Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update

TL;DR

This paper revisits how short-distance constraints affect the calculation of the muon's anomalous magnetic moment, showing recent solutions agree despite different methods and updating estimates with new perturbative corrections.

Contribution

It provides a comparative analysis of recent solutions for the hadronic light-by-light amplitude and updates the impact estimate on muon g-2 with recent perturbative corrections.

Findings

Recent solutions agree within uncertainties on short-distance constraint impacts.

The axial anomaly's effect on $a_\mu$ is limited.

Updated estimates incorporate new perturbative corrections.

Abstract

We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, $a_\mu=(g-2)_\mu/2$, by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on $a_\mu$ and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on $a_\mu$, despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.