Hadronic light-by-light scattering in the muon g-2: a Dyson-Schwinger equation approach

TL;DR

This paper calculates the hadronic light-by-light scattering contribution to the muon g-2 using Dyson-Schwinger equations, improving gauge invariance constraints and providing a revised total estimate.

Contribution

It introduces a Dyson-Schwinger equation approach to hadronic light-by-light scattering, enhancing previous models with gauge invariance constraints for more accurate results.

Findings

Pseudoscalar meson exchange contribution aligns with prior calculations.

Quark loop contribution is significantly larger due to gauge invariance constraints.

Revised total muon g-2 estimate incorporates these improved calculations.

Abstract

We determine the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon using the framework of Dyson-Schwinger and Bethe-Salpeter equations of QCD. Our result for the pseudoscalar ($\pi^0, \eta, \eta'$) meson exchange diagram is commensurate with previous calculations. In our calculation of the quark loop contribution we improve previous approaches by implementing constraints due to gauge invariance. As a consequence, our value $a_\mu^{\textrm{LBL;quarkloop}} = (136 \pm 59)\times 10^{-11}$ is significantly larger. Taken at face value, this then leads to a revised estimate of the total $a_\mu=116\,591\,891.0(105.0)\times 10^{-11}$.