Two-loop QCD corrections for real and off-shell diphoton and triphoton production via quark loops

TL;DR

This paper presents a comprehensive, numerically implementable framework for computing two-loop QCD corrections to real and off-shell diphoton and triphoton production via quark loops. It combines local infrared, ultraviolet, and threshold subtractions in loop momentum space with loop-tree duality and a multi-channel Monte Carlo, enabling finite, gauge-invariant amplitudes to be evaluated by Monte Carlo integration. The authors validate their squared matrix elements against analytic benchmarks and extend results to heavy-quark loops and off-shell final states, providing new double-virtual corrections after convolution with PDFs. The approach advances the multi-scale, multi-leg frontier in perturbative QCD and lays groundwork for applying these techniques to broader electroweak boson production processes at NNLO.

Abstract

We compute squared matrix elements at next-to-next-to-leading order in perturbative quantum chromodynamics for the production of two or three (on- or off-shell) photons mediated via (light or heavy) quark loops. Our method handles all cases in a unified framework, using simultaneous subtraction of infrared, ultraviolet, and threshold singularities in loop momentum space to produce a locally finite integrand suitable for numerical integration. We confirm agreement with available analytic benchmarks at fixed phase-space points and provide new results otherwise. We also compute the double-virtual corrections to the cross section for on- and off-shell diphoton and on-shell triphoton production by combining the Monte Carlo integration over loop and phase space.

Figures (5)

• Figure 1: Examples of planar and non-planar two-loop diagrams contributing to the $2\to 2$ process.
• Figure 2: Examples of planar two-loop diagrams contributing to the $2\to 3$ process.
• Figure 3: Diagrams that contribute to the amplitude with coefficient $\sum_{f=1}^{N_f}Q_f^r$, where $r= n - l-1 \geq 1$ is the number of photons attached to the fermion loop in the figure. We explicitly assign the loop momenta labels $k_1$ and $k_2$ of the corresponding integrand built with conventional Feynman rules. It is also useful to denote by $k_{g_{1}}$ and $k_{g_{2}}$ the gluon momenta in the direction specified by the figure.
• Figure 4: Possible Cutkosky cuts identifying the threshold singularities.
• Figure 5: Replacement that turns the planar and non-planar diagrams, $G_\text{P}$ and $G_\text{NP}$, from the $2\to2$ in fig. \ref{['fig:2to2thresholds']} into those of the $2\to3$ process, with thresholds.