Yukawa coupling unification inSO(10)with positiveμand a heavier gluino

Abstract

The $t\mathrm{\text{\ensuremath{-}}}b\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ unification with positive Higgs mass parameter $\ensuremath{\mu}$ in the minimal supersymmetric standard model prefers ``just so'' Higgs splitting and a light gluino $\ensuremath{\lesssim}500\text{ }\text{ }\mathrm{GeV}$ which appears to be ruled out by the recent LHC searches. We reanalyze constraints on soft supersymmetry breaking parameters in this scenario, allowing independent splittings among squarks and Higgs doublets at the grand unification scale, and show that it is possible to obtain $t\mathrm{\text{\ensuremath{-}}}b\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ unification and satisfy experimental constraints on gluino mass without raising supersymmetry breaking scale to very high value $\ensuremath{\sim}20\text{ }\text{ }\mathrm{TeV}$. We discuss the origin of independent squark and Higgs splittings in realistic $SO(10)$ models. Just so Higgs splitting can be induced without significantly affecting the $t\mathrm{\text{\ensuremath{-}}}b\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ unification in $SO(10)$ models containing Higgs fields transforming as $10+\overline{126}+126+210$. This splitting arises in the presence of nonuniversal boundary conditions from mixing between 10 and other Higgs fields. Similarly, if additional matter fields are introduced then their mixing with the matter multiplet 16 is shown to generate the squark splitting required to raise the gluino mass within the $t\mathrm{\text{\ensuremath{-}}}b\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ unified models with positive $\ensuremath{\mu}$.