This paper computes the complete next-to-leading order (NLO) electroweak (EW) corrections to diphoton production from gluon fusion at the Large Hadron Collider (LHC). In plain terms: the authors calculated how electroweak forces change the probability that two gluons inside colliding protons produce two photons, including for the first time the full effect of the third quark family (the heavy top quark) and the Higgs boson at two-loop order. Diphoton production is a key process at the LHC because it is both a clean test of the theory and an important background when searching for or measuring the Higgs boson and other new phenomena. Matching the experimental precision at the percent level requires such detailed theoretical inputs.

The technical challenge is that the electroweak corrections appear at two-loop order and involve many integrals with several mass scales. The authors reduced the problem to a large set of so-called master integrals: their reduction produced 189 distinct integral families and more than 7,200 master integrals. Instead of deriving closed-form analytic formulas, they solved differential equations for these integrals numerically. They computed the integrals at 19,380 phase-space points and validated their numerical values against independent evaluations, achieving high numerical precision.

At a high level the method works by writing how each master integral changes when kinematic variables change, then integrating those relations numerically. To make this feasible they chose an optimized basis of integrals so the differential equations are smaller and more stable than in a straightforward reduction. Because all external particles in the process are electrically neutral, the two-loop electroweak corrections are infrared finite by themselves, which simplifies the calculation: no infrared subtraction is needed, and the one-loop real-photon emission piece vanishes by symmetry.