The MFV limit of the MSSM for low tan β: mmmmeson mixings revisited

We apply the effective field theory definition of Minimal Flavour Violation (MFV) to the MSSM. We explicitly show how, by this definition, the new sources of flavour and CP violation present in the MSSM become functions of the SM Yukawa couplings, and cannot be simply set to zero, as is common wisdom in phenomenological MSSM studies that assume MFV. We apply our approach to the MSSM ΔB = 2 Hamiltonian at low tan β. The limit of MFV amounts to a striking increase in the predictivity of the model. In particular, SUSY corrections to meson-antimeson mass differences ΔM _d,s are always found to be positive with respect to the SM prediction. This feature is due to an interesting interplay between chargino and gluino box diagrams (the dominant contributions) in the different mass regimes one can consider. Finally, we point out that, due to the presence of gluinos, the MFV MSSM does not belong - even at low tan β - to the class of models with the so-called 'constrained' MFV (CMFV), in which only the SM operator (V-A) ⊗ (V-A) contributes to ΔM _d,s. Consequently, for the MSSM and in the general case of MFV, one should not use the Universal Unitarity Triangle (UUT), relevant for CMFV models, but a MFV-UT constructed from β _ψKS and |V _ub| or γ from tree-level decays. In particular, with the measured value of β _ψKS, MFV implies a testable correlation between |V _ub| and γ. With the present high value of |V _ub|, MFV favours 80̂$">γ>80°.