Hadronic contribution to the muon g-2 from a Dyson-Schwinger perspective

TL;DR

This paper introduces a Dyson-Schwinger equations approach to calculate the hadronic contributions to the muon g-2, providing results consistent with previous work and highlighting the impact of vertex dressing effects.

Contribution

It presents a novel Dyson-Schwinger equations method for all momentum scales to evaluate hadronic effects on muon g-2, including off-shell amplitudes.

Findings

Pseudoscalar meson exchange contribution: (84 ± 13)×10^{-11}

Quark loop contribution: (107 ± 48)×10^{-11}

Estimated muon g-2 deviation: 1.9 sigma from experiment

Abstract

A novel approach towards the hadronic contributions to the anomalous magnetic moment of the muon $a_{\mu}$ is presented, namely the Dyson-Schwinger equations of QCD. It has the advantage of being valid for all momentum scales and has the potential to address off-shell amplitudes. We present our first results for the pseudoscalar (PS) meson exchange and the quark loop contributions. The meson exchange ($\pi^0, \eta, \eta'$), $a_\mu^{\textrm{LBL;PS}}=(84 \pm 13)\times 10^{-11}$, is commensurate with previous calculations, while the quark loop contribution $a_\mu^{\textrm{LBL;quarkloop}} = (107 \pm 48)\times 10^{-11}$, is strongly enhanced by vertex dressing effects in the quark photon vertex. Taken seriously this leads to the estimate of $a_\mu=116\,591\,865.0(96.6)\times 10^{-11}$, giving a 1.9 $\sigma$ deviation between theory and experiment.