Mixed leptonic and hadronic corrections to the anomalous magnetic moment of the muon

TL;DR

This paper estimates mixed leptonic and hadronic corrections to the muon's anomalous magnetic moment, finding their impact is negligible at current experimental precision levels.

Contribution

It provides the first estimate of mixed leptonic and hadronic corrections at order ${ m O}(\alpha^4)$, completing the understanding of higher-order effects.

Findings

Mixed corrections are limited to $oxed{ extless} 1 imes 10^{-11}$

Impact is negligible for Fermilab $g-2$ precision

Completes higher-order correction analysis for muon $g-2$

Abstract

Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at ${\mathcal O}(\alpha^4)$. Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to $\lesssim 1\times 10^{-11}$ and thus negligible at the level of the final precision of the Fermilab $g-2$ experiment.