Position-space approach to hadronic light-by-light scattering in the muon $g-2$ on the lattice

TL;DR

This paper introduces a position-space method for calculating the hadronic light-by-light scattering contribution to the muon g-2 using lattice QCD, aiming to improve theoretical precision.

Contribution

It presents a novel position-space integral formulation for HLbL in muon g-2 and tests it with a semi-analytic calculation of the $C0^0$-pole contribution.

Findings

Developed a continuum position-space kernel function for HLbL

Validated the approach with a $C0^0$-pole contribution calculation

Lays groundwork for lattice QCD computation of HLbL in muon g-2

Abstract

The anomalous magnetic moment of the muon currently exhibits a discrepancy of about three standard deviations between the experimental value and recent Standard Model predictions. The theoretical uncertainty is dominated by the hadronic vacuum polarization and the hadronic light-by-light (HLbL) scattering contributions, where the latter has so far only been fully evaluated using different models. To pave the way for a lattice calculation of HLbL, we present an expression for the HLbL contribution to $g-2$ that involves a multidimensional integral over a position-space QED kernel function in the continuum and a lattice QCD four-point correlator. We describe our semi-analytic calculation of the kernel and test the approach by evaluating the $\pi^0$-pole contribution in the continuum.