Advances in High Energy Physics

Volume 2015 (2015), Article ID 980687, 12 pages

http://dx.doi.org/10.1155/2015/980687

## The Higgs Sector of the Minimal SUSY Model

^{1}Universitè de Strasbourg, IPHC, 23 rue du Loess, 67037 Strasbourg, France^{2}CNRS, UMR7178, 67037 Strasbourg, France

Received 23 April 2015; Revised 17 June 2015; Accepted 25 June 2015

Academic Editor: Kai Schmidt-Hoberg

Copyright © 2015 Lorenzo Basso. 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

I review the Higgs sector of the extension of the minimal supersymmetric standard model (MSSM). I will show that the gauge kinetic mixing plays a crucial role in the Higgs phenomenology. Two light bosons are present, a MSSM-like one and a -like one, which mix at one loop solely due to the gauge mixing. After briefly looking at constraints from flavour observables, new decay channels involving right-handed (s)neutrinos are presented. Finally, how model features pertaining to the gauge extension affect the model phenomenology, concerning the existence of *R*-Parity-conserving minima at loop level and the Higgs-to-diphoton coupling, will be reviewed.

#### 1. Introduction

The recently discovered Higgs boson is considered as the last missing piece of the standard model (SM) of particle physics. Nonetheless, several firm observations univocally call for its extension, mainly, but not limited to, the presence of dark matter, the neutrino masses and mixing pattern, the stability of the SM vacuum, and the hierarchy problem. Supersymmetry (SUSY) has long been considered as the most appealing framework to extend the SM. Its minimal realisations (MSSM and its constrained versions (for a review, see [1])) start however to feel considerable pressure to accommodate the recent findings, especially the measured Higgs mass of GeV. Despite not in open contrast with the MSSM, the degree of fine tuning required to achieve it is more and more felt as unnatural. In order to alleviate this tension, nonminimal SUSY realisations can be considered. One can either extend the MSSM by the inclusion of extra singlets (e.g., NMSSM [2]) or by extending its gauge group. Concerning the latter, one of the simplest possibilities is to add an additional Abelian gauge group. I will focus here on the presence of group which can be a result of an heterotic string theory (and hence M-theory) [3–5]. This model, the minimal -Parity-conserving supersymmetric standard model (BLSSM in short), was proposed in [6, 7] and neutrino masses are obtained via a type I seesaw mechanism. Furthermore, it could help to understand the origin of -Parity and its possible spontaneous violation in supersymmetric models [6–8] as well as the mechanism of leptogenesis [9, 10].

It was early pointed out that the presence of two Abelian gauge groups in this model gives rise to kinetic mixing terms of the formwhich are allowed by gauge and Lorentz invariance [11], as and are gauge-invariant quantities by themselves; see, for example, [12]. Even if these terms are absent at tree level at a particular scale, they will in general be generated by RGE effects [13, 14]. These terms can have a sizable effect on the mass spectrum of this model, as studied in detail in [15], and on the dark matter, where several scenarios would not work if kinetic mixing is neglected, as thoroughly investigated in [16]. In this work, I will review the properties of the Higgs sector of the model. Two light states exist, a MSSM-like boson and a -like boson. After reviewing the model, I will show that a large portion of parameter space exists where the SM-like Higgs boson has a mass compatible with its measure, both in a “normal” ( GeV) and in an “inverted” hierarchy ( GeV), also in agreement with bounds from low energy observables and dark matter relic abundance. The phenomenological properties of the two lightest Higgs bosons will be systematically investigated, where once again the gauge mixing is shown to be fundamental. The presence of extra D-terms arising from the new sector, as compared to models based on the SM gauge symmetry, has a large impact on the model phenomenology. They affect both the vacuum structure of the model and the Higgs sector, in particular enhancing the Higgs-to-diphoton coupling. Both of these issues will be reviewed here, although the latter is disfavoured by recent data [17], to show model features beyond the MSSM.

#### 2. The Model

For a detailed discussion of the masses of all particles as well as of the corresponding one-loop corrections, we refer to [15]. Attention will be paid to the main aspects of the kinetic mixing since it has important consequence for the scalar sector. For the numerical investigations that will be shown, we used the SPheno version [22, 23] created with SARAH [24–28] for the BLSSM. For the standardised model definitions, see [29], while for a review of the model implementation in SARAH, see [30]. This spectrum calculator performs a two-loop RGE evaluation and calculates the mass spectrum at one loop. In addition, it calculates the decay widths and branching ratios (BRs) of all SUSY and Higgs particles as well as low energy observables like . We will discuss the most constrained scenario with a universal scalar mass , a universal gaugino mass , and trilinear soft-breaking couplings proportional to the superpotential coupling () at the GUT scale. Other input parameters are , , , , and . They will be defined in the following section. The numerical study here presented has been performed by randomly scanning over the independent input parameters above described via the SSP toolbox [31], while low energy observables such as BR() and BR() have been evaluated with the FlavourKit package [32]. Furthermore, during the scans, all points have been checked with HiggsBounds-4.1.1 [33–36], both in the “normal” hierarchy and in the “inverted” hierarchy case.

##### 2.1. Particle Content and Superpotential

The model consists of three generations of matter particles including right-handed neutrinos which can, for example, be embedded in 16-plets. Moreover, below the GUT scale, the usual MSSM Higgs doublets are present as well as two fields and responsible for the breaking of . The field is also responsible for generating a Majorana mass term for the right-handed neutrinos and thus we interpret its charge as its lepton number. The same goes for , and we call these fields bileptons since they carry twice the lepton number of (anti)neutrinos. The quantum numbers of the chiral superfields with respect to are summarised in Table 1.