Family Symmetry, Fermion Mass Matrices and Cosmic Texture

Abstract

The observed replication of fermions in three families is undoubtedly a reflection of a deeper symmetry underlying the standard model. In this paper we investigate one very elementary possibility, that physics above the grand unification scale is described by the symmetry group $G\timesSU(3)_{fam}$ with $G$ a gauged grand unified group, and $SU(3)_{fam}$ a global family symmetry. The breaking of this symmetry at the GUT scale produces global texture, providing a mechanism for structure formation in the universe, and sets strong constraints on the low energy fermion mass matrix. With the addition of a ${\bf 45}$ Higgs and certain assumptions about the relative strength of Higgs couplings, the simplest $SU(5)$ theory yields an eight parameter form for the fermion mass matrices, which we show is consistent with the thirteen observable masses and mixing angles. We discuss the natural suppression of flavour changing neutral currents (FCNCs) and emphasise the rich low energy Higgs sector. With minor assumptions, the theory unifies consistently with the recent LEP data. We consider the extension to $G=SO(10)$, where some simplification and further predictiveness emerges. Finally we discuss the dynamics of $SU(3)_{fam}$ texture and show that the known constraints on unification `predict' a GUT symmetry breaking scale of the order required for cosmic structure formation, and by the recent detection of cosmic microwave anisotropy by COBE.