$M_W$ helps select $Z^{\prime }$ models for $b\to s\ell \ell$ anomalies

Abstract

As shown in Ref. \cite{Allanach:2021kzj}, the Third Family Hypercharge ($Y_3$) Model changes the Standard Model prediction for $M_W$ whilst simultaneously explaining anomalies in $b\to s\ell \ell$ transitions via a heavy $Z^{\prime }$ gauge boson which is spawned by a spontaneously broken gauged $U(1{)}_{Y_3}$ symmetry. The 2022 CDF II measurement of $M_W$, which is far from the Standard Model prediction, somewhat disfavours the $Y_3$ model. Here, we generalise the gauge charge assignments to the anomaly-free combination $s{Y}_3+t(B_3-L_3)$ and show that incorporating the 2022 CDF II measurement of $M_W$ selects a viable domain of integers $s$ and $t$. For example, $s=1,t=-3$ yields a $p-$value of .12 in a two-parameter global fit to 277 electroweak and flavour changing $b$ data, much improving a SM $p-$value of $5\times 10^{-6}$.

Comments: 21 pages, 3 figures. Ancillary information contains all plots including additional ones not present in the draft, main programs and all plot-making and data files. Includes re-calculation of theoretical uncertainties: no qualitative changes, but some p-values have increased. Version accepted for publication in EPJC