A model-independent framework for determining finite-volume effects of spatially nonlocal operators

TL;DR

This paper introduces a model-independent method to estimate finite-volume effects on matrix elements of spatially-separated current operators using elastic form factors, applicable to lattice QCD calculations.

Contribution

It develops a framework that relates finite-volume corrections to elastic form factors, avoiding reliance on effective field theories and enabling non-perturbative estimates.

Findings

Finite-volume effects can be estimated from elastic form factors.

The formalism applies to scalar theories in 2D and 4D.

The approach is model-independent and non-perturbative.

Abstract

We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially-separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e. amplitudes coupling single-particle states via two current insertions. We show that the infrared behavior of these matrix elements is dominated by the single-particle pole, which is approximated by the elastic form factors of the lowest-lying hadron. Therefore, given lattice data on the relevant elastic form factors, the finite-volume effects can be estimated non-perturbatively and without recourse to effective field theories. For illustration purposes, we investigate the implications of the proposed formalism for a class of scalar theories in two and four dimensions.