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NNLO QCD subtraction for top-antitop production in the $q\bar{q}$ channel

Gabriel Abelof, Aude Gehrmann-De Ridder, Philipp Maierhöfer, Stefano Pozzorini

TL;DR

This work advances NNLO QCD predictions for top-antitop production in the q qbar channel by developing and validating an antenna subtraction framework tailored to massive final states. It introduces a new massive initial-final four-parton antenna A4^0 and a one-loop A3^1 antenna to handle double real and real-virtual contributions at leading colour, with OpenLoops providing the one-loop amplitudes for q qbar -> t tbar g. The authors demonstrate explicit pole cancellations and robust numerical stability across unresolved limits, using a combination of double-precision computations and targeted quadruple-precision rescues, and they lay out a clear path toward a full NNLO event generator for ttbar observables. The results mark a significant step toward precise, differential NNLO predictions for top-quark production at hadron colliders, enabling improved tests of QCD and top-quark properties. Remaining tasks include completing the VV and U contributions and integrating the new integrated antenna pieces into a fully differential NNLO framework.

Abstract

We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The $q \bar q \to t \bar{t} g$ amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits.

NNLO QCD subtraction for top-antitop production in the $q\bar{q}$ channel

TL;DR

This work advances NNLO QCD predictions for top-antitop production in the q qbar channel by developing and validating an antenna subtraction framework tailored to massive final states. It introduces a new massive initial-final four-parton antenna A4^0 and a one-loop A3^1 antenna to handle double real and real-virtual contributions at leading colour, with OpenLoops providing the one-loop amplitudes for q qbar -> t tbar g. The authors demonstrate explicit pole cancellations and robust numerical stability across unresolved limits, using a combination of double-precision computations and targeted quadruple-precision rescues, and they lay out a clear path toward a full NNLO event generator for ttbar observables. The results mark a significant step toward precise, differential NNLO predictions for top-quark production at hadron colliders, enabling improved tests of QCD and top-quark properties. Remaining tasks include completing the VV and U contributions and integrating the new integrated antenna pieces into a fully differential NNLO framework.

Abstract

We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits.

Paper Structure

This paper contains 50 sections, 120 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Top-antitop production in the $q\bar{q}$ channel at NLO
  3. Notation and conventions
  4. $t\bar{t}$ production at LO
  5. $t\bar{t}$ production at NLO
  6. Real radiation contributions
  7. Virtual contributions
  8. The mass factorisation counter term at NLO
  9. The massive initial-final antenna $A_4^0(1_Q,3_g,4_g,\hat{2}_q)$
  10. Universal double unresolved factors
  11. Double soft factor of two colour-connected gluons
  12. Soft-collinear factor in the colour-connected configuration
  13. Triple collinear factor
  14. Infrared limits of $A_4^0(1_Q,3_g,4_g,\hat{2}_q)$
  15. The massive initial-final antenna $A_3^1(1_Q,3_g,\hat{2}_q)$
  16. ...and 35 more sections

Figures (10)

  • Figure 1: (a) Sketch of a double soft event. (b) Cumulative distributions of $\delta_{\rm RR}$ for $10^4$ double soft phase space points with three different values of $x$
  • Figure 2: (a) Sketch of a triple collinear event. (b) Cumulative distributions of $\delta_{\rm RR}$ for $10^4$ triple collinear phase space points with three different values of $x$
  • Figure 3: (a) Sketch of a soft-collinear event. (b) Cumulative distributions of $\delta_{\rm RR}$ for $10^4$ soft-collinear phase space points with three different values of $x$ and $y$
  • Figure 4: (a) Sketch of a double collinear event. (b) Cumulative distributions of $\delta_{\rm RR}$ for $10^4$ double collinear phase space points with three different values of $x$
  • Figure 5: (a) Sketch of a single soft event. (b) Cumulative distributions of $\delta_{\rm RR}$ for $10^4$ single soft phase space points with three different values of $x$
  • ...and 5 more figures