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

TL;DR

The paper delivers fully analytic, planar, leading-color two-loop helicity amplitudes for the QCD process $q\bar q \to \gamma\gamma\gamma$, expressed in the Chicherin-Sotnikov basis to support NNLO predictions for $pp\to \gamma\gamma\gamma$. The authors combine analytic IBP solutions, finite-field reconstruction, and Chen's projection method to obtain compact rational coefficients multiplying a uniform-transcendental function basis, enabling efficient numerical evaluation. They validate their results against independent computations (notably Abreu et al. 2020) and cross-check against previous work (Chawdhry et al. 2019bji) despite methodological differences. The work provides a versatile, automated framework for two-loop massless 5-point amplitudes and is directly applicable to high-precision LHC phenomenology, particularly for three-photon production at NNLO.

Abstract

We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $q\bar q\to γγγ$. 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 $pp\to γγγ$ [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.

Figures (2)

• Figure 1: Representative two-loop diagrams and their color/charge factors.
• Figure 2: The integral topologies $C_1$ and $C_2$.