$B_s$-$\bar B_s$ mixing interplay with $B$ anomalies

TL;DR

This paper examines the impact of updated theoretical calculations of the $B_s$-$ar B_s$ mixing mass difference on new physics models, highlighting tensions with experimental anomalies in semi-leptonic B decays and the challenges in explaining both with a single mediator.

Contribution

It provides a detailed analysis of the interplay between $B_s$ mixing and $B$ decay anomalies, emphasizing the difficulty of reconciling them within simple new physics models.

Findings

Updated $ ext{SM}$ prediction shows a 1.8$\sigma$ tension with experimental data.

Single mediator models struggle to explain both $B_s$ mixing and decay anomalies simultaneously.

The tension suggests the need for more complex new physics explanations.

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, $\Delta M_s^{\rm SM}$, 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 $\Delta M_s^{\rm SM} > \Delta M_s^{\rm exp}$. 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.