Minimal flavour violation waiting for precise measurements of ΔMs, Sψφ, AsSL, vertical bar Vub vertical bar, γ and B0s,d→μ+μ-

We emphasize that the recent measurements of the B0s- B-bar 0s mass difference ΔMs by the CDF and DO collaborations offer an important model independent test of minimal flavour violation (MFV). The improved measurements of the angle γ in the unitarity triangle and of Vub from tree level decays, combined with future accurate measurements of ΔMs, SψKS, Sψφ, Br(Bd,s→μ+μ-), Br(B→Xd,sνν-bar ), Br(K+→π+νν-bar ) and Br(KL→π0νν-bar ) and improved values of the relevant non-perturbative parameters, will allow to test the MFV hypothesis in a model independent manner to a high accuracy. In particular, the difference between the reference unitarity triangle obtained from tree level processes and the universal unitarity triangle (UUT) in MFV models would signal either new flavour violating interactions and/or new local operators that are suppressed in MFV models with low tan β, with the former best tested through Sψφ and KL→π0νν-bar . A brief discussion of non-MFV scenarios is also given. In this context we identify in the recent literature a relative sign error between Standard Model and new physics contributions to Sψφ, that has an impact on the correlation between Sψφ and AsSL. We point out that the ratios Sψφ/AsSL and ΔMs/ΔΓs will allow to determine ΔMs/(ΔMs)SM. Similar proposals for the determination of ΔMd/(ΔMd)SM are also given