Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD

TL;DR

The paper delivers the first complete NNLO QCD prediction for the photon plus two-jet final state with exact five-point two-loop amplitudes in full colour, matching ATLAS 13 TeV event selections. It introduces a robust computational pipeline using finite-field reconstruction, IBP with syzygies, and momentum-twistor parametrization to obtain analytic two-loop helicity amplitudes for the $0\to ar{q}qgg\gamma$ and $0\to q\bar{q}Q\bar{Q}\gamma$ channels, including their finite remainders. The authors implement these results numerically, validate them against independent codes, and integrate them into a full NNLO calculation for $pp\to\gamma jj$ using Stripper, with two scale choices and a smooth/hard-cone photon isolation to mimic experiment. The NNLO predictions generally improve agreement with ATLAS data for key observables and show that sub-leading colour effects are negligible within remaining scale uncertainties, though electroweak corrections and fragmentation remain potential sources of residual deviations at high energies. This work completes the NNLO description of a two-to-three process with photons and jets without relying on leading-colour approximations and provides a benchmark for precision QCD against LHC measurements.

Abstract

In this work, we provide a comprehensive set of differential cross-section distributions for photon + di-jet production in proton-proton collisions with next-to-next-to-leading order precision in massless QCD. The event selection corresponds to recent measurements by the ATLAS collaboration. We observe an improved description of data in comparison to lower-order calculations in the case of observables that are expected to be well described by perturbation theory. The results also show better agreement with data than parton-shower-matched and multi-jet-merged predictions generated for the ATLAS analysis using the \textsc{Sherpa} Monte Carlo. A particular highlight of our study is the use of exact five-point two-loop virtual amplitudes. This is the first calculation of a complete two-to-three hadron-collider process at next-to-next-to-leading order in QCD that does not rely on the leading-colour approximation at two loops. We demonstrate, nevertheless, that the sub-leading-colour effects present in the infrared- and ultraviolet-finite double-virtual contributions are negligible in view of the remaining scale uncertainties.

Figures (9)

• Figure 1: Representative two-loop Feynman diagrams for the $0\to \bar{q}qgg\gamma$ partonic process, together with the partial amplitudes they contribute to.
• Figure 2: Representative two-loop Feynman diagrams for the $0\to q\bar{q}Q\bar{Q}\gamma$ partonic process, together with the partial amplitudes they contribute to.
• Figure 3: Fraction of phase-space points with a given number of correct digits with respect to the total number of points. The labels "L1: sd,sd", "L2: sd,dd", and "L3: dd,qd" denote the implementation levels L1, L2 and L3. The labels "sd", "dd", and "qd" refer to single-double, double-double, and quad-double precision. Further details are given in the text.
• Figure 4: Differential cross sections w.r.t. the transverse energy of the photon $E_{\perp}(\gamma)$ in the inclusive (left plot) and direct-enriched (right plot) phase space at LO (green), NLO (blue) and NNLO (red) QCD compared to data (black) and Sherpa (purple) prediction provided by ATLASATLAS:2019iaa. The top panels show the absolute values for the $H_T$ scale choice. The middle (bottom) panel shows the ratio to NLO QCD using the $H_T$ ($E_{\perp}(\gamma)$) scale. The coloured bands show scale variation and the vertical coloured bars indicate statistical uncertainties.
• Figure 5: The same as \ref{['fig:diffxs_ET']} but for the $p_T^{\text{jet}}$ observable.