Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders

TL;DR

The paper delivers the first publicly available set of planar two-loop five-point QCD amplitudes for the process pp → γγγ, enabling NNLO QCD predictions for triphoton production. It combines two-loop numerical unitarity with analytic reconstruction to obtain analytic master-integral coefficients and finite remainders expressed in a pentagon-function basis, valid to all orders in the dimensional regulator. The authors provide a public C++ library, FivePointAmplitudes, for efficient on-the-fly evaluation of the finite remainders and the squared two-loop contributions, and demonstrate robust numerical stability across phase space. The work is validated against known results, cross-checked with independent approaches, and has already been employed to achieve NNLO predictions in modern phenomenology frameworks, marking a significant advance for high-multiplicity, two-loop QCD calculations. These results pave the way for more precise tests of the Standard Model and tighter constraints on new physics in multi-photon final states.

Abstract

We compute the two-loop helicity amplitudes for the production of three photons at hadron colliders in QCD at leading-color. Using the two-loop numerical unitarity method coupled with analytic reconstruction techniques, we obtain the decomposition of the two-loop amplitudes in terms of master integrals in analytic form. These expressions are valid to all orders in the dimensional regulator. We use them to compute the two-loop finite remainders, which are given in a form that can be efficiently evaluated across the whole physical phase space. We further package these results in a public code which assembles the helicity-summed squared two-loop remainders, whose numerical stability across phase-space is demonstrated. This is the first time that a five-point two-loop process is publicly available for immediate phenomenological applications.

Figures (6)

• Figure 1: Contribution proportional to $C_F^2$
• Figure 2: Contribution proportional to $C_FC_A$
• Figure 3: Contribution proportional to $N_f$
• Figure 4: Contribution proportional to $\sum_f {Q^2_f}$
• Figure 6: The logarithmic distribution of correct decimal digits (as defined in \ref{['eq:relerr']}) for 90000 double-precision evaluations of the $H^{(2)}$ function. The phase-space points are sampled from a distribution representative of typical phenomenological studies.