Abstract :
The predictions for the Bs,d–Bs,d mixing mass differences ΔMs,d and the branching ratios Br(Bs,d→μμ̄) within the Standard Model (SM) and its extensions suffer from considerable hadronic uncertainties present in the Bs,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(Bq→μμ̄)/ΔMq (q=s,d) do not depend on FBq and the CKM matrix elements. They involve in addition to the short distance functions and B-meson lifetimes only the non-perturbative parameters Bs,d. The latter are under much better control than FBs,d. Consequently in these models the predictions for Br(Bq→μμ̄) have only small hadronic uncertainties once ΔMq are experimentally known. Of particular interest is also the relation Br(Bs→μμ̄)Br(Bd→μμ̄)=BdBsτ(Bs)τ(Bd)ΔMsΔMd that is practically free of theoretical uncertainties as Bs/Bd=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(Bs→μμ̄)=(3.4±0.5)×10−9 and Br(Bd→μμ̄)=(1.00±0.14)×10−10 were in the first case we assumed as an example ΔMs=(18.0±0.5)/ps.
