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arXiv · hep-ph/9911277

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

Kirill Melnikov·Timo van Ritbergen
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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.

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Kirill Melnikov, Timo van Ritbergen. 1999-11-10. The three loop slope of the Dirac form factor and the 1S Lamb shift in hydrogen. https://doi.org/10.1103/physrevlett.84.1673

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