Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders

TL;DR

This paper computes the full-colour two-loop QCD corrections for gluon-initiated diphoton plus jet production at hadron colliders by analytically reconstructing finite remainders in the pentagon-function basis from finite-field evaluations. The authors implement the results in the NJet library, employing momentum-twistor parametrizations and a suite of finite-field reconstruction techniques (linear-relations, univariate slicing, and on-the-fly partial fractions) to obtain compact analytic expressions. They reveal a notably simple all-plus configuration and provide a robust, fast, and stable C++ code suitable for phenomenological use, including scale uncertainties and interferences with one-loop amplitudes. The methods promise broad applicability to other challenging high-multiplicity two-loop calculations and contribute to improved NNLO predictions and potential N^3LO refinements for diphoton production at the LHC.

Abstract

We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.

Figures (3)

• Figure 1: Independent integral families for the $gg \to g \gamma \gamma$ amplitude. The non-planar topologies appear only in the leading-colour amplitude.
• Figure 2: The colour factor of each diagram in the $gg \to g \gamma \gamma$ follows from the representative three-gluon, two-loop diagrams with a closed fermion loop shown here.
• Figure 3: Histogram of the error estimate on the two-loop evaluations as given by the scaling test. We use the evaluation strategy with a target accuracy of three digits and show errors for all precision levels. We see 1.8% of points failing f64/f64 evaluation, with 1.2% passing at f128/f64 and 0.6% passing at f128/f128. The evaluation strategy achieves target accuracy for all of the 100000.0 physical phase-space points tested.