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Two-loop leading colour QCD corrections to $q \bar{q} \to γγg$ and $q g \to γγq$

Bakul Agarwal, Federico Buccioni, Andreas von Manteuffel, Lorenzo Tancredi

TL;DR

The paper advances the precision frontier for diphoton production with an associated jet by computing the leading-color and light-fermion planar two-loop QCD corrections for the qq̄→gγγ and qg→qγγ channels. It combines state-of-the-art IBP reduction, multivariate partial fraction decomposition, and master-integral techniques to obtain compact analytic results and an efficient numerical implementation, with results validated against Catani’s IR factorisation. Finite remainders for the one- and two-loop interferences are presented in a minimally factorised form, and a public C++ library enables rapid evaluation across phase space using double or quadruple precision. The work provides essential ingredients for NNLO (and toward N3LO) predictions of diphoton plus jet at hadron colliders and showcases techniques that can be extended to other multiloop, multi-leg amplitudes.

Abstract

We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

Two-loop leading colour QCD corrections to $q \bar{q} \to γγg$ and $q g \to γγq$

TL;DR

The paper advances the precision frontier for diphoton production with an associated jet by computing the leading-color and light-fermion planar two-loop QCD corrections for the qq̄→gγγ and qg→qγγ channels. It combines state-of-the-art IBP reduction, multivariate partial fraction decomposition, and master-integral techniques to obtain compact analytic results and an efficient numerical implementation, with results validated against Catani’s IR factorisation. Finite remainders for the one- and two-loop interferences are presented in a minimally factorised form, and a public C++ library enables rapid evaluation across phase space using double or quadruple precision. The work provides essential ingredients for NNLO (and toward N3LO) predictions of diphoton plus jet at hadron colliders and showcases techniques that can be extended to other multiloop, multi-leg amplitudes.

Abstract

We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

Paper Structure

This paper contains 8 sections, 47 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Kinematics and Notation
  3. Structure of the scattering amplitude
  4. Diagrammatic calculation and integral reductions
  5. Renormalisation and infrared factorisation
  6. Exploiting linear dependencies of rational functions
  7. Numerical implementation
  8. Conclusions

Figures (2)

  • Figure 1: Examples of two-loop diagrams which contribute to the various colour factors in (\ref{['eq:colourfactorstl']}).
  • Figure 2: Probability of finding an event with an instability level $\mathcal{D}$ defined in (\ref{['eq:instabilitydefinition']}) larger than $\mathcal{D}_{\mathrm{min}}$ for the two colour factors $\mathcal{W}^{(1),\mathrm{fin}}_{02}$ and $\mathcal{W}^{(4),\mathrm{fin}}_{02}$. The labels "dp" and "rescue" are described in the text. Events were generated according to (\ref{['eq:events']}).