Hadronic vacuum polarization and muon g-2 from magnetic susceptibilities on the lattice

TL;DR

This paper introduces a novel lattice simulation method using susceptibilities to accurately compute the hadronic vacuum polarization, significantly reducing errors and improving the determination of muon g-2 contributions.

Contribution

The paper presents a new susceptibility-based approach for lattice calculations of vacuum polarization, enhancing precision and error suppression over previous methods.

Findings

Statistically smaller errors in vacuum polarization calculations.

Disconnected contributions are negligible within small errors.

Upper limits established for disconnected term contributions.

Abstract

We present and test a new method to compute the hadronic vacuum polarization function in lattice simulations. This can then be used, e.g., to determine the leading hadronic contribution to the anomalous magnetic moment of the muon. The method is based on computing susceptibilities with respect to external electromagnetic plane wave fields and allows for a precision determination of both the connected and the disconnected contributions to the vacuum polarization. We demonstrate that the statistical errors obtained with our method are much smaller than those quoted in previous lattice studies, primarily due to a very effective suppression of the errors of the disconnected terms. These turn out to vanish within small errors, enabling us to quote an upper limit. We also comment on the accuracy of the vacuum polarization function determined from present experimental R-ratio data.