Correlation between ΔMs and B0s, d→ μ+μ- in supersymmetry at large tan β

Considering the MSSM with the CKM matrix as the only source of flavour violation and heavy supersymmetric particles at large tanβ, we analyze the correlation between the increase of the rates of the decays B⁰_s,d→μ⁺μ^- and the suppression of ΔM_s, that are caused by the enhanced flavour changing neutral Higgs couplings to down-type quarks. We give analytic formulae for the neutral and charged Higgs couplings to quarks including large tanβ resumed corrections in the SU(2)×U(1) limit and comment briefly on the accuracy of this approximation. For 0.8⩽(ΔM_s)^exp/(ΔM_s)^SM⩽0.95 we find 6×10^-7⩾BR(B⁰_s→μ⁺μ^-)^max⩾4×10^-8 and 1.4×10^-8⩾BR(B⁰_d→μ⁺μ^-)^max⩾1×10^-9. For (ΔM_s)^exp⩾(ΔM_s)^SM substantial enhancements of B⁰_s,d→μ⁺μ^- relative to the expectations based on the Standard Model are excluded. With (ΔM_s)^exp>15.0/ps a conservative analysis of (ΔM_s)^SM gives BR(B⁰_s→μ⁺μ^-)≲1.2×10^-6 and BR(B⁰_d→μ⁺μ^-)≲3×10^-8. However, we point out that in the less likely scenario in which the squark mixing is so large that the neutral Higgs contributions dominate ΔM_s, the rates for B⁰_s,d→μ⁺μ^- increase with increasing ΔM_s and the bounds in question are weaker. Violation of all these correlations and bounds would indicate new sources of flavour violation.