Lattice QCD and the Timelike Pion Form Factor

TL;DR

This paper introduces a new formula for calculating the timelike pion form factor directly from lattice QCD data, reducing uncertainties in muon g-2 calculations without needing analytic continuation.

Contribution

It provides a novel method to determine the spectral function of a conserved current in a specific kinematic range from Euclidean lattice observables.

Findings

Enables calculation of the timelike pion form factor in lattice QCD.

Reduces theoretical uncertainty in muon anomalous magnetic moment.

Provides a rare example of spectral function determination without analytic continuation.

Abstract

We present a formula that allows one to calculate the pion form factor in the timelike region 2mpi <= sqrt{s} <= 4mpi in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.