Unified picture of the particle and sparticle masses in SUSY GUT

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.