Problem of flavour in SUSY GUT and horizontal symmetry

Abstract

The concept of non-abelian horizontal symmetry $SU(3)_H$ can greatly help in understanding the fermion and sfermion flavour structures in supersymmetric grand unification. For the sake of demonstration the $SU(5)\times SU(3)_H$ model, suggested earlier in ref. \cite{PLB85}, is revisited. We show that under very simple and natural assumption it links the sfermion mass pattern to those of fermions in a remarkable way. All dangerous supersymmetric flavour-changing contributions are naturally suppressed in a general case, independently of the concrete texture for fermion mass matrices. Nevertheless, within this framework we present an example of predictive model for fermion masses and mixing, which leads to 7 consistent predictions for the low energy observables. [Based on talks given at Int. Workshop {\em `SUSY 96'}, Univ. of Maryland, 29 May - 1 June 1996 (to appear on Proceedings), and II US-Polish Workshop {\em `Physics from Planck Scale to Electroweak Scale'}, Warsaw, 28-30 March 1996.]