Two-loop amplitudes for $\mathcal{O}(α_s^2)$ corrections to $Wγγ$ production at the LHC

TL;DR

This paper delivers the first complete two-loop, leading-colour helicity amplitudes for Wγγ production at the LHC, including non-planar contributions, and provides a numerical treatment for subleading-colour terms. The authors employ a modern finite-field reconstruction framework with NeatIBP to reduce IBP systems and express results in terms of pentagon functions, enabling efficient analytic and numerical evaluation. They validate the approach with gauge/invariance checks, pole cancellations, and cross-checks against OpenLoops, and analyze analytic properties of non-planar integrals. Ancillary files supply analytic LC results and detailed data structures, paving the way for NNLO QCD predictions and further phenomenological studies of Wγγ at the LHC.

Abstract

We present the two-loop helicity amplitudes contributing to the next-to-next-to-leading order QCD predictions for W-boson production in association with two photons at the Large Hadron Collider. We derived compact analytic expressions for the two-loop amplitudes in the leading colour limit, and provide numerical results for the subleading colour contributions. We employ a compact system of integration-by-part identities provided by the NeatIBP package, allowing for an efficient computation of the rational coefficients of the scattering amplitudes over finite fields.

Figures (5)

• Figure 1: Representative tree-level Feynman diagrams for the sub-amplitudes appearing in Eq. \ref{['eq:ampdecomposition']}. $A^{(L)}_{6,q}$ starts to contribute only at the two loop level.
• Figure 2: Sample two-loop Feynman diagrams contributing to the $W^+\gamma\gamma$ independent sub-amplitude currents $A^{(2)\mu}_{5,uu}$, $A^{(2)\mu}_{5,ud}$, $A^{(2)\mu}_{5,q}$, $A^{(2)\mu}_{4,u}$ and $A^{(2)\mu}_{3}$.
• Figure 3: Pictorial representation of the hexagon-triangle integral families entering the two-loop five-particle amplitude computation. The single line represents a massless particle while the double line depicts a massive particle.
• Figure 4: Tree level, one- and two-loop hard functions evaluated on the univariate phase-space slice defined by Eqs. \ref{['eq:unislice1']} and \ref{['eq:unisliceparams']} for all scattering channels of $W^+\gamma\gamma$ (upper panel) and $W^-\gamma\gamma$ (lower panel) production, with $\mu_R = 100$ GeV.
• Figure 5: Distribution of subleading colour corrections to the two-loop hard functions for the set of phase-space point defined in Eqs. \ref{['eq:unislice1']} and \ref{['eq:unisliceparams']}, for $W^+\gamma\gamma$ (left) and $W^-\gamma\gamma$ (right) production.