Computing the hadronic vacuum polarization function by analytic continuation

Understand

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.