Abstract :
The horizontal symmetry U(3)H can greatly help in solving the flavour problem in supersymmetric grand unification. For demonstration we revisit the SU(5)×U(3)H model suggested earlier by Z. Berezhiani [Phys. Lett. B 150 (1985) 177] and show that it can lead to a consistent picture of masses and mixing in both the fermion and sfermion sectors. In this model, under simple and natural assumptions on the heavy fermion content (only 10+10 states) and the supersymmetry breaking features (so called proportionality condition), all soft parameters appear to be related to the MSSM Yukawa constants in a very remarkable way, and all dangerous supersymmetric flavour-changing effects are naturally suppressed. The horizontal symmetry can be regarded as a local symmetry in a consistent way (without D-term problem), if one introduces the mirror SU(5)′ sector of the particles and interactions completely analogous to that in the visible SU(5) sector.
