Zemach and Friar radii of the proton and neutron from lattice QCD

TL;DR

This paper reports the first lattice-QCD calculations of the Zemach and Friar radii for proton and neutron, including systematic uncertainties, and finds results consistent with experimental data.

Contribution

First lattice-QCD determination of the Zemach and Friar radii for proton and neutron, including all relevant diagrams and systematic error analysis.

Findings

Proton Zemach radius: 1.013 ± 0.016 fm

Proton Friar radius: 1.301 ± 0.018 fm

Results are compatible with experimental studies.

Abstract

We present the first lattice-QCD result for the Zemach and Friar radii of the proton and neutron. Our calculation includes both quark-connected and -disconnected diagrams and assesses all sources of systematic uncertainties arising from excited-state contributions, finite-volume effects and the continuum extrapolation. At the physical point, we obtain for the proton $r_Z^p = ( 1.013 \pm 0.010\ (\mathrm{stat}) \pm 0.012\ (\mathrm{syst}) )~\mathrm{fm}$ and $r_F^p = ( 1.301 \pm 0.012\ (\mathrm{stat}) \pm 0.014\ (\mathrm{syst}) )~\mathrm{fm}$. These numbers suggest small values of the Zemach and Friar radii of the proton, but are compatible with most of the experimental studies.