Phenomenological Implications of an SU(5) x S4 x U(1) SUSY GUT of Flavour

We discuss the characteristic low energy phenomenological implications of an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) whose flavour structure is controlled by the family symmetry S4 x U(1), which provides a good description of all quark and lepton masses, mixings as well as CP violation. Although the model closely mimics Minimal Flavour Violation (MFV) as shown in arXiv:1511.07886, here we focus on the differences. We first present numerical estimates of the low energy mass insertion parameters, including canonical normalisation and renormalisation group running, for well-defined ranges of SUSY parameters and compare the naive model expectations to the numerical scans and the experimental bounds. Our results are then used to estimate the model-specific predictions for Electric Dipole Moments (EDMs), Lepton Flavour Violation (LFV), B and K meson mixing as well as rare B decays. The largest observable deviations from MFV come from the LFV process mu --> e gamma and the electron EDM.