Unified Explanation of the Anomalies in Semi-Leptonic $B$ decays and the $W$ Mass

TL;DR

This paper proposes that mixing between a new heavy $Z'$ boson and the Standard Model $Z$ can simultaneously explain anomalies in semi-leptonic $B$ decays and the recent $W$ mass measurement, linking new physics to electroweak symmetry breaking.

Contribution

It highlights the significance of $Z-Z'$ mixing in explaining $B$ anomalies and the $W$ mass, providing a unified new physics explanation with a $Z'$ mass between 1-5 TeV.

Findings

$Z-Z'$ mixing explains $B$ decay anomalies.

The same mixing accounts for the $W$ mass tension.

A $Z'$ with mass 1-5 TeV fits data well.

Abstract

The discrepancies between the measurements of rare (semi-)leptonic $B$ decays and the corresponding Standard Model predictions point convincingly towards the existence of new physics for which a heavy neutral gauge boson ($Z^\prime$) is a prime candidate. However, the effect of the mixing of the $Z^\prime$ with the SM $Z$, even though it cannot be avoided by any symmetry, is usually assumed to be small and thus neglected in phenomenological analyses. In this letter we point out that a mixing of the naturally expected size leads to lepton flavour universal contributions, providing a very good fit to $B$ data. Furthermore, the global electroweak fit is affected by $Z-Z^\prime$ mixing where the tension in the $W$ mass, recently confirmed and strengthened by the CDF measurement, prefers a non-zero value of it. We find that a $Z^\prime$ boson with a mass between $\approx 1-5\,\rm {TeV}$ can provide a unified explanations of the $B$ anomalies and the $W$ mass. This strongly suggests that the breaking of the new gauge symmetry giving raise to the $Z^\prime$ boson is linked to electroweak symmetry breaking with intriguing consequences for model building.