Chiral extrapolations for nucleon electric charge radii

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 (${m}_{$\pi${}}$\sim${}180\text{ }\text{ }\mathrm{MeV}$) are examined in order to confront the issue of how the chiral regime is approached. The electric charge radius of the nucleon isovector presents a forum for achieving consistent finite-volume corrections. Newly developed techniques within the framework of chiral effective field theory ($$\chi${}\mathrm{EFT}$) 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 $L$\gtrsim${}7\text{ }\text{ }\mathrm{fm}$ 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.