Yukawa Unification in SO(10)

In simple SO(10) SUSY GUTs the top, bottom and tau Yukawa couplings unify at the GUT scale. A naive renormalization group analysis, neglecting weak scale threshold corrections, leads to moderate agreement with the low energy data. However it is known that intrinsically large threshold corrections proportional to $\tan \beta \sim m_t(M_Z)\mathrm{/}{m}_b(M_Z)\sim 50$ can nullify these $t,b$, $\tau$ mass predictions. In this paper we turn the argument around. Instead of predicting fermion masses, we use the constraint of Yukawa unification and the observed values $M_t,m_b(m_b),M_{\tau }$ to constrain SUSY parameter space. We find a narrow region survives for $\mu >0$ with $\mu ,M_{1\mathrm{/}2}<<m_{16}$, $A_0 \approx - 1.9 m_{16}$and$m_{16} > 1200$ \gev. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses. In particular we find a light higgs with mass $m_h^0=114\pm 5\pm 3$ GeV and a light stop with $(m_{{\tilde{t}}_1}{)}_{MIN}\sim 450$ GeV and $m_{\tilde t_1} << m_{\tilde b_1}$. In addition, we find a light chargino and a neutralino LSP. It is also significant that in this region of parameter space the SUSY contribution to the muon anomalous magnetic moment $a_{\mu }^{SUSY}<16\times {10}^{-10}$.