# Using infinite volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

## TL;DR

This paper improves the calculation of the hadronic light-by-light contribution to the muon g-2 by using infinite volume, continuum QED to reduce finite volume errors in lattice QCD computations.

## Contribution

It introduces a method to treat muons and photons in infinite volume continuum QED, significantly reducing finite volume errors in lattice QCD calculations of muon g-2.

## Key findings

- Numerical results show exponential approach to infinite volume limit.
- Improved weighting function reduces discretization and finite volume effects.
- Results are consistent with known analytic solutions.

## Abstract

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g - 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD collaboration. However, the calculation is expected to suffer from a significant finite volume error that scales like $1/L^2$ where $L$ is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite volume, continuum QED, resulting in a weighting function that is pre-computed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite volume effects arising from the hadronic part of the amplitude.