Universal Unitarity Triangle 2016 and the tension between ΔM_s,d and ε_K in CMFV models

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering ΔM_s,d in B⁰_s,d- anti B⁰_s,d 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 vertical stroke V_ub vertical stroke / vertical stroke V_cb vertical stroke = 0.0864 ± 0.0025 and of the angle γ = (62.7 ± 2.1) ^circle. They follow in this framework from the experimental values of ΔM_d/ΔM_s and of the CP-asymmetry S_ψKS. 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 vertical stroke V_ts vertical stroke, vertical stroke V_td vertical stroke, vertical stroke V_cb vertical stroke and vertical stroke V_ub vertical stroke as functions of S(v) using the experimental value of ΔM_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 ε_K, which turns out to be significantly below its experimental value. This strategy avoids the use of tree-level determinations of vertical stroke V_ub vertical stroke and vertical stroke V_cb vertical stroke, which are presently subject to considerable uncertainties. On the other hand, if ε_K is used instead of ΔM_s as input, ΔM_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 ΔM_s,d and ε_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⁺ → π⁺νanti ν, K_L → π⁰νanti ν and B_s,d → μ⁺μ^- within the Standard Model. (orig.)