The Rumble in the Meson: a leptoquark versus a $Z^{\prime }$ to fit $b\to s{\mu }^{+}{\mu }^{-}$ anomalies including 2022 LHCb $R_{K^{(\ast )}}$ measurements

Abstract

We juxtapose global fits of two bottom-up models (an $S_3$ scalar leptoquark model and a $B_3-L_2$ $Z^{\prime }$ model) of \bsll\ 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 $Z^{\prime }$ 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 $Z^{\prime }$ explanations. In two-parameter fits to 247 flavour observables, including $B_{s/d}\to {\mu }^{+}{\mu }^{-}$ branching ratios for which we provide an updated combination and LHCb $R_{K^{(\ast )}}$ 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 $Z^{\prime }$ 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.

Comments: 31 pages, 6 figures. v3 is updated with a new fit including December 2022 LHCb reanalysis of $R_{K^{(\ast )}}$ measurements. Plots and fits significantly changed but the main conclusion is left unchanged. v4 has minor changes. v5 has a typo fixed in the caption of Fig 6, v6 has corrected vertical lines in Fig 6