Yukawa Unified Supersymmetric SO(10) Model: Cosmology, Rare Decays and Collider Searches

It has recently been pointed out that viable sparticle mass spectra can be generated in Yukawa unified SO(10) supersymmetric grand unified models consistent with radiative breaking of electroweak symmetry. Model solutions are obtained only if $\tan\beta \sim 50$, $\mu <0$ and positive $D$-term contributions to scalar masses from SO(10) gauge symmetry breaking are used. In this paper, we attempt to systematize the parameter space regions where solutions are obtained. We go on to calculate the relic density of neutralinos as a function of parameter space. No regions of the parameter space explored were actually cosmologically excluded, and very reasonable relic densities were found in much of parameter space. Direct neutralino detection rates could exceed 1 event/kg/day for a $^{73}$Ge detector, for low values of GUT scale gaugino mass $m_{1/2}$. We also calculate the branching fraction for $b\to s \gamma$ decays, and find that it is beyond the 95% CL experimental limits in much, but not all, of the parameter space regions explored. However, recent claims have been made that NLO effects can reverse the signs of certain amplitudes in the $b\to s\gamma$ calculation, leading to agreement between theory and experiment in Yukawa unified SUSY models. For the Fermilab Tevatron collider, significant regions of parameter space can be explored via $b\bar{b}A$ and $b\bar{b}H$ searches. There also exist some limited regions of parameter space where a trilepton signal can be seen at TeV33. Finally, there exist significant regions of parameter space where direct detection of bottom squark pair production can be made, especially for large negative values of the GUT parameter $A_0$.