Computing the hadronic vacuum polarization function by analytic continuation

TL;DR

This paper introduces a novel lattice-based method for calculating the hadronic vacuum polarization function at continuous momenta, bridging spacelike and timelike regions, with applications to muon g-2 calculations.

Contribution

The paper presents a new analytic continuation technique to compute the hadronic vacuum polarization function directly in Minkowski space from lattice data.

Findings

Method successfully computes the vacuum polarization function at continuous momenta.

Demonstrated application to QCD correction in muon g-2.

Provides an alternative approach to existing lattice calculations.

Abstract

We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method leads to the desired hadronic vacuum polarization function in Minkowski spacetime. We show with the example of the leading-order QCD correction to the muon anomalous magnetic moment that this approach can provide a valuable alternative method for calculations of physical quantities where the hadronic vacuum polarization function enters.