Master integrals for bipartite cuts of three-loop photon self energy

TL;DR

This paper computes master integrals for bipartite cuts of three-loop photon self energy diagrams in QED, expressing results in terms of polylogarithms and elliptic integrals, and provides their asymptotic behaviors.

Contribution

It introduces new calculations of master integrals for bipartite cuts, extending previous work to include the $4m$ cut and asymptotic analyses.

Findings

Master integrals expressed via Goncharov's polylogarithms and elliptic integrals.

Asymptotic behaviors at threshold and high-energy limits provided.

Results facilitate spectral density calculations in three-loop QED diagrams.

Abstract

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the $4m$ cut, reduce to Goncharov's polylogarithms. The master integrals for $4m$ cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for $4m$ cut.