Finite Volume Effects on the Extraction of Form Factors at Zero Momentum

TL;DR

This paper investigates finite volume effects on extracting hadronic form factors at zero momentum in lattice QCD, clarifying theoretical assumptions and using chiral perturbation theory to quantify finite volume corrections for the pion charge radius and moments.

Contribution

It establishes a theoretical framework for understanding finite volume effects on zero-momentum form factor extraction and demonstrates this with chiral perturbation theory calculations for the pion.

Findings

Finite volume effects significantly impact zero-momentum form factor calculations.

The charge radius and higher moments can be accurately computed at zero momentum.

Finite volume corrections can be systematically estimated using chiral perturbation theory.

Abstract

Hadronic matrix elements that depend on momentum are required for numerous phenomenological applications. Probing the low-momentum regime is often problematic for lattice QCD computations on account of the restriction to periodic momentum modes. Recently a novel method has been proposed to compute matrix elements at zero momentum, for which straightforward evaluation of the matrix elements would otherwise yield a vanishing result. We clarify an assumption underlying this method, and thereby establish the theoretical framework required to address the associated finite volume effects. Using the pion electromagnetic form factor as an example, we show how the charge radius and two higher moments can be calculated at zero momentum transfer, and determine the corresponding finite volume effects. These computations are performed using chiral perturbation theory to account for modified infrared physics, and can be generalized to ascertain finite volume effects for other hadronic matrix elements extracted at zero momentum.