Higher-order QCD corrections to top-quark pair production in association with a jet

TL;DR

This work delivers the first NNLO QCD predictions for top-quark pair production in association with a jet, $pp \to t\bar{t}j+X$, at $\sqrt{s}=13$ TeV, leveraging leading-color two-loop amplitudes and a four-dimensional sector-improved residue subtraction to achieve high-precision differential cross sections. The study implements a dynamical scale choice $\mu_R=\mu_F=\mu_0=H_T/n$ and analyzes theoretical uncertainties via seven-point scale variations and a theory-nuisance parameter (TNP) approach, reporting a substantial reduction in missing higher-order uncertainties and detailing the impact of subleading-color contributions. Differential observables, including $p_T(t\bar{t})$ and the mass-sensitive ratio observable $\rho$, exhibit improved perturbative stability with NNLO corrections typically reducing scale uncertainties to the few-percent level and revealing small but non-negligible shape distortions. The results also explore cross-section ratios to inclusive $t\bar{t}$ production, finding strong sensitivity to higher-order corrections at low invariant mass and improved stability at high invariant mass, while highlighting the need for future work on subleading color effects, top-quark decays, and potential N3LO developments.

Abstract

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the Standard Model of Particle Physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this article, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in Quantum Chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

Figures (3)

• Figure 1: The transverse momentum distribution of the top-quark pair in the soft-jet phase space, through LO (green), NLO (blue), and NNLO (red) QCD. The top panel shows absolute predictions, while the bottom panels show ratios relative to the central NLO QCD prediction. The solid lines show the central predictions and the colored bands the envelope of seven-point scale variations. In the bottom panel, the dashed lines indicate the TNP uncertainty bands for MHOU, and the grey hashed area indicates the uncertainty estimates for the sub-leading color terms.
• Figure 2: Same as Fig. \ref{['fig:soft_pTtt']} but for the $\rho$ observable.
• Figure 3: The R32 as a function of the top-quark pair invariant mass in the hard-jet phase space, through LO (green), NLO (blue), and NNLO (red) QCD. The top panel shows absolute predictions, while the bottom panel shows ratios relative to the central NLO QCD prediction. The solid lines show the central predictions and the colored bands the envelope of seven-point scale variations.