Insights into Grand Unified Theories from Current Experimental Data

Abstract

In this thesis, we investigate several ways how the structure of a high energy particle physics model constituting a grand unification theory (GUT) in supersymmetry (SUSY) can be inferred from multiple types of information obtained at low energy. First, we calculate the values and 1 sigma ranges of the running quark and lepton Yukawa couplings as well as of the quark mixing parameters at various energy scales to provide useful input for flavour model building in GUTs and other scenarios while including tan beta enhanced SUSY threshold corrections in a simple way. Next, we analyse the naturalness of the Minimal Supersymmetric Standard Model (MSSM) in the light of the discovery of the Higgs boson at the Large Hadron Collider (LHC). In particular, we find that among possible departures from the constrained MSSM (cMSSM) non-universal gaugino masses represent the most promising way to find parameter regions with a fine-tuning of only O(10) even for a Higgs mass of about 126 GeV, compared to O(100) for the cMSSM. In this context, we also discuss the preference for certain GUT-scale Yukawa coupling ratios over others based on fine-tuning. Following that, we study how also the recent determination of the leptonic mixing angle theta^pmns_13 can be accommodated in a simple scenario for GUT models of flavour via charged lepton corrections. This leads us to four conditions that can easily be implemented. In addition, the interplay of the value of theta^pmns_13 with future determinations of the Dirac CP phase delta^pmns is discussed using lepton mixing sum rules. Finally, we study how the double missing partner mechanism as a solution to the doublet-triplet splitting problem can be incorporated into SU(5) GUT models of flavour to comply with the bounds on proton decay. In this context, we argue that the introduction of two adjoints of SU(5) is a compelling idea and calculate its constraints on the GUT scale and dimension five proton decay suppression scale at two loops. We close with general comments on the calculation of the proton lifetime in the considered scenario for flavour models. Multiple appendices are included detailing non-obvious aspects of the calculation and other kinds of valuable information for GUT model building.