Bounding the MSSM Higgs sector from above with the Tevatron's B_s --> mu^+ mu^-

The discovery potential of the Tevatron CDF for the rare B-decay B_s --> mu^+ mu^- is analysed. We find that with an integrated luminosity of 2 fb^(-1), and using CDF as the example detector, a 5 sigma combined discovery reach of the Tevatron is possible if the Branching ratio for B_s --> mu^+ mu^- is (1.7 +- 0.46) \times 10^(-7). Such a possible signal for the decay B_s --> mu^+ mu^- will invite large tan(beta) values and set an upper bound on the heaviest mass of the MSSM Higgs sector in a complete analogy to the upper bound of the lightest observable supersymmetric particle set from the excess over the SM prediction of the muon anomalous magnetic moment. If for example, the decay B_s -->mu^+ mu^- is found at Tevatron with branching ratio 2 \times 10^(-7) then the heaviest Higgs boson mass in the MSSM should be less than 790 GeV for tan(beta) < 50 provided that the CKM matrix is the only source for (s)quark flavour changing processes.