On the massive two-loop corrections to Bhabha scattering

TL;DR

This paper reviews recent progress in calculating two-loop virtual corrections to Bhabha scattering, highlighting methods for systematic computation of complex integrals essential for precision predictions.

Contribution

It introduces a potential systematic approach using differential equations and Mellin-Barnes representations to compute two-loop box integrals in massive Bhabha scattering.

Findings

Two-loop virtual corrections have been partially derived from combined massless and electron-loop calculations.

Master integrals for self-energy and vertex diagrams are known, but most two-loop boxes remain uncalculated.

A promising method involving differential equations and Mellin-Barnes techniques is demonstrated for future calculations.

Abstract

We overview the general status of higher order corrections to Bhabha scattering and review recent progress in the determination of the two-loop virtual corrections. Quite recently, they were derived from combining a massless calculation and contributions with electron sub-loops. For a massive calculation, the self-energy and vertex master integrals are known, while most of the two-loop boxes are not. We demonstrate with an example that a study of systems of differential equations, combined with Mellin-Barnes representations for single masters, might open a way for their systematic calculation.