Soft Supersymmetry Breaking Parameters and Minimal SO(10) Unification

The minimal supersymmetric SO(10) model, in which not only the gauge but also the third generation fermion Yukawa couplings are unified, provides a simple and highly predictive theoretical scenario for the understanding of the origin of the low energy gauge interactions and fermion masses. In the framework of the MSSM, with universal soft supersymmetry breaking parameters at the grand unification scale, large values of the universal gaugino mass $M_{1/2}\geq 300$ GeV are needed in order to induce a proper breakdown of the electroweak symmetry. In addition, in order to obtain acceptable experimental values for both the pole bottom mass and the $b\rightarrow s\gamma$ decay rate, even larger values of the gaugino masses are required. The model is strongly constrained by theoretical and phenomenological requirements and a heavy top quark, with mass $M_t\geq 170$ GeV, is hard to accomodate within this scheme. However, we show that to accommodate a top quark mass $M_t\simeq180$ GeV, it is sufficient to relax the condition of universality of the scalar soft SUSY breaking parameters at the grand unification scale. Still, the requirement of a heavy top quark demands a very heavy squark spectrum, unless specific relations between the soft SUSY breaking parameters are fulfilled.