Extracting the electro-magnetic pion form factor from QCD in a finite volume

TL;DR

This paper develops a method to accurately extract the pion's electromagnetic form factor in finite volume QCD by canceling dominant zero-mode effects using correlator ratios, applicable broadly in lattice QCD calculations.

Contribution

It introduces a universal technique to remove zero-mode contributions in finite volume QCD correlators, improving the precision of form factor calculations in the epsilon regime.

Findings

Zero-mode contributions can be canceled using correlator ratios.

Remaining finite volume effects are perturbatively small.

Method is broadly applicable to various QCD correlators.

Abstract

We consider finite volume effects on the electromagnetic form factor of the pion. We compute the peudoscalar-vector-pseudoscalar correlator in the $\epsilon$ expansion of chiral perturbation theory up to the next-to-leading order and find a way to remove the dominant part, which comes from a contribution of the pion zero-mode. Inserting non-zero momentum to relevant operators (or taking a subtraction of the correlators at different time-slices), and taking an appropriate ratio of them, one can automatically cancel the zero-mode's contribution, which becomes non-perturbatively large $\sim \mathcal{O}(100 \%)$ in the $\epsilon$ regime. The remaining finite volume dependence, which comes from the non-zero momentum modes, is shown to be perturbatively small even in such an extremal case. Since the zero-mode's dominance is universal in any finite volume scaling, and we do not rely on any particular feature of the $\epsilon$ expansion, our method has a wide application to many other correlators of QCD.