NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction

Abstract: We compute the next-to-next-to-leading order QCD correction to the total inclusive top pair production cross-section in the reaction qg \to t\bar t + X. We find moderate O(1%) correction to central values at both Tevatron and LHC. The scale variation of the cross-section remains unchanged at the Tevatron and is significantly reduced at the LHC. We find that recently introduced approximation based on the high-energy limit of the top pair cross-section significantly deviates from the exact result. The results derived in the present work are included in version 1.4 of the program Top++. Work towards computing the reaction gg\to t\bar t+X is ongoing.

• The paper presents a detailed NNLO QCD computation for the quark-gluon channel, showing a moderate O(1%) effect on top pair production rates.
• It employs comprehensive numerical analysis and precise fits to capture cross-section behavior across Tevatron and LHC energy regimes.
• The study demonstrates a notable reduction in scale dependence at the LHC while challenging prior high-energy approximations, enhancing theoretical precision.

NNLO Corrections to Top Pair Production at Hadron Colliders: The Quark-Gluon Reaction

The paper by Czakon and Mitov provides a detailed computation of the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) corrections to the total inclusive top quark pair production cross-section in the quark-gluon ($qg$) channel at hadron colliders. This work addresses a crucial part of the complete NNLO framework for top pair production, which is a significant aspect of high-precision predictions necessary for both Tevatron and Large Hadron Collider (LHC) analyses.

Overview and Motivation

The study of top quark pair production has gained substantial attention with the progression seen at the LHC, notably in precision measurements of the top quark production cross-section and the strong coupling constant. As experimental observations reach unprecedented precision, the need for equally precise theoretical predictions becomes paramount. The integral link between Higgs physics and top quark measurements further accentuates the importance of achieving theoretical accuracy in top quark pair production processes.

While next-to-leading order (NLO) predictions have been extensively used and improved through techniques like threshold resummation, these approaches alone, based predominantly on next-to-next-to-leading logarithmic (NNLL) soft gluon resummation, could only marginally enhance the accuracy over NLO results. This limitation originates from numerically significant subleading effects in the soft gluon limit that NNLL resummation does not account for comprehensively.

Contribution of the Paper

This paper focuses on advancing beyond the NLO by computing the NNLO QCD correction for the $qg \to t\bar{t} + X$ channel. The computation features a thorough numerical analysis over the relevant range, providing fits that capture the behavior of the cross-section with high precision. The study indicates that the NNLO correction contributes a moderate $\mathcal{O}(1\%)$ amendment to the central cross-section value at both Tevatron and LHC energies.

Importantly, the scale variation at the Tevatron remains largely unaffected by the NNLO correction, whereas at the LHC, a notable reduction in scale dependence is achieved, enhancing the predictive power of the theoretical model.

Numerical Insights

The research reveals that the NNLO correction's influence on the quark-gluon initiated channel is substantial, particularly at higher energies like those encountered at the LHC. Table data and figures corroborate the hypothesis that existing high-energy approximations underestimate the impact of NNLO corrections, emphasizing discrepancies in the predicted versus exact effective cross-sections.

Theoretical and Practical Implications

From a theoretical perspective, this work underlines the significance of considering complete NNLO calculations and the insufficiency of relying solely on approximations derived from high-energy limits. The findings challenge the applicability of certain previously employed approximations, highlighting the importance of accurate, comprehensive computations.

On a practical level, the enhancements in prediction accuracy translate to improved consistency with existing experimental results, supporting more precise determinations of important parameters like the top quark mass and the strong coupling constant. Moreover, this increase in precision is crucial for studying phenomena that depend on intricate interference effects, such as the forward-backward asymmetry observed at the Tevatron.

Future Directions

The outcomes of this paper set a clear direction for subsequent research, particularly the necessity of incorporating NNLO corrections for remaining partonic contributions, such as $gg \to t\bar{t} + X$. The achievement of full NNLO precision across all partonic channels will substantially elevate the reliability of theoretical predictions related to top quark processes at current and future collider experiments.

In summary, Czakon and Mitov have contributed a significant piece of the puzzle towards complete NNLO coverage of top pair production, offering enhanced theoretical tools to meet the precision demanded by modern experimental capabilities. This work not only narrows the gap between theory and experiment but also ignites further development in theoretical methods and computational techniques within high-energy physics.