$\Delta M_s$ 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: $ΔM_s^{\rm SM} = \left(18.4^{+0.7}_{-1.2} \right) \mbox{ps}^{-1}$ and $ΔM_d^{\rm SM} = \left(0.533^{+0.022}_{-0.036} \right) \mbox{ps}^{-1}$ 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 $ΔM_s^\text{SM 2025} = \left(18.4 \pm 0.5\right) \mbox{ps}^{-1}$. 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.

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

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• Impact of $B\to K\nu \bar{\nu }$ measurements on beyond the Standard Model theories
• Perturbative unitarity constraints on generic Yukawa interactions
• Theory Motivation: What measurements are needed?