Minimal Flavour Violation Waiting for Precise Measurements of Delta Mₛ, Spsi phi, AˢₛL, |Vᵤb|, gamma and B⁰ₛ,d -> mu+ mu-

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We emphasize that the recent measurements of the B⁰ₛ - bar B⁰ₛ mass difference Delta Mₛ by the CDF and D0 collaborations offer an important model independent test of minimal flavour violation (MFV). The improved measurements of the angle gamma in the unitarity triangle and of |Vᵤb| from tree level decays, combined with future accurate measurements of Delta Mₛ, Spsi Kₛ, Spsi phi, Br(Bd,ₛ -> mu+ mu-), Br(B -> Xd,ₛ nu bar nu), Br(K+ -> pi+ nu bar nu) and Br(Kₗ -> pi⁰ nu bar nu) 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(beta), with the former best tested through Spsi phi and Kₗ -> pi⁰ nu bar nu. 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 Spsi phi, that has an impact on the correlation between Spsi phi and AˢₛL. We point out that the ratios Spsi phi/AˢₛL and (Delta Mₛ)/(Delta Gammaₛ) will allow to determine (Delta Mₛ)/(Delta Mₛ)ˢM. Similar proposals for the determination of (Delta Md)/(Delta Md)ˢM are also given.