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Light fermionic NNLO QCD corrections to top-antitop production in the quark-antiquark channel

Gabriel Abelof, Aude Gehrmann-De Ridder

TL;DR

This work computes NNLO QCD corrections to top pair production in the quark-antiquark channel that are proportional to the number of light flavors $N_l$, using a massive extension of antenna subtraction. The authors construct real-real, real-virtual, and virtual-virtual contributions with dedicated subtraction terms, proving analytic cancellation of infrared poles at the real-virtual and virtual-virtual levels. The results are implemented in a fully differential Monte Carlo generator, enabling NNLO differential distributions for $pp\to t\bar{t}$ in the $q\bar{q}$ channel, and showing that the $N_l$ corrections decrease the cross section by several percent compared to NLO, with leading and subleading color pieces contributing differently across phase space. This work represents a significant step toward a complete differential NNLO description of top-quark pair production and lays the groundwork for including all partonic channels. The approach demonstrates precise handling of infrared structure in processes with massive final states and provides a benchmark for future higher-order QCD calculations.

Abstract

We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors $N_l$. While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles cancel at the real-virtual and virtual-virtual levels respectively, thereby demonstrating the validity of the massive extension of the NNLO antenna formalism. These NNLO corrections are implemented in a Monte Carlo parton level generator providing full kinematical information on an event-by event basis. With this program, NNLO differential distributions in the form of binned histograms are obtained and presented here.

Light fermionic NNLO QCD corrections to top-antitop production in the quark-antiquark channel

TL;DR

This work computes NNLO QCD corrections to top pair production in the quark-antiquark channel that are proportional to the number of light flavors , using a massive extension of antenna subtraction. The authors construct real-real, real-virtual, and virtual-virtual contributions with dedicated subtraction terms, proving analytic cancellation of infrared poles at the real-virtual and virtual-virtual levels. The results are implemented in a fully differential Monte Carlo generator, enabling NNLO differential distributions for in the channel, and showing that the corrections decrease the cross section by several percent compared to NLO, with leading and subleading color pieces contributing differently across phase space. This work represents a significant step toward a complete differential NNLO description of top-quark pair production and lays the groundwork for including all partonic channels. The approach demonstrates precise handling of infrared structure in processes with massive final states and provides a benchmark for future higher-order QCD calculations.

Abstract

We present the NNLO corrections to top pair production in the quark-antiquark channel proportional to the number of light quark flavors . While the double real corrections were derived previously, here we compute the real-virtual and virtual-virtual contributions in this partonic channel. Using the antenna subtraction formalism, we show that the subtraction terms correctly approximate the real-virtual contributions in all their infrared limits. Combined with the integrated forms of the double real and real-virtual subtraction terms, we show analytically that the explicit infrared poles cancel at the real-virtual and virtual-virtual levels respectively, thereby demonstrating the validity of the massive extension of the NNLO antenna formalism. These NNLO corrections are implemented in a Monte Carlo parton level generator providing full kinematical information on an event-by event basis. With this program, NNLO differential distributions in the form of binned histograms are obtained and presented here.

Paper Structure

This paper contains 31 sections, 94 equations, 8 figures.

Table of Contents

  1. Introduction
  2. General structure of the NNLO contributions to top pair production in the $q\bar{q}$ channel
  3. Real-real contributions to $q\bar{q} \rightarrow t \bar{t}$: the $N_l$ part
  4. Real-virtual contributions to $q\bar{q} \rightarrow t \bar{t}$: the $N_l$ part
  5. Real-virtual contributions
  6. The real-virtual subtraction term: ${\rm d}\hat{\sigma}^T$
  7. Explicit infrared singularity subtraction
  8. The implicit infrared substraction term: ${\rm d}\hat{\sigma}^{VS}$
  9. Renormalisation scale dependent subtraction
  10. The real-virtual subtraction term ${\rm d}\hat{\sigma}^T$
  11. Numerical tests of soft and collinear cancellations
  12. Virtual-virtual contributions to $q\bar{q} \rightarrow t\bar{t}$: the $N_l$ part
  13. The virtual-virtual contributions
  14. The mass factorisation counterterm ${\rm d}\hat{\sigma}^{MF,2}$
  15. The virtual-virtual subtraction term ${\rm d}\hat{\sigma}^{U}$
  16. ...and 16 more sections

Figures (8)

  • Figure 1: Sample Feynman diagrams for the $N_l$ part of the one-loop amplitude ${\cal M}^1_{q_1 \bar{q}_2\rightarrow t_3 \bar{t}_4 g_5}$. The thick solid lines represent massive fermions.
  • Figure 2: (a) Sketch of soft event limit. (b) Distribution of $R$ for $10^4$ soft phase space points with three different values of $x$
  • Figure 3: (a) Sketch of collinear event limit. (b) Distribution of $R$ for $10^4$ collinear phase space points with three different values of $x$
  • Figure 4: Transverse momentum distribution of a single top quark ${\rm d}\sigma / {\rm d} p_T^t$ for $\sqrt{s}=7$ TeV at LO (red), NLO (green), and NNLO (blue). The lower panel shows the ratios of LO, NLO and NNLO cross sections.
  • Figure 5: Rapidity distribution of a single top quark ${\rm d}\sigma / {\rm d} y^t$ for $\sqrt{s}=7$ TeV at LO (red), NLO (green), and NNLO (blue). The lower panel shows the ratios of LO, NLO and NNLO cross sections.
  • ...and 3 more figures