Comment on "Nucleon spin-averaged forward virtual Compton tensor at large Q^2"

TL;DR

This paper discusses the compatibility of large-$Q^2$ amplitude calculations with low-$Q^2$ chiral EFT results and corrects an overestimate in the two-photon contribution to muonic hydrogen Lamb shift.

Contribution

It clarifies the consistency between operator product expansion and chiral EFT results and corrects an overestimate in the two-photon Lamb shift contribution.

Findings

Large-$Q^2$ amplitude $W_1(0,Q^2)$ aligns with chiral EFT extrapolations.

The two-photon Lamb shift estimate was previously overestimated.

Correction reduces uncertainty in muonic hydrogen Lamb shift calculations.

Abstract

In recent work, Hill and Paz apply the operator product expansion to forward doubly virtual Compton scattering. The resulting large-$Q^2$ form of the amplitude $W_1(0,Q^2)$ is compatible with the one we obtain by extrapolation of low-$Q^2$ results from a chiral effective field theory, providing support for our approach. That paper also presents a result for the two-photon contribution to the Lamb shift in muonic hydrogen that has a much larger uncertainty than in previous work. We show that this an overestimate arising from the inclusion of the proton pole term in the subtracted dispersion relation for $W_1$.