CMFV models facing the recent progress in lattice calculations of $B_{s,d}$ mixing

TL;DR

Recent high-precision lattice calculations of $B_{s,d}$ mixing matrix elements reveal a significant tension with Standard Model predictions, suggesting the need for new sources of flavour violation beyond CMFV models.

Contribution

The paper assesses the impact of new lattice results on CMFV models, showing they cannot resolve the tension with experimental data, indicating possible new physics in $ ext{Δ}F=2$ processes.

Findings

Standard Model predictions are in tension with experimental measurements.

CMFV models cannot alleviate the tension when considering $ ext{ε}_K$ correlation.

New lattice results imply potential new sources of flavour violation.

Abstract

Recent results by the Fermilab Lattice and MILC collaborations on the hadronic matrix elements entering $B_{s,d}-\bar B_{s,d}$ mixing have reached an unprecedented precision. Interestingly the Standard Model (SM) predictions using these updated values, together with the CKM elements obtained from tree-level decays, exhibit a significant tension with the measured values of the mass differences $\Delta M_s$, $\Delta M_d$ and their ratio. Assessing this tension in a model-independent way, it can be shown that models with Constrained Minimal Flavour Violation can not improve the situation with respect to the SM, in particular when the correlation with the CP-violating parameter $\varepsilon_K$ is taken into account. The new lattice results, if eventually confirmed by independent calculations, therefore imply the presence of new sources of flavour violation in the $\Delta F=2$ sector.