Renormalization-group improved fully differential cross sections for top pair production

TL;DR

The paper advances top-quark pair production predictions by incorporating semi-leptonic decays within a narrow-width, fully differential framework using RG-improved NNLL resummation to produce approximate NNLO production kernels. Implemented in a flexible parton-level Monte Carlo, the approach compares PIM and 1PI kinematics to study a broad class of IR-safe observables and provides a robust error framework that combines scale variation with kinematic envelope. Key findings show that approximate NNLO predictions often align well with full NLO for many observables and reduce theoretical uncertainties, though missing delta-function pieces and phase-space approximations can cause a modest underprediction relative to full NNLO for total cross sections. The results lay out a practical, differential tool for current and future collider analyses, while outlining concrete avenues for achieving full NNLO accuracy, including improved decay corrections and off-shell effects.

Abstract

We extend approximate next-to-next-to-leading order results for top-pair production to include the semi-leptonic decays of top quarks in the narrow-width approximation. The new hard-scattering kernels are implemented in a fully differential parton-level Monte Carlo that allows for the study of any IR-safe observable constructed from the momenta of the decay products of the top. Our best predictions are given by approximate NNLO corrections in the production matched to a fixed order calculation with NLO corrections in both the production and decay subprocesses. Being fully differential enables us to make comparisons between approximate results derived via different (PIM and 1PI) kinematics for arbitrary distributions. These comparisons reveal that the renormalization-group framework, from which the approximate results are derived, is rather robust in the sense that applying a realistic error estimate allows us to obtain a reliable prediction with a reduced theoretical error for generic observables and analysis cuts.

Figures (8)

• Figure 1: Graphical representation of the cross sections reported in Table \ref{['tab:totalcs']} including the error bands for the theoretical scale uncertainty. We show the results for the LHC 8 TeV, LHC 14 TeV and the Tevatron. The red bands refer to the NLO and nLO results while the green bands refer to the NNLO and nNLO results. The nNLO cross sections are matched with fixed-order NLO calculations.
• Figure 2: Invariant mass of reconstructed top-pair system (left) and transverse momentum of reconstructed top quark (right) for LHC8. Results without (with) analysis cuts shown as solid (dashed) lines. Production corrections only.
• Figure 3: Invariant mass of reconstructed top-pair system (left) and transverse momentum of reconstructed top quark (right) for $gg$ partonic channel at LHC8, without cuts (upper bands) and with analysis cuts (lower bands). Production corrections only.
• Figure 4: $M(W^+,W^-,J_b,J_{\bar{b}})$ (left) and $p_T(W^+,J_b)$ (right) distributions for LHC, with analysis cuts. The NLO uncertainty band is shown in all plots in red. The green bands are the nLO predictions, with PIM predictions shown in the top two plots whilst those of 1PI shown in the bottom two.
• Figure 5: Invariant mass of reconstructed top-pair system (left) and transverse momentum of reconstructed top quark (right) LHC8 with analysis cuts.