Leading-order calculation of hadronic contributions to the muon $g-2$ using the Dyson-Schwinger approach

TL;DR

This paper calculates the hadronic vacuum polarization contribution to the muon g-2 using Dyson-Schwinger equations, achieving results close to experimental and lattice data, and discusses implications for light-by-light scattering.

Contribution

It introduces a Dyson-Schwinger approach with a phenomenological model to compute the hadronic contributions to muon g-2, providing a complementary method to lattice calculations.

Findings

Calculated $a_\mu^{HVP}$ as $6760\times 10^{-11}$, within 2% of experimental value.

Found good agreement with recent lattice results for $a_\mu^{HVP}$.

Discussed implications for hadronic light-by-light scattering contributions.

Abstract

We present a calculation of the hadronic vacuum polarization (HVP) tensor within the framework of Dyson--Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, $a_\mu$. We find $a_\mu^{HVP}= 6760\times 10^{-11}$ which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of $a_\mu^{HVP}$ and find good agreement within our approach. We also discuss the implications of our result for a corresponding calculation of the hadronic light-by-light scattering contribution to $a_\mu$.