English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We have evaluated with 1100 digits of precision the contribution of all the891 mass-independent four-loop Feynman diagrams contributing to the slope ofthe Dirac form factor in QED. The total 4-loop contribution is $ m^2F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745...\left(\frac{\alpha}{\pi}\right)^4$. We have fit a semi-analytical expression tothe numerical value. The expression contains harmonic polylogarithms ofargument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$,one-dimensional integrals of products of complete elliptic integrals and sixfinite parts of master integrals, evaluated up to 4800 digits. I show thecorrection on the shift of the energy levels of the hydrogen atom due to theslope.

High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor