New Aspects of Flavour Model Building in Supersymmetric Grand Unification

We derive predictions for Yukawa coupling ratios within GUTs generated from operators with mass dimension four and five. These relations are a characteristic property of unified flavour models and can reduce the large number of free parameters related to the flavour sector of the SM. The Yukawa couplings of the down-type quarks and charged leptons are affected within SUSY models by tan beta-enhanced threshold corrections. We analyse these corrections and give simple analytic expressions and numerical estimates for them. The threshold corrections sensitively depend on the soft SUSY breaking parameters. Especially, they determine if the affected Yukawa couplings are enhanced or suppressed. In a first approach, we make some plausible assumptions about the soft SUSY parameters. In a second, more sophisticated approach we use three common breaking schemes in which all the soft breaking parameters at the electroweak scale can be calculated from only a handful of parameters. Within this approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example y_mu/y_s = 9/2 or 6 or y_tau/y_b = 3/2 in SU(5). Furthermore, we study a special class of quark mass matrix textures for small tan beta where theta_13^u = theta_13^d = 0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases delta_12^u and delta_12 ^d and the right unitarity triangle angle alpha which suggests a simple phase structure for the quark mass matrices. To complement the aforementioned considerations, we give two explicit examples in an SU(5) context, one for large and one for small tan beta which implement the Yukawa coupling relations mentioned before. The models have interesting phenomenological consequences like, for example, quasi-degenerate neutrino masses in the case of small tan beta