Flavour model building in the framework of Grand Unification and supergravity

Abstract

In this thesis, we study new aspects of flavour model building in the context of supersymmetric Grand Unified Theories, where the focus lies on models with an SU(5) or SO(10) gauge group. In the framework of supergravity, we discuss how a typical flavon sector of a flavour model with spontaneously broken family symmetry can be combined with a SUSY breaking sector in a consistent manner. To demonstrate the predictive power of such an implementation, an example calculation for a flavour GUT model, which is based on an SU(5) gauge group, an A_4 family symmetry and a Z^R_4 R-symmetry, is performed. Assuming hidden sector SUSY breaking, we determine the structure of the soft SUSY breaking terms at the GUT scale and investigate the predictions for observables at low energy scales, such as the sparticle spectrum, the dark matter relic density and flavour violating processes. Next, we carry out a systematic analysis of a class of predictive SU(5) flavour GUT models with the CSD2 setup in the neutrino sector, and where the ratios of the Yukawa couplings in the down-quark and charged lepton sector are fixed by Clebsch-Gordan coefficients at the GUT scale, following the principle of single operator dominance. Alongside the identification of viable model candidates by performing a fit to experimental data for different combinations of CG coefficients, we calculate, among others, the predictions for the 2-3 mixing angle theta^PMNS_23 and the CP violating phase delta^PMNS in the lepton sector. In the context of SO(10) Grand Unification, a class of non-renormalizable Yukawa operators of the schematic form 16_I 16_J H 45^n 210^m is investigated, where H in {10,120,126bar} contains SU(2)_L doublet and antidoublet states, and 16_I,J the SM fermions. Moreover, the representations 45 and 210 acquire SM singlet vevs at the GUT scale. We provide general formulas to compute the resulting Yukawa couplings in the different fermion sectors of the MSSM, and discuss the construction of such operators from renormalizable interactions by using heavy mediators. In addition, we show that the alignment of the MSSM Higgs (anti)doublets H_u and H_d in the space of all SU(2)_L (anti)doublets of a concrete model is a central aspect for the prediction of Yukawa ratios at the GUT scale. Finally, we specify the numerical procedure to quantitatively calculate nucleon decay from dimension 5 operators in SUSY models, and apply the analysis to an example model with an SU(5) GUT symmetry.