Flavour in supersymmetric Grand Unification: a democratic approach

Abstract

We consider the flavour problem in a supersymmetric Grand Unified theory with gauged SU(6) group, where the Higgs doublets are understood as pseudo-Goldstone bosons of a larger $\SU(6)\otimes\SU(6)$ global symmetry of the Higgs superpotential. A key element of this work is that we never appeal to any flavour symmetry. One main interesting feature emerges: only one of the light fermions, an up-type quark, to be identified with the top, can get a Yukawa coupling at renormalizable level. This fact, together with bottom-tau Yukawa unification, also implied in our scheme, gives rise to a characteristic correlation between the top and the Higgs mass. By including a flavour-blind discrete symmetry and requiring that all higher dimensional operators be mediated by the exchange of appropriate heavy multiplets, it is possible to give an approximate description of all masses and mixing angles in term of a hierarchy of grand unified scales. A special ``texture'' arises, implying a relation between the top mass and the third generation mixing angles. Several other possible consequences of this approach are pointed out, concerning the $μ/s$ mass ratio, the Cabibbo angle and the proton decay.