Viable $t$-$b$-$τ$ Yukawa Unification in SUSY SO(10)

Abstract

The supersymmetric SO(10) GUT with $t$--$b$--$τ$ Yukawa coupling unification has problems with correct electroweak symmetry breaking, experimental constraints (especially $b\rightarrow sγ$) and neutralino abundance, if the scalar masses are universal at the GUT scale. We point out that non-universality of the scalar masses at the GUT scale generated both by (1) renormalization group running from the Planck scale to the GUT scale and (2) $D$--term contribution induced by the reduction of the rank of the gauge group, has a desirable pattern to make the model phemenologically viable (in fact the only one which is consistent with experimental and cosmological constraints). At the same time the top quark mass has to be either close to its quasi IR--fixed point value or below $\sim$170 GeV. We also briefly discuss the spectrum of superpartners which is then obtained.