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Double real radiation corrections to $t\bar{t}$ production at the LHC: the $gg\rightarrow t\bar{t}q\bar{q}$ channel

Gabriel Abelof, Aude Gehrmann-De Ridder

TL;DR

The paper advances NNLO QCD predictions for top-quark pair production by computing the double real radiation contributions from the gluon-gluon channel gg → tt̄ qq̄ using an antenna subtraction framework tailored for massive quarks. It introduces and analyzes genuine NNLO four-parton massive antennae (including new E-type and flavour-violating A-type antennas), derives their infrared limits, and constructs comprehensive subtraction terms to capture all single and double unresolved configurations in leading and subleading colour. The authors perform detailed numerical tests showing that the subtraction terms reproduce the real-emission matrix elements across double soft, triple collinear, and double/initial-final collinear limits, validating the IR cancellation required for stable NNLO numerics. This work represents a substantial step toward the full NNLO tt̄ cross section at the LHC, with future work targeting remaining gluon channels and mixed real-virtual contributions.

Abstract

We present the double real radiation contributions to the $t \bar t$ hadronic production cross section stemming from the partonic process $gg\rightarrow t\bar{t}q\bar{q}$. We explicitly construct the antenna subtraction terms for this gluon-gluon initiated process starting from the double soft behaviour of the double real radiation matrix elements using soft currents. Those subtraction terms, given in leading and subleading colour contributions, require the use of new genuine NNLO four-parton antenna functions involving massive fermions. Those are also presented together with their infrared limits in this paper. We checked the validity of our subtraction terms numerically by showing that the ratio between the real radiation matrix elements and the subtraction terms approaches unity in all single and double unresolved regions of phase space.

Double real radiation corrections to $t\bar{t}$ production at the LHC: the $gg\rightarrow t\bar{t}q\bar{q}$ channel

TL;DR

The paper advances NNLO QCD predictions for top-quark pair production by computing the double real radiation contributions from the gluon-gluon channel gg → tt̄ qq̄ using an antenna subtraction framework tailored for massive quarks. It introduces and analyzes genuine NNLO four-parton massive antennae (including new E-type and flavour-violating A-type antennas), derives their infrared limits, and constructs comprehensive subtraction terms to capture all single and double unresolved configurations in leading and subleading colour. The authors perform detailed numerical tests showing that the subtraction terms reproduce the real-emission matrix elements across double soft, triple collinear, and double/initial-final collinear limits, validating the IR cancellation required for stable NNLO numerics. This work represents a substantial step toward the full NNLO tt̄ cross section at the LHC, with future work targeting remaining gluon channels and mixed real-virtual contributions.

Abstract

We present the double real radiation contributions to the hadronic production cross section stemming from the partonic process . We explicitly construct the antenna subtraction terms for this gluon-gluon initiated process starting from the double soft behaviour of the double real radiation matrix elements using soft currents. Those subtraction terms, given in leading and subleading colour contributions, require the use of new genuine NNLO four-parton antenna functions involving massive fermions. Those are also presented together with their infrared limits in this paper. We checked the validity of our subtraction terms numerically by showing that the ratio between the real radiation matrix elements and the subtraction terms approaches unity in all single and double unresolved regions of phase space.

Paper Structure

This paper contains 30 sections, 79 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Double real radiation contributions to heavy quark pair production
  3. Antenna functions
  4. Infrared limits of massive NNLO antennae
  5. Double unresolved factors
  6. Single and double unresolved limits of the four-parton antennae
  7. Top quark pair production at the LHC
  8. Conventions
  9. Double real radiation contributions
  10. Subtraction terms
  11. Double soft behaviour of amplitudes
  12. The construction of ${\rm d}\hat{\sigma}^{S,b}_{gg\to Q\bar{Q}q\bar{q}}$
  13. Construction of the ${\rm d}\hat{\sigma}^{S,a}_{gg\to Q\bar{Q}q\bar{q}}$ and ${\rm d}\hat{\sigma}^{S,d}_{gg\to Q\bar{Q}q\bar{q}}$ subtraction terms
  14. Numerical results
  15. Double soft limit
  16. ...and 15 more sections

Figures (5)

  • Figure 1: \ref{['fig.pic1']} Ilustration of a double soft $q \bar{q}$ event. \ref{['fig.ds']} Distribution of R for 10000 double soft phase space points.
  • Figure 2: \ref{['fig.pic1']} Ilustration of a triple collinear event. \ref{['fig.ds']} Distribution of R for 10000 triple collinear phase space points.
  • Figure 3: \ref{['fig.pic1']} Ilustration of a double collinear event. \ref{['fig.ds']} Distribution of R for 10000 double collinear phase space points.
  • Figure 4: \ref{['fig.pic1']} Ilustration of a final-final single collinear event. \ref{['fig.ds']} Distribution of R for 10000 final-final single collinear phase space points.
  • Figure 5: \ref{['fig.pic1']} Ilustration of an initial-final single collinear event. \ref{['fig.ds']} Distribution of R for 10000 initial-final single collinear phase space points.