Di-photon amplitudes in three-loop Quantum Chromodynamics

TL;DR

This paper presents the first complete three-loop QCD calculation of di-photon production amplitudes, providing compact analytic results using advanced polylogarithmic functions, which advances precision in particle physics predictions.

Contribution

It introduces a novel method for calculating three-loop four-point scattering amplitudes in full QCD with compact analytic expressions.

Findings

First three-loop four-point amplitude in full QCD

Analytic results expressed with harmonic and multiple polylogarithms

Efficient calculation of helicity amplitudes using projectors

Abstract

We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in Quantum Chromodynamics (QCD). We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results, that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.