Di-photon amplitudes in three-loop Quantum Chromodynamics

TL;DR

This is the first calculation of a three-loop four-point scattering amplitude in full QCD, and it is obtained in terms of harmonic polylogarithms or, alternatively, multiple polylogrithms of up to depth three.

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.

Figures (1)

• Figure 1: The real part of the three-loop finite remainder functions $\alpha^{(3),\text{fin}}(x)$ and $\beta^{(3),\text{fin}}(x)$ which determine the helicity amplitudes $\mathcal{A}_{L--}$ and $\mathcal{A}_{L-+}$, respectively, for $u\bar{u}\to\gamma\gamma$ and $\mu^2=s$.