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.
Highlights
The predictions for the Bs,d − Bs,d mixing mass differences ∆Ms,d and the branching ratios Br(Bs,d → μμ) 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
∆Ms ∆Md 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 → μμ) = (3.4±0.5)·10−9 and Br(Bd → μμ) = (1.00±0.14)·10−10 were in the first case we assumed as an example ∆Ms = (18.0 ± 0.5)/ps
Among the possible extentions of the Standard Model (SM), of particular interest are the models with minimal flavour violation (MFV), where the only source for flavour mixing is still given by the CKM matrix
Summary
The predictions for the Bs,d − Bs,d mixing mass differences ∆Ms,d and the branching ratios Br(Bs,d → μμ) 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. In this letter we would like to point out the existence of simple relations between the Bs,d − Bs,d mixing mass differences ∆Ms,d and the branching ratios for the rare decays Bs,d → μμthat are valid in models with minimal flavour violation (MFV) as defined in [1]. 2. Within the MFV models ∆Ms,d and Br(Bs,d → μμ) are given as follows (q = d, s) [10]
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