# Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment

## TL;DR

This paper derives model-independent short-distance constraints for the hadronic light-by-light contribution to the muon g-2, showing the quark loop dominates at high energies and computing a small correction related to QCD vacuum susceptibility.

## Contribution

It establishes a rigorous operator product expansion for HLbL in the high-momentum regime and computes the first power correction, providing valuable constraints for theoretical models.

## Key findings

- Perturbative quark loop dominates at high virtual momenta.
- First nonzero power correction related to QCD vacuum magnetic susceptibility.
- Numerical estimate shows the correction is small.

## Abstract

We derive short-distance constraints for the hadronic light-by-light contribution (HLbL) to the anomalous magnetic moment of the muon in the kinematic region where the three virtual momenta are all large. We include the external soft photon via an external field leading to a well-defined Operator Product Expansion. We establish that the perturbative quark loop gives the leading contribution in a well defined expansion. We compute the first nonzero power correction. It is related to to the magnetic susceptibility of the QCD vacuum. The results can be used as model-independent short-distance constraints for the very many different approaches to the HLbL contribution. Numerically the power correction is found to be small.