Yukawa Unification: The Good, The Bad and The Ugly

Abstract

We analyze some consequences of grand unification of the third-generation Yukawa couplings, in the context of the minimal supersymmetric standard model. We address two issues: the prediction of the top quark mass, and the generation of the top-bottom mass hierarchy through a hierarchy of Higgs vacuum expectation values. The top mass is strongly dependent on a certain ratio of superpartner masses. And the VEV hierarchy always entails some tuning of the GUT-scale parameters. We study the RG equations and their semi-analytic solutions, which exhibit several interesting features, such as a focusing effect in the limit of certain symmetries and a correlation between the $A$ terms (which contribute to $b\rightarrow s\gamma$) and the gaugino masses. This study shows that non-universal soft-SUSY-breaking masses are favored (in particular for splitting the Higgs doublets via D-terms and for allowing more natural scenarios of symmetry breaking), and hints at features desired in Yukawa-unified models. Several phenomenological implications are also revealed.