Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory

TL;DR

This paper develops a systematic operator product expansion (OPE) approach to analyze short-distance contributions to the hadronic light-by-light scattering in the muon g-2, including non-perturbative effects, providing insights beyond perturbation theory.

Contribution

It introduces a novel OPE framework for the short-distance behavior of the HLbL correlator in QCD, incorporating non-perturbative effects and establishing a renormalization scheme.

Findings

Higher-order contributions are numerically small.

The leading term is the massless quark loop.

Non-perturbative effects are systematically included.

Abstract

The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared ($Q_i^2$) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three $Q_i^2$ are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small.