Supersymmetric models with minimal flavour violation and their running

We revisit the formulation of the principle of minimal flavor violation (MFV) in the minimal supersymmetric extension of the standard model, both at moderate and large tan(beta), and with or without new CP-violating phases. We introduce a counting rule which keeps track of the highly hierarchical structure of the Yukawa matrices. In this manner, we are able to control systematically which terms can be discarded in the soft SUSY breaking part of the Lagrangian. We argue that for the implementation of this counting rule, it is convenient to introduce a new basis of matrices in which both the squark (and slepton) mass terms as well as the trilinear couplings can be expanded. We derive the RGE for the MFV parameters and show that the beta functions also respect the counting rule. For moderate tan(beta), we provide explicit analytic solutions of these RGE and illustrate their behaviour by analyzing the neighbourhood (also switching on new phases) of the SPS-1a benchmark point. We then show that even in the case of large tan(beta), the RGE remain valid and that the analytic solutions obtained for moderate tan(beta) still allow us to understand the most important features of the running of the parameters, as illustrated with the help of the SPS-4 benchmark point.