Relations between ΔMs,d and Bs,d→μ(μ)over-bar in models with minimal flavour violation

The predictions for the B-s,B-d-(B) over bar (s,d) mixing mass differences DeltaM(s,d) and the branching ratios Br(B-s,B-d --> mumu) within the Standard Model (SM) and its extensions suffer from considerable hadronic uncertainties present in the B-s,B-d-meson decay constants FBs,d that enter these quantities quadratically. We point out that in the restricted class of models with minimal flavour violation (MFV) in which only the SM low energy operators are relevant, the ratios Br(B-q --> mumu)/DeltaM(q) (q = s,d) do not depend on F-Bq and the CKM matrix elements. They involve in addition to the short distance functions and B-meson lifetimes only the non-perturbative parameters (B) over cap (s,d). The latter are under much better control than F-Bs,F-d. Consequently in these models the predictions for Br(B-q --> mumu) have only small hadronic uncertainties once DeltaM(q) are experimentally known. Of particular interest is also the relation Br(B-s-->mumu)/Br(B-d-->mumu) = (B) over cap (d)/(B) over cap (s) tau(B-s)/tau(B-d) DeltaM(s)/DeltaM(d) that is practically free of theoretical uncertainties as (B) over cap (s)/(B) over cap (d) = 1 up to small SU(3) breaking corrections. Using these ideas within the SM we find much more accurate predictions than those found in the literature: Br(B-s --> mumu) = (3.4 +/- 0.5) x 10(-9) and Br(B-d --> mumu) = (1.00 +/- 0.14) x 10(-10) were in the first case we assumed as an example DeltaM(s) = (18.0 +/- 0.5)/ps. (C) 2003 Published by Elsevier B.V.