High-precision calculation of the 4-loop contribution to the electron g -2 in QED

Abstract

I have evaluated up to 1100 digits of precision the contribution of the 891 4-loop Feynman diagrams contributing to the electron g-2 in QED. The total mass-independent 4-loop contribution isae=−1.912245764926445574152647167439830054060873390658725345…(απ)4. I 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.