$B_s$-${\bar{B}}_s$ mixing interplay with $B$ anomalies

Abstract

After reviewing the theoretical uncertainties entering the Standard Model determination of the mass difference of the neutral $B_s$-${\bar{B}}_s$ meson system, $\Delta M_s^{\mathrm{SM}}$, we discuss the implications of its updated value for new physics models addressing the experimental anomalies in semi-leptonic $B$ decays. Using the most recent FLAG average of lattice results for the non-perturbative matrix elements and the CKM-fitter determination of $V_{cb}$ points to a $1.8\sigma$ discrepancy in $\Delta M_s^{\mathrm{SM}}>\Delta M_s^{\exp }$. Extending the analysis in Ref. [1] we show that the latter tension cannot be easily accommodated within single mediator models, whenever the same mediator is also responsible for the $b\to s\ell \ell$ anomalies.

Comments: 20 pages, 5 figures. Talk given at the 10th International Workshop on the CKM Unitarity Triangle. Heidelberg University, September 17-21 2018