Hints for new sources of flavour violation in meson mixing

Abstract

The recent results by the Fermilab Lattice and MILC collaborations on the hadronic matrix elements entering $B_{d,s}-\bar B_{d,s}$ mixing show a significant tension of the measured values of the mass differences $\Delta M_{d,s}$ with their SM predictions. We review the implications of these results in the context of Constrained Minimal Flavour Violation models. In these models, the CKM elements $\gamma$ and $|V_{ub}|/|V_{cb}|$ can be determined from $B_{d,s}-\bar B_{d,s}$ mixing observables, yielding a prediction for $\gamma$ below its tree-level value. Determining subsequently $|V_{cb}|$ from the measured value of either $\Delta M_s$ or $\varepsilon_K$ gives inconsistent results, with the tension being smallest in the Standard Model limit. This tension can be resolved if the flavour universality of new contributions to $\Delta F = 2$ observables is broken. We briefly discuss the case of $U(2)^3$ flavour models as an illustrative example.