Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel

TL;DR

This paper presents a semi-analytical, coordinate-space method using lattice QCD to accurately compute the hadronic light-by-light scattering contribution to the muon g-2, reducing uncertainties in the Standard Model prediction.

Contribution

It introduces a novel semi-analytical calculation of the QED kernel in coordinate space, improving the precision of lattice QCD computations for muon g-2.

Findings

Detailed semi-analytical QED kernel calculation provided

Coordinate-space approach reduces finite-size effects

Publicly available code implementation included

Abstract

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor $g$ of the muon to deviate from the value of two predicted by Dirac's theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon $(g-2)$. Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.