+1)HDM), where one of the scalar doublets is inert (since it has no vacuum expectation value and does not couple to fermions) has an advantage over the 2HDM since it provides a good Dark Matter (DM) candidate, namely the lightest inert scalar. Motivated by the existence of three fermion families, here we consider a model with two scalar doublets plus one Higgs doublet (I(2+1)HDM), where the two scalar doublets are inert. The I(2+1)HDM has a richer phenomenology than either the I(1+1)HDM or the 2HDM. We discuss the new regions of DM relic density in the I(2+1)HDM with simplified couplings and address the possibility of constraining the model using recent results from the Large Hadron Collider (LHC) and DM direct detection experiments. 1 Introduction 2 3 4 Constructing the I(2+1)HDM potential Mass eigenstates Constraints on parameters Theoretical constraints Experimental constraints Collider constraints Dark matter constraints DM (co)annihilation in the I(2+1)HDM Coannihilation scenarios relevant for DM relic density studies The simplified I(2+1)HDM Simplified couplings in the I(2+1)HDM The k = 0 case The k = 1 case with vanishing mixing Open invisible channels (mDM < mh/2) Closed invisible channels (mW > mDM > mh/2) Heavy DM mass (mDM Summary of k = 1 results for fixed DM mass The k 6= 1 with vanishing mixing case The k 6= 1 with small non-vanishing mixing case A Feynman rules A.1 Scalar couplings A.2 Gauge couplings Introduction The ATLAS and CMS experiments at the Large Hadron Collider (LHC) have found eviearlier predictions performed using Electro-Weak (EW) precision data [1, 2]. Further studies are needed in order to determine whether this particle belongs to the Standard Model (SM) or to one of its extensions. However, so far, there are no reports of detection of physics Beyond the SM (BSM), neither by discovery of new particles, nor by any significant deviation from the SM prediction of the Higgs signal strengths, and strong bounds are set for the most common BSM models. On the other hand, new physics is expected for various theoretical and experimental reasons. One of the most important is the existence of Dark Matter (DM), stable on cosmological time scales, cold, i.e., non-relativistic at the onset of galaxy formation, nonbaryonic, neutral and weakly interacting component of the Universe [3]. Strong premises for its existence come from the galactic, cluster and horizon scales, making the modifiedgravity based explanations of the observed phenomena less likely. Various candidates for such a state exist in the literature, the most well-studied being the Weakly Interacting Massive Particles (WIMPs) [46]. WIMPs mass may change roughly between a few GeV and a few TeV, and the annihilation cross section is of approximately weak strength. The relic density of WIMPs is calculated with the assumption that they were in thermal equilibrium with the SM particles after inflation. Once the rate of reactions DM DM SM SM becomes smaller than the Hubble expansion rate of the Universe, the WIMPs freeze-out, i.e., drop out of the thermal equilibrium. After freeze-out the co-moving WIMP density remains essentially constant, with the current value estimated by the Planck experiment to be [3]: WIMPs are usually stable due to the conservation of a certain discrete symmetry. In case of the most-studied candidate in Supersymmetric (SUSY) models, neutralino (a Majorana fermion), it is the R-parity related to the imposed R-symmetry [7, 8]. Bosonic candidates appear in the models with Universal Extra Dimensions (UED) and are made stable by the KK-parity, the remnant of momentum conservation in the extra dimension [9, 10]. One could also consider the scalar candidates, stabilized, for example, by the conserved ZN discrete symmetry in the scalar potential, see, e.g., [1118]. One of the simplest models that provide a scalar DM candidate is the model with One Inert Doublet plus One Higgs Doublet (I(1+1)HDM),1 proposed in 1976 [13], and which has been studied extensively for the last few years (see, e.g., [14, 16, 17]). In this model one SU(2)W doublet with the same quantum numbers as the SM Higgs doublet is introduced. One of the possible vacuum states in this model is (v, 0) where the second doublet does not develop a Vacuum Expectation Value (VEV)2 and therefore does not take part in the EW Symmetry Breaking (EWSB). Since this doublet does not couple to fermions, and it is by construction the only Z2-odd field in the model, it provides a stable DM candidate: the lightest state among scalar, pseudo-scalar and charged Z2-odd particles. The I(1+1)HDM can be treated as an example of the Higgs-portal type of DM model, where the DM sector communicates with the SM sector through the Higgs boson exchange [1921]. As a result, the DM-Higgs coupling, gDMh, governs the DM annihilation 1This model is known in the literature as the Inert Doublet Model (IDM). We refer to it as I(1+1)HDM though for the clarification of the number of scalar doublets. 2The doublet that acquires a VEV is called the active doublet and the one with no VEV is called the DM particles, (middle) DM-nucleon scattering in direct detection experiments, (right) Higgs invisible decay into two DM particles. (see figure 1). Normally, fulfilling current experimental constraints for these three types of processes at the same time is a very difficult task, as shown for e.g. in [2224]. A possible solution to this problem is destroying the simple relation between the annihilation rate and the direct detection cross-section by introducing coannihilation processes, between DM and other inert particles, which are close in mass. Coannihilation processes lead to an increase or decrease of the effective annihilation cross-section, which in turn gives respectively smaller or larger DM relic density values. In the I(1+1)HDM, for example, the DM candidate could coannihilate with neutral and/or charged Z2-odd particles. In models with a richer particle spectrum, more coannihilation processes could come to play. One could simply ex (...truncated)