The hadronic vacuum polarization with twisted boundary conditions

TL;DR

This paper addresses the challenge of calculating the hadronic vacuum polarization for the muon g-2 using twisted boundary conditions on the lattice, proposing a method to remove artifacts caused by non-transversality.

Contribution

It introduces a technique to identify and subtract the non-transversal, divergent term in the vacuum polarization when using twisted boundary conditions in lattice QCD.

Findings

Successfully removes non-transversal divergence from vacuum polarization

Enables access to a continuous range of momenta in finite-volume lattice calculations

Improves precision of muon g-2 theoretical estimates

Abstract

The leading-order hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over the subtracted hadronic vacuum polarization. This integral is dominated by euclidean momenta of order the muon mass, i.e., momenta not accessible on current lattice volumes with periodic boundary conditions. Twisted boundary conditions can in principle help in accessing momenta of any size even in a finite volume, but their use leads to a modification of the Ward-Takahashi identity that normally guarantees transversality of the vacuum polarization. As a result, the vacuum polarization contains a non-transversal, quadratically divergent term, which arises as an artifact of using twisted boundary conditions in a finite volume. In this article, we show how to determine and remove this term from the vacuum polarization.