Correlation between ΔMS and BS,d0 → 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 tan beta, we analyze the correlation between the increase of the rates of the decays B-s,d(0) --> mu(+) mu(-) and the suppression S, of DeltaMs, 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 tang resumed corrections in the SU(2) x U(1) limit and comment briefly on the accuracy of this approximation. For 0.8 less than or equal to (DeltaM(S))(exp)/(DeltaM(S))(SM) less than or equal to 0.95 we find 6 x 10(-7) greater than or equal to BR(B-S(0) -->mu(+)mu(-))(max) s 4 x 10(-8) and 1.4 x 10(-8) greater than or equal to BR(B-d(0) --> mu(+)mu(-))(max) greater than or equal to 1 x 10(-9). For (DeltaM(S))(exp) greater than or equal to (DeltaM(S))(SM) d substantial enhancements of B-Sd(0) --> mu(+)mu(-) relative to the expectations based on the Standard Model are excluded. With (DeltaM(S))(exp) > 15.0/ps a conservative analysis of (DeltaM(S))(SM) gives BR(B-S(0) --> mu(+)mu(-)) less than or similar to 1.2 x 10(-6) and BR(B-d(0) --> mu(+)mu(-)) 3 x 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 DeltaMs, therates for B-S,d(0) --> mu(+)mu(-) increase with increasing DeltaM(S) and thebounds in question are weaker. Violation of all these correlations and bounds would indicate new sources of flavour violation. (C) 2002 Elsevier Science B.V. All rights reserved.