Correlation between ΔMs and B0s,d→μ+μ− in supersymmetry at large tanβ

Abstract 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 B0s,d→μ+μ− and the suppression of ΔMs, 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⩽(ΔMs)exp/(ΔMs)SM⩽0.95 we find 6×10−7⩾BR(B0s→μ+μ−)max⩾4×10−8 and 1.4×10−8⩾BR(B0d→μ+μ−)max⩾1×10−9. For (ΔMs)exp⩾(ΔMs)SM substantial enhancements of B0s,d→μ+μ− relative to the expectations based on the Standard Model are excluded. With (ΔMs)exp>15.0/ps a conservative analysis of (ΔMs)SM gives BR(B0s→μ+μ−)≲1.2×10−6 and BR(B0d→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 ΔMs, the rates for B0s,d→μ+μ− increase with increasing ΔMs and the bounds in question are weaker. Violation of all these correlations and bounds would indicate new sources of flavour violation.