NNLO QCD corrections to three-photon production at the LHC

TL;DR

This work delivers the first NNLO QCD calculation for a 2→3 process by evaluating pp → γγγ + X at the LHC using the STRIPPER framework. The key theoretical advance is a complete, analytic two-loop q q̄ → γγγ amplitude in the leading-color approximation, complemented by exact tree- and one-loop amplitudes, with careful handling of IR singularities and phase-space integration. Phenomenologically, NNLO corrections bring theory into good agreement with ATLAS 8 TeV data across fiducial cross-sections and a broad set of differential distributions, while revealing large higher-order corrections and discussing perturbative convergence. The study demonstrates the feasibility and importance of NNLO for multi-photon final states and sets the stage for future refinements, including the remaining two-loop contributions and potential N3LO effects.

Abstract

We compute the NNLO QCD corrections to three-photon production at the LHC. This is the first NNLO QCD calculation for a $2\to 3$ process. Our calculation is exact, except for the scale-independent part of the two-loop finite remainder which is included in the leading color approximation. We estimate the size of the missing two-loop corrections and find them to be phenomenologically negligible. We compare our predictions with available 8 TeV measurement from the ATLAS collaboration. We find that the inclusion of the NNLO corrections eliminates the existing significant discrepancy with respect to NLO QCD predictions, paving the way for precision phenomenology in this process.

Figures (6)

• Figure 1: Predictions for the fiducial cross-section in LO (green), NLO (blue) and NNLO (red) QCD versus ATLAS data (black). Shown are predictions for six scale choices. The error bars on the theory predictions reflect scale variation only. For two of the scales only the central predictions are shown.
• Figure 2: $p_T$ distribution of the hardest photon $\gamma_1$ (left), $\gamma_2$ (center) and the softest one $\gamma_3$ (right). Top plot shows the absolute distribution at NNLO (red), NLO (blue) and LO (green) versus ATLAS data (black). Middle plot shows same distributions but normalized to the NLO. Bottom plot shows central NNLO predictions for 6 different scale choices (only the central scale is shown) with respect to the default choice $\mu_0=H_T/4$. The bands represent the 7-point scale variations about the corresponding central scales.
• Figure 3: As in fig. \ref{['fig:PT']} but for the $\Delta\Phi(\gamma_i,\gamma_j)$ distributions.
• Figure 4: As in fig. \ref{['fig:PT']} but for the $|\Delta\eta(\gamma_i,\gamma_j)|$ distributions.
• Figure 5: As in fig. \ref{['fig:PT']} but for the $m(\gamma_i,\gamma_j)$ and $m(\gamma_1,\gamma_2,\gamma_3)$ distributions.