Impact of correlations between $a_\mu$ and $\alpha_{QED}$ on the EW fit

TL;DR

This paper investigates how correlations between the muon's anomalous magnetic moment and the QED coupling affect electroweak fits, especially considering tensions between different theoretical and experimental determinations of hadronic contributions.

Contribution

It introduces a detailed analysis of the impact of correlated uncertainties in $a_$ and $_{QED}$ on electroweak fits, considering various scenarios and their implications.

Findings

Large impact in improbable scenarios with global shifts of HVP

Smaller impact when shifts are limited to lower mass ranges

Correlations reduce the effect of shifts on fit quality

Abstract

We study the potential impact on the electroweak (EW) fits due to the tensions between the current determinations of the hadronic vacuum polarisation (HVP) contributions to the anomalous magnetic moment of the muon ($a_\mu$), based on either phenomenological dispersion integrals using measured hadronic spectra or on Lattice QCD calculations. The impact of the current tension between the experimental measurement of $a_\mu$ and the total theoretical prediction based on the phenomenological calculations of the HVP are also studied. The correlations between the uncertainties of the theoretical predictions of $a_\mu$ and of the running of $\alpha_{QED}$ are taken into account in the studies. We conclude that the impact on the EW fit can be large in improbable scenarios involving global shifts of the full HVP contribution, while it is much smaller if the shift is restricted to a lower mass range and/or if the shift in $\alpha_{QED}$ is obtained from that in $a_\mu$ through appropriate use of the correlations. Indeed, the latter scenarios only imply at most a 2.6/16 increase in the $\chi^2/n.d.f.$ of the EW fits and relatively small changes for the resulting fit parameter values.