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

• DOI: 10.1016/j.physletb.2017.06.056
• Publication Date: 2017-06-22T19:17:50Z
• Authors: Stefano Laporta
• Keywords: Elliptic integral; Expression (computer science); Feynman integral

I have evaluated up to 1100 digits of precision the contribution 891 4-loop Feynman diagrams contributing electron $g$-$2$ in QED. The total mass-independent is $ a_e = -1.912245764926445574152647167439830054060873390658725345{\ldots} \left(\frac{\alpha}{\pi}\right)^4$. fit a semi-analytical expression numerical value. contains harmonic polylogarithms argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals products complete elliptic and six finite parts master integrals, 4800 digits.