Chiral extrapolations for nucleon electric charge radii

TL;DR

This paper discusses how to accurately extrapolate nucleon electric charge radii from lattice QCD simulations to physical conditions, addressing finite-volume effects and chiral behavior using effective field theory.

Contribution

It introduces new chiral effective field theory techniques for robustly extrapolating charge radii to physical pion mass and infinite volume, accounting for finite-volume effects.

Findings

Finite-volume effects are significant and require L > 7 fm for 2% accuracy.

Chiral extrapolations show notable volume dependence near the physical point.

Guidelines are provided for future lattice simulation volume requirements.

Abstract

Lattice simulations for the electromagnetic form factors of the nucleon yield insights into the internal structure of hadrons. The logarithmic divergence of the charge radius in the chiral limit poses an interesting challenge in achieving reliable predictions from finite-volume lattice simulations. Recent results near the physical pion mass are examined in order to confront the issue of how the chiral regime is approached. The electric charge radius of the nucleon presents a forum for achieving consistent finite-volume corrections. Newly-developed techniques within the framework of chiral effective field theory are used to achieve a robust extrapolation of the electric charge radius to the physical pion mass, and to infinite volume. The chiral extrapolations exhibit considerable finite-volume dependence; lattice box sizes of L > 7 fm are required in order to achieve a direct lattice simulation result within 2% of the infinite-volume value at the physical point. Predictions of the volume-dependence are provided to guide the interpretation of future lattice results.