2-loop short-distance constraints for the $g-2$ HLbL

TL;DR

This paper calculates the perturbative QCD correction to the massless quark-loop in the hadronic light-by-light contribution to muon g-2, providing insights to reduce theoretical uncertainties in Standard Model predictions.

Contribution

It introduces the first perturbative QCD correction to the massless quark-loop in the short-distance expansion relevant for muon g-2 calculations.

Findings

QCD correction is about -10% of the massless quark-loop for scales above 1 GeV.

The correction is relatively small, indicating the dominance of the leading term.

Results help refine theoretical estimates of the hadronic light-by-light contribution.

Abstract

The recent experimental measurement of the muon $g-2$ at Fermilab National Laboratory, at a $4.2\sigma$ tension with the Standard Model prediction, highlights the need for further improvements on the theoretical uncertainties associated to the hadronic sector. In the framework of the operator product expansion in the presence of a background field, the short-distance behaviour of the hadronic light-by-light contribution was recently studied. The leading term in this expansion is given by the massless quark-loop, which is numerically dominant compared to non-perturbative corrections. Here, we present the perturbative QCD correction to the massless quark-loop and estimate its size numerically. In particular, we find that for scales above 1 GeV it is relatively small, in general roughly $-10\%$ the size of the massless quark-loop. The knowledge of these short-distance constraints will in the future allow to reduce the systematic uncertainties in the Standard Model prediction of the hadronic light-by-light contribution to the $g-2$.