Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics

In the context of the minimal supersymmetric standard model (MSSM), we analyse the thermal relic abundance of lightest neutralino, which is the lightest supersym-metric particle (LSP). We show that the combined large hadron collider (LHC) and relic abundance constraints rule out most of the MSSM parameter space except a very narrow region with very large tan Ý ({u223C}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 limit by at least two orders of magni- tude. Also, we argue that non-thermal dark matter (DM) scenario may relax the constraints imposed on the MSSM parameter space. Motivated by a{u223C}3v excess recorded by the CMS experiment at the LHC around a mass of order{u223C}137 GeV in ZZ{u2217}{u2192}4l and ÞÞ samples, we analyse the potential discovery of a second neutral higgs boson in the supersymmetric B-L extension of the standard model (BLSSM) at the CERN machine. We con{uFB01}rm that a double Higgs peak structure can be generated in this framework, with CP-even Higgs boson masses at{u223C}125 GeV and{u223C}137 GeV, unlike the case of the MSSM. In addition we consider the BLSSM with Inverse seesaw, which provides new DM candidates (lightest right-handed sneutrino and lightest B-L neutralino) with mass of order few hundreds GeV. We emphasize that the thermal relic abundance and direct detection experiments via relic neutralino scattering with nuclei impose stringent constraints on the B-L neutralinos. These constraints can be satis{uFB01}ed by few points in the parameter space, which cannot explain the observed galactic center (GC) gamma-ray excess measured by Fermi-LAT. We show that for a wide region of parameter space the lightest right-handed sneutrino can satisfy the limits of the relic abundance, the scattering cross section with nuclei and the observed GC gamma-ray results

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