On the Correlations between Flavour Observables in Minimal U(2)³ Models

The stringent correlations between flavour observables in models with CMFV are consistent with the present data except for the correlation Delta M_{s,d}-epsilon_K. Motivated by the recent work of Barbieri et al, we compare the CMFV correlations with the ones present in a special class of models with an approximate global U(2)^3 flavour symmetry, constrained by a minimal set of spurions governing the breakdown of this symmetry and the assumption that only SM operators are relevant in flavour physics. This analog of CMFV to be called MU(2)^3 allows to avoid the Delta M_{s,d}-epsilon_K tension in question because of reduced flavour symmetry and implied non-MFV contributions to Delta M_{s,d}. While the patterns of flavour violation in K meson system is the same as in CMFV models, the CP-violation in B_{s,d} meson systems can deviate from the one in the SM and CMFV models. We point out a stringent triple S_{psi K_S}-S_{psi phi}-|V_ub| correlation in this class of models that could in the future provide a transparent distinction between different MU(2)^3 models and in the context of these models determine |V_ub| by means of precise measurements of S_{psi K_S} and S_{psi phi} with only small hadronic uncertainties. For fixed S_{psi K_S} the correlation between B(B^+ -> tau^+nu_tau) and S_{psi phi} follows. We also find that MU(2)^3 models could in principle accommodate a negative value of S_{psi phi}, provided |V_ub| is found to be in the ballpark of exclusive determinations and the particular MU(2)^3 model provides a 25% enhancement of epsilon_K. A supersymmetric U(2)^3 model worked out in the Barbieri-School appears to satisfy these requirements. However if B(B^+ -> tau^+nu_tau)>1.0 10^{-4} will be confirmed by future experiments only positive S_{psi phi} is allowed in this framework. We summarize briefly the pattern of flavour violation in rare K and B_{s,d} decays in MU(2)^3 models.