The Rumble in the Meson: a leptoquark versus a Z′ to fit b → sμ$^{+}$μ$^{−}$ anomalies including 2022 LHCb $ {R}_{K^{\left(\ast \right)}} $ measurements

We juxtapose global fits of two bottom-up models (an S$_{3}$ scalar leptoquark model and a B$_{3}$ – L$_{2}$Z′ model) of b → sμ$^{+}$μ$^{−}$ anomalies to flavour data in order to quantify statistical preference or lack thereof. The leptoquark model couples directly to left-handed di-muon pairs, whereas the Z′ model couples to di-muon pairs with a vector-like coupling. $ {B}_s-\overline{B_s} $ mixing is a focus because it is typically expected to disfavour Z′ explanations. In two-parameter fits to 247 flavour observables, including B$_{s/d}$→ μ$^{+}$μ$^{−}$ branching ratios for which we provide an updated combination and LHCb $ {R}_{K^{\left(\ast \right)}} $ measurements from December 2022, we show that each model provides a similar improvement in quality-of-fit of $ \sqrt{\Delta {\chi}^2} $ = 3.6 with respect to the Standard Model. The main effect of the $ {B}_s-\overline{B_s} $ mixing constraint in the Z′ model is to disfavour values of the s$_{L}$– b$_{L}$ mixing angle greater than about 5|V$_{cb}$|. This limit is rather loose, meaning that a good fit to data does not require ‘alignment’ in either quark Yukawa matrix. No curtailment of the s$_{L}$− b$_{L}$ mixing angle is evident in the S$_{3}$ model.