Calculation of one-loop integrals for four-photon amplitudes by functional reduction method

TL;DR

This paper introduces a functional reduction method to analytically compute one-loop four-photon scattering integrals, providing compact expressions in four dimensions for complex quantum electrodynamics processes.

Contribution

The paper presents a novel functional reduction technique for calculating one-loop Feynman integrals with four external photons, yielding new analytic results.

Findings

Analytic expressions for master integrals in d dimensions.

Compact formulas in four dimensions involving logarithms and dilogarithms.

Application to light-by-light scattering, photon splitting, and Delbruck scattering.

Abstract

The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of light by light, the photon splitting in an external field and Delbr\"{u}ck scattering are considered. For master integrals in $d$ - dimensions, new analytic results are presented. For $d=4$, these integrals are given by compact expressions in terms of logarithms and dilogarithms.