Detection of B_s->mu mu at the Tevatron Run II and Constraints on the SUSY Parameter Space

A measurement of the branching ratio for the rare decay mode B_s->mu mu at the Tevatron is an opportunity to test various supersymmetric scenarios. We investigate the prospects for studying this mode in Run II and estimate that CDF would be sensitive to this decay for a branching ratio > 1.2 \times 10^{-8} with 15 \invfb (or, if a similar analysis holds for D0, >6.5\times 10^{-9} for the combined data). We calculate the branching ratio in minimal supergravity (mSUGRA) parameter space, and find that tan\beta > 30 can be probed. (This mSUGRA parameter space cannot be probed by direct production of SUSY particles at Run II.) Including other experimental constraints on the mSUGRA parameter space, one finds that CDF \bsmumu measurements would be able to cover the full mSUGRA parameter space for tan\beta = 50 if the muon g_{\mu} - 2 anomaly exceeds \sim 11 \times 10^{-10}, and about half the allowed parameter space for tan\beta = 40. A large branching ratio > 7(14) \times 10^{-8} (feasible with only 2 \invfb) would be sufficient to exclude the mSUGRA model for tan\beta\leq 50(55). Dark matter neutralino-proton detection cross sections are examined in the allowed region, and should be large enough to be accessible to future planned experiments. Combined measurements of \bsmumu the Higgs mass m_h and the muon g_{\mu}-2 anomaly would be sufficient to determine the \mu>0 mSUGRA parameters (or show the model is inconsistent with the data). We also briefly discuss the \bsmumu decay in R parity violating models. There, for some models, the branching ratio can be large enough to be detected even for small $\tan\beta$ and large \mhalf.