Two-loop leading-color helicity amplitudes for three-photon production at the LHC

TL;DR

This paper presents the analytic calculation of two-loop helicity amplitudes for three-photon production at the LHC, providing essential contributions for NNLO QCD predictions and demonstrating advanced computational techniques.

Contribution

It introduces a fully analytic form of two-loop helicity amplitudes for q q̄ → 3γ, using modern methods like IBP solutions, finite-field reconstruction, and efficient helicity projection.

Findings

Results agree with recent independent calculations.

Provides analytic expressions useful for NNLO QCD computations.

Demonstrates the effectiveness of modern computational techniques.

Abstract

We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $q\bar q\to \gamma\gamma\gamma$. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process $pp\to \gamma\gamma\gamma$ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.