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

We calculate all planar contributions to the two-loop massless helicity amplitudes for the process q (q) over bar -> 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 -> 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.

Automated summary

The study calculates all planar contributions to the two-loop massless helicity amplitudes for the q (q) over bar -> gamma gamma gamma process and presented the results in analytic form using the functional basis proposed by Chicherin and Sotnikov. The research combines various modern computational techniques and agrees with a recent calculation of the same amplitude performed using different techniques, suggesting that the framework is suitable for calculating two-loop multi-leg amplitudes.