Bounding the MSSM Higgs sector from above with the Tevatron's Bs→μ+μ−

Abstract The discovery potential of the Tevatron CDF for the rare B-decay B s → μ + μ − is analysed. We find that with an integrated luminosity of 2 fb−1, and using CDF as the example detector, a 5σ combined discovery reach of the Tevatron is possible if the branching ratio for B s → μ + μ − is ( 1.7 ± 0.46 ) × 10 − 7 . Such a possible signal for the decay B s → μ + μ − will invite large tan β 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 → μ + μ − is found at Tevatron with Br ( B s → μ + μ − ) = 2 × 10 − 7 then the heaviest Higgs boson mass in the MSSM should be less than 790 GeV for tan β ≲ 50 provided that the CKM matrix is the only source for (s)quark flavour changing processes.