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arXiv · 1704.06996

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

Stefano Laporta
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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 is $ a_e = -1.912245764926445574152647167439830054060873390658725345{\ldots} \left(\frac{\alpha}{\pi}\right)^4$. I have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits.

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Stefano Laporta. 2017-04-23. High-precision calculation of the 4-loop contribution to the electron g-2 in QED. https://doi.org/10.1016/j.physletb.2017.06.056

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