A derivative-based approach for the leading order hadronic contribution to $g_\mu-2$

TL;DR

This paper introduces a lattice-based derivative method to accurately compute the leading-order hadronic contribution to the muon's anomalous magnetic moment, improving precision in low-momentum regions.

Contribution

It presents a novel lattice momentum derivative technique for calculating the hadronic vacuum polarization scalar at low momenta.

Findings

Method successfully tested on a Wilson-quark lattice ensemble.

Achieves a smooth, integrable function in low-momentum region.

Potential for improved precision in g-2 calculations.

Abstract

We describe a lattice approach to calculating the leading-order hadronic contribution to the anomalous magnetic moment of the muon. We employ lattice momentum derivatives, in both the spatial and temporal directions, to determine the hadronic vacuum polarization scalar at low momenta and construct a smooth, intregrable function in this momentum region. The method is tested on one hex-smeared Wilson-quark lattice ensemble with physical pion masses.