Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_{\mu}-2$

TL;DR

This paper proposes a novel lattice QCD method using Mellin transform moments of the spectral function to accurately evaluate the hadronic vacuum polarization contribution to the muon's anomalous magnetic moment, enabling new tests against experimental data.

Contribution

It introduces a Mellin transform-based approach to compute the HVP contribution in lattice QCD, offering a new series of tests and potential improvements over existing methods.

Findings

HVP contribution can be approximated by a few Mellin moments.

Mellin moments can be computed in lattice QCD.

Method enables comparison with experimental data.

Abstract

I suggest a new approach to the determination of the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_{\mu}^{\rm HVP}$ in lattice QCD. It is based on properties of the Mellin transform of the hadronic spectral function and their relation to the HVP self energy in the Euclidean. I show how $a_{\mu}^{\rm HVP}$ is very well approximated by a few moments associated to this Mellin transform and how these moments can be evaluated in lattice QCD, providing thus a series of tests when compared with the corresponding determinations using experimental data.