Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

TL;DR

This paper calculates the proton polarisability contribution to the Lamb shift in muonic hydrogen using fourth-order chiral perturbation theory, reducing theoretical uncertainties and clarifying the discrepancy in proton charge radius measurements.

Contribution

It provides a model-independent, fourth-order chiral perturbation theory calculation of the proton's polarisability effect on the Lamb shift, refining previous estimates.

Findings

Reduces uncertainty in proton polarisability contribution to Lamb shift.

Finds no large effect to explain proton radius discrepancy.

Emphasizes importance of consistent amplitude definitions.

Abstract

We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.