Advances in High Energy Physics

Volume 2016 (2016), Article ID 5687463, 10 pages

http://dx.doi.org/10.1155/2016/5687463

## MSSM Dark Matter in Light of Higgs and LUX Results

^{1}Center for Fundamental Physics, Zewail City of Science and Technology, 6th of October City, Giza 12588, Egypt^{2}Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Received 26 September 2015; Accepted 6 December 2015

Academic Editor: Enrico Lunghi

Copyright © 2016 W. Abdallah and S. Khalil. 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

The constraints imposed on the Minimal Supersymmetric Standard Model (MSSM) parameter space by the Large Hadron Collider (LHC) Higgs mass limit and gluino mass lower bound are revisited. We also analyze the thermal relic abundance of lightest neutralino, which is the Lightest Supersymmetric Particle (LSP). We show that the combined LHC and relic abundance constraints rule out most of the MSSM parameter space except a very narrow region with very large (~50). Within this region, we emphasize that the spin-independent scattering cross section of the LSP with a proton is less than the latest Large Underground Xenon (LUX) limit by at least two orders of magnitude. Finally, we argue that nonthermal Dark Matter (DM) scenario may relax the constraints imposed on the MSSM parameter space. Namely, the following regions are obtained: TeV and GeV for low (~10); TeV or TeV and GeV for large (~50).

#### 1. Introduction

The most recent observations by the Planck satellite confirmed that 26.8% of the universe content is in the form of DM and the usual visible matter only accounts for 5% [1]. The LSP remains one of the best candidates for the DM [2, 3]. It is a Weakly Interacting Massive Particle (WIMP) that can naturally account for the observed relic density of DM.

Despite the absence of direct experimental verification, Supersymmetry (SUSY) is still the most promising candidate for a unified theory beyond the Standard Model (SM). SUSY is a generalization of the space-time symmetries of the quantum field theory that links the matter particles (quarks and leptons) with the force-carrying particles and implies that there are additional “superparticles” necessary to complete the symmetry. In this regard, SUSY solves the problem of the quadratic divergence in the Higgs sector of the SM in a very elegant natural way. The most simple supersymmetric extension of the SM, which is the most widely studied, is known as the MSSM [4–11]. In this model, certain universality of soft SUSY breaking terms is assumed at grand unification scale. Therefore, the SUSY spectrum is determined by the following four parameters: universal scalar mass , universal gaugino mass , universal trilinear coupling , and the ratio of the vacuum expectation values of Higgs bosons . In addition, due to -parity conservation, SUSY particles are produced or destroyed only in pairs and therefore the LSP is absolutely stable, implying that it might constitute a possible candidate for DM, as first suggested by Goldberg in 1983 [12]. So although the original motivation of SUSY has nothing to do with the DM problem, it turns out that it provides a stable neutral particle and, hence, a candidate for solving the DM problem.

The landmark discovery of the SM-like Higgs boson at the LHC, with mass ~125 GeV [13, 14], might be an indication for the presence of SUSY. Indeed, the MSSM predicts that there is an upper bound of 130 GeV on the Higgs mass. However, this mass of lightest Higgs boson implies that the SUSY particles are quite heavy. This may justify the negative searches for SUSY at the LHC run-I [15–18]. However, it is clearly generating a new “little hierarchy problem.”

Moreover, the relic density data [1] and upper limits on the DM scattering cross sections on nuclei (LUX [19] and other direct detection experiments [20, 21]) impose stringent constraints on the parameter space of the MSSM [22–25]. In fact, combining the collider, astrophysics, and rare decay constraints [26–36] almost rules out the MSSM. It is tempting therefore to explore well motivated extensions of the MSSM, such as NMSSM [37, 38] and BLSSM [39, 40], which may alleviate the little hierarchy problem of the MSSM through additional contributions to Higgs mass [37, 38, 41] and also provide new DM candidates [42–45] that may account for the relic density with no conflict with other phenomenological constraints.

In this paper, we analyze the constraints imposed by the Higgs mass limit and the gluino lower bound, which are the most stringent collider constraints, on the constrained MSSM (minimal SUGRA model, hereafter referred to as MSSM) parameter space. In particular, these constraints imply that the gaugino mass, , resides within the mass range: GeV, while the other parameters are much less constrained. We study the effect of the measured DM relic density on the MSSM allowed parameter space. We emphasized that in this case all parameter space is ruled out except for few points around , TeV, and TeV. We also investigate the direct detection rate of the LSP at these allowed points in light of the latest LUX result. Finally, we show that if one assumes nonstandard scenario of cosmology with low reheating temperature, where the LSP may reach equilibrium before the reheating time, then the relic abundance constraints on can be significantly relaxed.

The paper is organized as follows. In Section 2, we briefly introduce the MSSM and study the constraints on plane from Higgs and gluino mass experimental limits. In Section 3, we study the thermal relic abundance of the LSP in the allowed region of parameter space. We show that the combined LHC and relic abundance constraints rule out most of the parameter space except the case of very large . We also provide the expected rate of direct LSP detection at these points with large and TeV masses. Section 4 is devoted to nonthermal scenario of DM and how it can relax the constraints imposed on MSSM parameter space. Finally, we give our conclusions in Section 5.

#### 2. MSSM after the LHC Run-I

The particle content of the MSSM is three generations of (chiral) quark and lepton superfields; the (vector) superfields are necessary to gauge gauge of the SM, and two (chiral) doublet Higgs superfields. The introduction of a second Higgs doublet is necessary in order to cancel the anomalies produced by the fermionic members of the first Higgs superfield and also to give masses to both up and down type quarks. The interactions between Higgs and matter superfields are described by the superpotentialHere, contains (s)quark doublets and , are the corresponding singlets, (s)lepton doublets and singlets reside in and , respectively. and denote Higgs superfields with hypercharge . Further, due to the fact that Higgs and lepton doublet superfields have the same quantum numbers, we have additional terms that can be written asThese terms violate baryon and lepton number explicitly and lead to proton decay at unacceptable rates. To forbid these terms, a new symmetry, called -parity, is introduced, which is defined as , where and are baryon and lepton number and is the spin. There are two remarkable phenomenological implications of the presence of -parity: (i) SUSY particles are produced or destroyed only in pair; (ii) the LSP is absolutely stable and, hence, it might constitute a possible candidate for DM.

In the MSSM, a certain universality of soft SUSY breaking terms at grand unification scale GeV is assumed. These terms are defined as , the universal scalar soft mass, , the universal gaugino mass, , the universal trilinear coupling, , and the bilinear coupling (the soft mixing between the Higgs scalars). In order to discuss the physical implication of soft SUSY breaking at low energy, we need to renormalize these parameters from down to electroweak scale, which has been performed using SARAH [46], and the spectrum has been calculated using SPheno [47, 48]. In addition, the MSSM contains another two free SUSY parameters: and . Two of these free parameters, and , can be determined by the electroweak breaking conditions: Thus, the MSSM has only four independent free parameters, , besides the sign of , which determine the whole spectrum.

In the MSSM, the mass of the lightest Higgs state can be approximated, at the one-loop level, as [49–52] Therefore, if one assumes that the stop masses are of order TeV, then the one-loop effect leads to a correction of order GeV, which implies that The two-loop corrections reduce this upper bound by few GeVs [53–55]. Hence, the MSSM predicts the following upper bound for the Higgs mass: GeV, which was consistent with the measured value of Higgs mass (of order 125 GeV) at the LHC [13, 14].

In Figure 1, we display the contour plot of the SM-like Higgs boson: GeV in plane for different values of and . It is remarkable that the smaller the value of is, the smaller the value of is needed to satisfy this value of Higgs mass. It is also clear that the scalar mass remains essentially unconstrained by Higgs mass limit. It can vary from few hundred GeVs to few TeVs. Such large values of seem to imply a quite heavy SUSY spectrum, much heavier than the lower bound imposed by direct searches at the LHC experiments in centre of mass energies TeV and total integrated luminosity of order . Furthermore, the LHC lower limit on the gluino mass, TeV [56, 57], excluded the values of GeV which was allowed by Higgs mass constraints for TeV. Furthermore, this region is shown with dashed lines in Figure 1.