Minimal flavour violation waiting for precise measurements of ΔM _s, S_ψφ, A_SL^s, |V _ub|, γ and B_s,d⁰ → μ⁺μ^-

We emphasize that the recent measurements of the B_s ⁰-B̄_s⁰ mass difference ΔM _s by the CDF and DØ 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 |V_ub| from tree level decays, combined with future accurate measurements of ΔM _s, S_ψKS, S_ψφ, Br(B_d,s → μ⁺μ^-), Br(B → X_d,sνν), Br(K⁺ → π⁺νν) and Br(K_L → π⁰νν) 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 S_ψφ and K_L → π⁰νν. 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 S_ψφ, that has an impact on the correlation between S _ψφ and A_SL^s. We point out that the ratios S_ψφ/A_SL^s and ΔM _s/ΔΓ_s will allow to determine ΔM _s/(ΔM_s)^SM. Similar proposals for the determination of ΔM_d/(ΔM_d)^SM are also given.