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

Understand

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.