Finite-volume corrections to charge radii

TL;DR

This paper discusses how to properly correct lattice QCD calculations of nucleon charge radii for finite-volume effects by applying corrections directly to electric form factors, addressing a key challenge in finite-volume extrapolations.

Contribution

It introduces a new procedure for finite-volume corrections that are applied directly to electric form factors, improving the accuracy of lattice QCD results for charge radii.

Findings

Finite-volume effects distort the pion cloud around hadrons.

Correcting electric form factors directly yields more reliable charge radii.

The method improves comparison between lattice results and experimental data.

Abstract

The finite-volume nature of lattice QCD entails a variety of effects that must be handled in the process of performing chiral extrapolations. Since the pion cloud that surrounds hadrons becomes distorted in a finite volume, hadronic observables must be corrected before one can compare with the experimental values. The electric charge radius of the nucleon is of particular interest when considering the implementation of finite-volume corrections. It is common practice in the literature to transform electric form factors from the lattice into charge radii prior to analysis. However, there is a fundamental difficulty with using these charge radii in a finite-volume extrapolation. The subtleties are a consequence of the absence of a continuous derivative on the lattice. A procedure is outlined for handling such finite-volume corrections, which must be applied directly to the electric form factors themselves rather than to the charge radii.