The three loop slope of the Dirac form factor and the 1S Lamb shift in hydrogen

TL;DR

This paper calculates the three-loop contribution to the hydrogen energy levels from the Dirac form factor slope, refining the proton charge radius estimate using QED and Lamb shift data.

Contribution

It provides the first analytical evaluation of the three-loop slope contribution to hydrogen energy levels, improving precision in proton radius determination.

Findings

The three-loop slope contribution shifts hydrogen nS levels by 3.016/n^3 kHz.

The proton charge radius is estimated as 0.883 ± 0.014 fm.

Enhanced understanding of high-order QED effects in hydrogen.

Abstract

The last unknown contribution to hydrogen energy levels at order m alpha ^7, due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n^3 kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius r_p=0.883 \pm 0.014 fm.