Superparticle mass spectra from $\mathrm{SO}\left(10\right)\mathrm{}$ grand unified models with Yukawa coupling unification

We examine the spectrum of superparticles obtained from the minimal $\mathrm{SO}\left(10\right)\mathrm{}$ grand unified model, where it is assumed the gauge symmetry breaking yields the minimal supersymmetric standard model (MSSM) as the effective theory at $M_{\mathrm{GUT}}\sim 2\times {10}^{16}$ GeV. In this model, unification of Yukawa couplings implies a value of $\tan \beta \sim 45–55.$ At such high values of $\tan \beta ,$ 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 $\mathrm{SO}\left(10\right)\mathrm{}$ plus extra D-term contributions associated with the reduction in rank of the gauge symmetry group when $\mathrm{SO}\left(10\right)\mathrm{}$ spontaneously breaks to $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right).$ We comment upon the consequences of the sparticle mass spectrum for collider searches for supersymmetry. One implication of $\mathrm{SO}\left(10\right)\mathrm{}$ 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 $e^{+}{e}^{-}$ colliders.