$\Delta M_s$ theory precision confronts flavour anomalies

Abstract

Based on recent HQET sum rule and lattice calculations we present updated Standard Model predictions for the mass differences of neutral $B$ mesons: $\Delta M_s^{\mathrm{SM}}=\left(18.4_{-1.2}^{+0.7}\right)\text{mbox}{ps}^{-1}$ and $\Delta M_d^{\mathrm{SM}}=\left(0.533_{-0.036}^{+0.022}\right)\text{mbox}{ps}^{-1}$ and study their impact on new physics models that address the present hints of anomalous data in $b\to s\ell \ell$ transitions. We also examine future prospects of further reducing the theory uncertainties and discuss the implications of a 2025 scenario with $\Delta M_s^{\text{SM 2025}}=\left(18.4\pm 0.5\right)\text{mbox}{ps}^{-1}$. In particular, the latter yields upper bounds $M_{Z^{\prime }}\lesssim 9\text{TeV}$ and $M_{S_3}\lesssim 30\text{TeV}$ for the minimal $Z^{\prime }$ and $S_3$ lepto-quark explanations of the $b\to s\ell \ell$ anomalies, respectively.

Comments: 34 pages, 8 figures. v2 fixes missing text in Section 3.4, adds references