Solving the SUSY Flavour and CP Problems with Non-Abelian Family Symmetry and Supergravity

Abstract

Can a theory of flavour capable of describing the spectrum of fermion (including neutrino) masses and mixings also contain within it the seeds for a solution of the SUSY flavour and CP problems? We argue that supergravity together with a non-Abelian family symmetry can completely resolve the SUSY flavour and CP problems in a broad class of theories in which family symmetry and CP is spontaneously broken in the flavon sector. We show that a simple superpotential structure can suppresses the F-terms of the flavons and GUT scale Higgs fields and that, if this mechanism is implemented, the resulting flavour and CP violation is suppressed and comfortably within the experimental limits. For illustration, we study a specific model based on SU(3) family symmetry, but similar models based on non-Abelian (continuous or discrete) family symmetry will lead to similar results.