This paper presents the first full next-to-next-to-next-to-leading order (N3LO) quantum chromodynamics (QCD) prediction for the production of two isolated photons (diphotons) in proton–proton collisions at the Large Hadron Collider (LHC). Diphoton production is an important process at the LHC: it forms a background for Higgs boson studies and has been measured precisely by the ATLAS and CMS experiments. Until now, theoretical predictions through next-to-next-to-leading order (NNLO) showed large shifts and growing uncertainty when the order was increased. The authors report that the N3LO result finally shows perturbative convergence and a significant reduction of the main theory uncertainty coming from scale choices.

At a high level, the calculation splits the observable by the transverse momentum qT of the photon pair. Events with very small qT are treated using a factorization formula that replaces the complicated radiation pattern with well‑studied transverse‑momentum‑dependent parton distributions and matching kernels calculated up to N3LO. Events with larger qT are obtained from an NNLO calculation for diphoton plus a jet. This so-called qT‑slicing method needs a small cutoff in qT to be accurate, which creates large numerical challenges that the authors address with several technical improvements.

To make the NNLO diphoton+jet piece practical at the tiny qT cutoff, the team upgraded their STRIPPER implementation (a software framework for handling QCD infrared singularities) and improved numerical stability. They used a hybrid floating‑point scheme that switches between double and quadruple precision where needed, redesigned a selector function to avoid extreme angular cancellations, and replaced numerically fragile one‑loop amplitude libraries with compact analytic expressions. Those analytic one‑loop amplitudes for six‑point processes were obtained with modern algebraic techniques: the amplitudes were computed on many numerical probes in finite number fields and then reconstructed as rational functions, a procedure called rational reconstruction.