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

Abstract

Abstract We juxtapose global fits of two bottom-up models (an S3 scalar leptoquark model and a B3 – L2Z′ 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. $$ {B}_s-\overline{B_s} $$ B s − B s ¯ mixing is a focus because it is typically expected to disfavour Z′ explanations. In two-parameter fits to 247 flavour observables, including Bs/d→ μ+μ− branching ratios for which we provide an updated combination and LHCb $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ measurements from December 2022, we show that each model provides a similar improvement in quality-of-fit of $$ \sqrt{\Delta {\chi}^2} $$ ∆ χ 2 = 3.6 with respect to the Standard Model. The main effect of the $$ {B}_s-\overline{B_s} $$ B s − B s ¯ mixing constraint in the Z′ model is to disfavour values of the sL– bL mixing angle greater than about 5|Vcb|. 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 sL− bL mixing angle is evident in the S3 model.