Three-loop helicity amplitudes of four-lepton scattering in QED

TL;DR

This paper provides detailed three-loop virtual correction formulas for helicity amplitudes in four-fermion scattering in massless QED, advancing precision calculations in quantum electrodynamics.

Contribution

It introduces analytic expressions for three-loop helicity amplitudes in massless QED, including explicit results for key scattering processes, using optimized integral reduction techniques.

Findings

Explicit three-loop helicity amplitudes for four-fermion scattering

Results expressed in terms of generalized polylogarithms up to weight six

Applications to dimuon production, electron-muon scattering, and Bhabha scattering

Abstract

We present the analytic expressions of the three-loop virtual corrections to the helicity amplitudes of 2 -> 2 four-fermion scattering processes in massless QED. The contributing Feynman diagrams are grouped into integrand families characterised by independent Symanzik polynomials and decomposed in terms of master integrals using an optimised integration-by-parts strategy. Upon the renormalisation of the ultraviolet divergences and the extraction of the universal infrared pole structure, the finite results are expressed in terms of generalised polylogarithms up to transcendental weight six. Amplitudes for dimuon production in electron-positron annihilations, electron-muon scattering, and Bhabha scattering are explicitly derived.