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

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.