Sparticle Mass Spectra from SO(10) Grand Unified Models with Yukawa Coupling Unification

We examine the spectrum of superparticles obtained from the minimal $SO(10)$ grand unified model, where it is assumed there exists direct gauge symmetry breaking to the Minimal Supersymmetric Standard Model (MSSM) at $M_{GUT}\sim 2\times 10^{16}$ GeV. In this model, unification of Yukawa couplings implies a value of $\tan\beta\sim 50-60$. At such high values of $\tan\beta$, the usual mechanism of radiative electroweak symmetry breaking breaks down, assuming universality of scalar masses. 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 $SO(10)$ plus extra $D$-term contributions associated with the reduction in rank of $SO(10)$ to $SU(3)\times SU(2)\times U(1)$ gauge symmetry. We comment upon the consequences of the sparticle mass spectrum for collider searches for supersymmetry. One implication of $SO(10)$ 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 $p\bar{p}$ and $e^+e^-$ colliders.