Abstract
We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent 4-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution ism2F1(4)′(0)=0.886545673946443145836821730610315359390424032660064745…(απ)4. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument eiπ3, e2iπ3, eiπ2, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction on the shift of the energy levels of the hydrogen atom due to the slope.
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