Universal Unitarity Triangle 2016 and the tension between Δ Ms,d Δ M s , d and ε K ε K in CMFV models

Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering Δ Ms,d in Bs,d⁰ – B̄s,d⁰ 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 |Vub|/|Vcb|=0.0864± 0.0025 and of the angle γ =(62.7± 2.1)^∘ . They follow in this framework from the experimental values of Δ Md/Δ Mₛ and of the CP-asymmetry Sψ KS . 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 |Vₜₛ| , |Vtd| , |Vcb| and |Vub| as functions of S(v) using the experimental value of Δ Mₛ 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 |Vub| and |Vcb| , which are presently subject to considerable uncertainties. On the other hand, if ε K is used instead of Δ Mₛ as input, Δ Ms,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 Δ Ms,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 ⁺ν ν ̄ , KL→ π ⁰ν ν ̄ and Bs,d→ μ ⁺μ ⁻ within the Standard Model.