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 $\tan \beta \sim m_t{(M}_Z{)/m}_b{(M}_Z)\sim 50$ can nullify these t, b, τ 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 $\mu >0\mathrm{}$ with $\mu ,$ $M_{1/2}\ll m_{16},$ $A_0\approx -1.9m_{16}$ and $m_{16}>1200\mathrm{}\hspace{0.5em}\mathrm{GeV}.$ Demanding Yukawa unification thus makes definite predictions for Higgs boson and sparticle masses. In particular, we find a light Higgs boson with a mass $m_h^0=114\mathrm{}\pm 5\pm 3\hspace{0.5em}\mathrm{GeV}$ and a light top squark with ${(m}_{t_1}{)}_{\mathrm{MIN}}\sim 450\hspace{0.5em}\mathrm{GeV}$ and $m_{t_1}\ll m_{b_1}.$ 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 $a_{\mu }^{\mathrm{SUSY}}<16\mathrm{}\times {10}^{-10}.$