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2019

$\Delta M_s$ theory precision confronts flavour anomalies

Di Luzio, Luca, Kirk, Matthew, Lenz, Alexander et al.

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Based on recent HQET sum rule and lattice calculations we present updated Standard Model predictions for the mass differences of neutral $B$ mesons: $\Delta M_s^{\rm SM} = \left(18.4^{+0.7}_{-1.2} \right) \mbox{ps}^{-1}$ and $\Delta M_d^{\rm SM} = \left(0.533^{+0.022}_{-0.036} \right) \mbox{ps}^{-1}$ 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 $\Delta M_s^\text{SM 2025} = \left(18.4 \pm 0.5\right) \mbox{ps}^{-1}$.
In particular, the latter yields upper bounds $M_{Z'}\lesssim 9~\text{TeV}$ and $M_{S_3}\lesssim 30~\text{TeV}$ for the minimal $Z'$ and $S_3$ lepto-quark explanations of the $b \to s \ell \ell$ anomalies, respectively.