Minimal flavour violation waiting for precise measurements of ΔMs,Sψphi,AsSL, |Vub|, γ andB0s,d→μ+μ−

We emphasize that the recent measurements of the B^0_s - bar B^0_s massdifference Delta M_s by the CDF and D0 collaborations offer an important modelindependent test of minimal flavour violation (MFV). The improved measurementsof the angle gamma in the unitarity triangle and of |V_ub| from tree leveldecays, combined with future accurate measurements of Delta M_s, S_{psi K_S},S_{psi phi}, Br(B_{d,s} -> mu+ mu-), Br(B -> X_{d,s} nu bar nu), Br(K+ -> pi+nu bar nu) and Br(K_L -> pi^0 nu bar nu) and improved values of the relevantnon-perturbative parameters, will allow to test the MFV hypothesis in a modelindependent manner to a high accuracy. In particular, the difference betweenthe reference unitarity triangle obtained from tree level processes and theuniversal unitarity triangle (UUT) in MFV models would signal either newflavour violating interactions and/or new local operators that are suppressedin MFV models with low tan(beta), with the former best tested through S_{psiphi} and K_L -> pi^0 nu bar nu. A brief discussion of non-MFV scenarios is alsogiven. In this context we identify in the recent literature a relative signerror between Standard Model and new physics contributions to S_{psi phi}, thathas an impact on the correlation between S_{psi phi} and A^s_SL. We point outthat the ratios S_{psi phi}/A^s_SL and (Delta M_s)/(Delta Gamma_s) will allowto determine (Delta M_s)/(Delta M_s)^SM. Similar proposals for thedetermination of (Delta M_d)/(Delta M_d)^SM are also given.Comment: 22 pages, 8 figures, 1 table. Extended discussion of the correlation between S_{psi phi} and A^s_SL and new proposals to determine Delta M_q/(Delta M_q)^SM from future measurements, with respect to the first version. Minor changes and few references adde