Minimal Flavour Violation Waiting for Precise Measurements of Delta M_s, S_{psi phi}, A^s_SL, |V_ub|, gamma and B^0_{s,d} -> mu+ mu-

Abstract

We emphasize that the recent measurements of the B^0_s - bar B^0_s mass difference Delta M_s 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 |V_ub| from tree level decays, 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 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 S_{psi phi} and K_L -> pi^0 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 S_{psi phi}, that has an impact on the correlation between S_{psi phi} and A^s_SL. We point out that the ratios S_{psi phi}/A^s_SL and (Delta M_s)/(Delta Gamma_s) will allow to determine (Delta M_s)/(Delta M_s)^SM. Similar proposals for the determination of (Delta M_d)/(Delta M_d)^SM are also given.