Model Building in the LHC Era: Vector-like Leptons and SUSY GUTs

In this thesis, we study the phenomenology of some models beyond the Standard Model (SM). First, we analyze a model in which the SM is extended by a family of vector-like (VL) leptons. We find that the strongest constraints are coming from the muon anomalous magnetic moment, the deviation from the SM of Higgs bosons decaying to muons, the deviation from the SM of Higgs bosons decaying to photons, and the branching ratio of muon decaying to electron. Although VL leptons couple to all three families of the SM leptons, electron-VL couplings are highly constrained. The second model that we consider is a three family SO(10) SUSY GUT with Yukawa unification. We perform a global chi-squared analysis and show that SUSY effects do not decouple even though the best fit universal scalar mass parameter at the GUT scale is approximately $25\,\text{TeV}$. The fit to $\sin(2\beta)$, and up and down quark masses of this model, however, are not great. We show that the fits can be improved by choosing a Pati-Salam (PS) group as the gauge group and modifying the Yukawa sector. The best-fit point, consistent with the bound obtain from reinterpreting gluino simplified model analyses by the ATLAS and CMS collaborations, has gluino mass equals $1.9\,\text{TeV}$ and chi-squared per degrees of freedom approximately 1.12. Finally, we study the reheating and the baryogenesis (via leptogenesis) of this PS model extended by an inflation sector. This model reheats via instant preheating due to bosonic and fermionic broad parametric resonances. The lepton asymmetry is obtained from the CP asymmetric right-handed neutrino (RHN) decay. The leptogenesis analysis is performed by including all three families of the RHNs because, by fitting to the low-energy observables, the heaviest RHN decays to produce a lepton asymmetry with the correct sign, while the two lighter RHNs decay to produce the wrong sign.