New aspects of flavour model building in supersymmetric grand unification

We derive predictions for Yukawa coupling ratios within Grand Unified Theories 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 Standard Model. The Yukawa couplings of the down-type quarks and charged leptons are affected within supersymmetric models by tan β-enhanced threshold corrections which can be sizeable if tan β is large. In this case their careful inclusion in the renormalisation group evolution is mandatory. We analyse these corrections and give simple analytic expressions and numerical estimates for them. The threshold corrections sensitively depend on the soft supersymmetry breaking parameters. Especially, they determine the overall sign of the corrections and therefore if the affected Yukawa couplings are enhanced or suppressed. In the minimal supersymmetric extension of the Standard Model many free parameters are introduced by supersymmetry breaking about which we make some plausible assumptions in our first simplified approach. 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 the second approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example yμ/ys=9/2 or 6 or yτ/yb=3/2 in SU(5). Furthermore, we study a special class of quark mass matrix textures for small tan β where θu13=θd13=0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases δu12 and δd12 and the right unitarity triangle angle α which suggests a simple phase structure for the quark mass matrices where one matrix element is purely imaginary and the remaining ones are purely real. To complement the aforementioned considerations, we give two explicit flavour models in a SU(5) context, one for large and one for small tan β 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 β. (orig.)