Family symmetries and the origin of fermion masses and mixings

Abstract

Family symmetries are possibly the most conservative extension of the Standard Model that attempt explanations of the pattern of fermion masses and mixings. The observed large mixing angles in the lepton sector may be the first signal for the presence of a non-Abelian family symmetry. We investigate the possibilities of simultaneously explaining the observed pattern of masses of the quarks (hierarchical masses and small mixing angles) and of the leptons (near tri-bi-maximal mixing, thus large mixing angles). We show that such contrasting observations can be achieved naturally via the seesaw mechanism, whether in models with continuous or discrete family symmetries. We consider also in some detail the constraints on flavour changing neutral currents arising from introducing a continuous family symmetry. We show that, for a restricted choice of the flavon sector, continuous family symmetries are consistent with even the most conservative limits both for the case of gauge mediated supersymmetry breaking and the case of gravity mediated supersymmetry breaking.