Superparticle mass spectra fromSO(10)grand unified models with Yukawa coupling unification

Abstract

We examine the spectrum of superparticles obtained from the minimal $\mathrm{SO}(10)$ grand unified model, where it is assumed the gauge symmetry breaking yields the minimal supersymmetric standard model (MSSM) as the effective theory at ${M}_{\mathrm{GUT}}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{16}$ GeV. In this model, unification of Yukawa couplings implies a value of $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}45--55.$ At such high values of $\mathrm{tan}\ensuremath{\beta},$ assuming universality of scalar masses, the usual mechanism of radiative electroweak symmetry breaking breaks down. We show that a set of weak scale sparticle masses consistent with radiative electroweak symmetry breaking can be generated by imposing non-universal GUT scale scalar masses consistent with universality within $\mathrm{SO}(10)$ plus extra D-term contributions associated with the reduction in rank of the gauge symmetry group when $\mathrm{SO}(10)$ spontaneously breaks to $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1).$ We comment upon the consequences of the sparticle mass spectrum for collider searches for supersymmetry. One implication of $\mathrm{SO}(10)$ unification is that the light bottom squark can be by far the lightest of the squarks. This motivates a dedicated search for bottom squark pair production at $p\overline{p}$ and ${e}^{+}{e}^{\ensuremath{-}}$ colliders.