Supersymmetric dark matter and Yukawa unification

An analysis of supersymmetric dark matter under the Yukawa unification constraint is given. The analysis utilizes the recently discovered region of the parameter space of models with gaugino mass nonuniversalities where large negative supersymmetric corrections to the b quark mass appear to allow $b-\tau$ unification for a positive $\mu$ sign consistent with the $\overrightarrow{b}s+\gamma$ and $g_{\mu }-2$ constraints. In the present analysis we use the revised theoretical determination of $a_{\mu }^{\mathrm{SM}}$ $\left[a_{\mu }{=(g}_{\mu }-2\right)/2]$ in computing the difference $a_{\mu }^{\mathrm{expt}}-a_{\mu }^{\mathrm{SM}}$ which takes into account a reevaluation of the light by light contribution, which has a positive sign. The analysis shows that the region of parameter space with nonuniversalities of the gaugino masses that allows for unification of Yukawa couplings also contains regions that allow the satisfaction of the relic density constraint. Specifically, we find that the lightest neutralino mass consistent with the relic density constraint, $b\tau$ unification for SU(5), and $b-t-\tau$ unification for SO(10), in addition to other constraints, lies in the region below 80 GeV. An analysis of the maximum and the minimum neutralino-proton scalar cross sections for the allowed parameter space, including the effect of a new determination of the pion-nucleon sigma term, is also given. It is found that the full parameter space for this class of models can be explored in the next generation of proposed dark matter detectors.