Universal Unitarity Triangle 2016 and the tension between [Formula: see text] and [Formula: see text] in CMFV models.

Abstract

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering Delta M_{s,d} in B_{s,d}^0–bar{B}_{s,d}^0 mixing, we determine the universal unitarity triangle (UUT) in models with constrained minimal flavour violation (CMFV). Of particular importance are the very precise determinations of the ratio |V_{ub}|/|V_{cb}|=0.0864pm 0.0025 and of the angle gamma =(62.7pm 2.1)^circ . They follow in this framework from the experimental values of Delta M_{d}/Delta M_s and of the CP-asymmetry S_{psi K_S}. As in CMFV models the new contributions to meson mixings can be described by a single flavour-universal variable S(v), we next determine the CKM matrix elements |V_{ts}|, |V_{td}|, |V_{cb}| and |V_{ub}| as functions of S(v) using the experimental value of Delta M_s as input. The lower bound on S(v) in these models, derived by us in 2006, implies then upper bounds on these four CKM elements and on the CP-violating parameter varepsilon _K, which turns out to be significantly below its experimental value. This strategy avoids the use of tree-level determinations of |V_{ub}| and |V_{cb}|, which are presently subject to considerable uncertainties. On the other hand, if varepsilon _K is used instead of Delta M_s as input, Delta M_{s,d} are found to be significantly above the data. In this manner we point out that the new lattice data have significantly sharpened the tension between Delta M_{s,d} and varepsilon _K within the CMFV framework. This implies the presence of new physics contributions beyond this framework that are responsible for the breakdown of the flavour universality of the function S(v). We also present the implications of these results for K^+rightarrow pi ^+nu bar{nu }, K_{L}rightarrow pi ^0nu bar{nu } and B_{s,d}rightarrow mu ^+mu ^- within the Standard Model.