The three loop slope of the Dirac form factor and the 1S Lamb shift in hydrogen
Kirill Melnikov, Timo van Ritbergen
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/n3 kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius rp=0.883 0.014 fm.
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