Exploring the CP-violating Inert-Doublet Model

B. Grzadkowski 3 O.M. Ogreid 1 P. Osland 2 A. Pukhov 0 M. Purmohammadi 2 0 Skobeltsyn Inst. of Nuclear Physics, Moscow State University , Moscow 119991, Russia 1 Bergen University College , Postboks 7030, N-5020 Bergen, Norway 2 Department of Physics, University of Bergen , Postboks 7803, N-5020 Bergen, Norway 3 Institute of Theoretical Physics, Faculty of Physics, University of Warsaw , Hoza 69, PL-00-681 Warsaw, Poland We have explored properties of an extension of the Inert Doublet Model by the addition of an extra non-inert scalar doublet. The model offers a possibility of CP violation in the scalar sector and a candidate for the Dark Matter. Allowed regions in the plane spanned by the mass of the Dark-Matter particle and the lightest neutral Higgs particle have been identified, and constraints from direct-detection experiments have been studied. For favorable parameter regions one may observe long-lived charged particles produced at the LHC. Contents 1 Introduction 2 IDM2 model and notation 2.1 Fields and potential 2.2 Mass eigenstates of the IDM2 Theoretical and experimental constraints 3.1 Theoretical constraints 3.2 Experimental constraints Annihilation mechanisms 4.1 DM couplings 4.2 Representative branching ratios 4.2.1 Low- and medium-mass region 4.2.2 High-mass region 3 4 5 Parameters and scan strategy 5.1 Model parameters 5.2 General scanning strategy 5.3 Positivity and unitarity 6 Overview 7 Low-medium DM mass regime 7.1 Scanning strategy 7.2 Results for MS < 100 GeV 7.3 Results for new viable region 7.4 Summary of low-medium region High DM mass regime 8.1 Scanning strategy 8.2 Results CP violation 10 Direct detection 11 LHC prospects 11.1 MS < M < MA 11.2 MS < MA < M 12 Summary A Couplings of the inert sector B Invariants Im J1,2,3 The Inert Doublet Model (IDM) was introduced to accommodate or explain neutrino masses [1] and independently, to alleviate the little hierarchy problem while also providing a dark matter (DM) candidate [2]. The model represents a very minimal extension of the Standard Model (SM), it just contains an extra weak scalar doublet, which is odd under an unbroken Z2 symmetry, rendering the lightest member stable. The other members of this doublet are another neutral particle and a pair of charged ones. These particles can all be produced at colliders via their couplings to electroweak gauge bosons, subject to the constraint of the Z2 symmetry. The collider phenomenology has been explored in [3, 4] and the Early Universe phenomenology has been studied in some detail in [5] and [6]. While the IDM has many attractive features, simplicity being an important one, it was felt that the introduction of CP violation in the scalar sector would make the model more attractive, therefore an extension to a Two-Higgs-Doublet Model (2HDM) plus an inert doublet model was proposed [7]. This also allows for an alleviation of the little hierarchy problem. We shall refer to the resulting model as IDM2. It has been found that the IDM permits a DM particle with a mass in one of three regions: light (m mW ) [11, 12], medium (m mW ) [2, 5] or heavy (m > 535 GeV) [5, 6, 8]. Two of these mass regions (m mW and m > 500 GeV) were also found to yield solutions for the IDM2 [7]. The aim of the present paper is to explore the IDM2 in more detail, determine the allowed mass regions for the DM particle, its dominant annihilation channels, and the corresponding mass regions for the lightest Higgs boson H1. Furthermore, we will confront the model with constraints from direct-detection experiments, and briefly comment on possible signals in LHC experiments. The paper is organized as follows. In section 2 we review the model, and in section 3 we discuss the theoretical and experimental constraints. In section 4 we consider various annihilation channels and in section 5 we present the scan strategy adopted to search for allowed regions in the parameter space. In section 6 we give an overview of allowed regions of DM particle masses, whereas in sections 7 and 8 we explore in more detail parameters that are compatible with all the constraints in the low and high DM mass regions, respectively. Then, in section 10 we discuss constraints from direct detection experiments, in section 11 we briefly explore relevant LHC phenomenology, and in section 12 we summarize. The relevant couplings of the model are given in an appendix. IDM2 model and notation Fields and potential We denote the doublets of the 2HDM as where the 2HDM and inert-sector potentials read + 1 (11)2 + 2 (22)2 + 3(11)(22) 2 2 no CP-violation mediated by charged scalars. However, since m212 6= 0, CP is violated in the neutral non-inert scalar sector in the same way as in the 2HDM. In the absence of the potential (2.6), one would have to require m2 > 0 in order to ensure hi = 0. However, the non-zero expectation values of the other fields, v1/2 and v2/2, lead to an overall coefficient of the term that is bilinear in of the form Mass eigenstates of the IDM2 The neutral states of 1, 2 will in general mix to form three neutral states H1, H2, H3. These are linear combinations of 1, 2, and 3, where 3 sin 1+cos 2 is orthogonal to the neutral Goldstone boson G0 = cos 1+ sin 2 and the rotation matrix R is parametrized in terms of three angles 1, 2 and 3 according to the convention of [13]. For the quartic couplings describing the interaction between and 1 and 2, we adopt for simplicity the dark democracy: where m is a mass parameter of the potential (2.5). We shall take the scalar, S, to be the DM particle, i.e., MS < MA. The other choice would simply correspond to c c, without any modification of the phenomenology described in the following. It is instructive to invert the relations (2.10): MS2 MA2 . Thus, these couplings of the inert doublet to the non-inert Higgs sector can be expressed in terms of the mass splittings (including also the soft mass parameter m). It is convenient to introduce the abbreviation L 12 (a + b + c) = which is automatically satisfied by our choice of input parameters. Theoretical and experimental constraints We here present a summary of the constraints imposed on the model. Some of the theoretical ones (positivity, in particular) are absolute, whereas the experimental ones are quantitative, and subject to experimental precision. Theoretical constraints CP violation We do not impose CP conservation on the neutral Higgs sector. The amount of CP violation that remains after all constraints are imposed is determined afterwards. For a detailed discussion of the conditions for CP to be violated in this model, see appendix B of ref. [7]. Stability or positivity The potential should be bounded from below for any values of the fields 1, 2 and . This condition is rather involved for the potential (2.3). The full set of conditions are given in appendix A of [7]. For the somewhat simpler case of dark democracy considered here, we must impose x y2 (...truncated)