NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

Abstract: This is a second paper in our ongoing calculation of the next-to-next-to-leading order (NNLO) QCD correction to the total inclusive top-pair production cross-section at hadron colliders. In this paper we calculate the reaction $q\bar q \to t\bar t + q\bar q$ which was not considered in our previous work on $q\bar q \to t\bar t +X$ due to its phenomenologically negligible size. We also calculate all remaining fermion-pair-initiated partonic channels $qq', q\bar q'$ and $qq$ that contribute to top-pair production starting from NNLO. The contributions of these reactions to the total cross-section for top-pair production at the Tevatron and LHC are small, at the permil level. The most interesting feature of these reactions is their characteristic logarithmic rise in the high energy limit. We compute the constant term in the leading power behavior in this limit, and achieve precision that is an order of magnitude better than the precision of a recent theoretical prediction for this constant. All four partonic reactions computed in this paper are included in our numerical program Top++. The calculation of the NNLO corrections to the two remaining partonic reactions, $qg\to t\bar t+X$ and $gg\to t\bar t+X$, is ongoing.

• The paper rigorously computes NNLO QCD corrections to all-fermionic scattering channels in top-pair production.
• It details the calculation of six-fermion final states, showing sub-permil corrections at both Tevatron and LHC.
• The refined results enhance theoretical QCD predictions and provide a precise benchmark for future collider experiments.

Overview of NNLO Corrections to Top-Pair Production: All-Fermionic Scattering Channels

This paper provides a rigorous computation of Next-to-Next-to-Leading Order (NNLO) QCD corrections relevant to top-pair production at hadron colliders, specifically addressing the all-fermionic scattering channels previously deemed negligible. This work is an extension of prior analyses focusing on NNLO corrections, which primarily addressed dominant channels such as $q\bar q \to t\bar t + X$. In this contribution by Czakon and Mitov, reactions like $q\bar q \to t\bar t + q\bar q$ as well as $qq',~ q\bar q'$, and $qq$ channels are examined in detail.

Key Technical Contributions

• The analysis includes computation of contributions from partonic channels, where the contributions to the top-pair production cross-section from exclusive six-fermion final states are explicitly calculated and subtracted.
• The study finds these corrections contribute at the sub-permil level to the total cross-section for top-pair production at both the Tevatron and LHC, aligning with predictions that their contribution would be small.
• A notable feature of these processes is their logarithmic growth in the high-energy limit, characterized by a computed constant term with improved precision over prior theoretical models.
• The Closed expression for these contributions is made available through the numerical tool {\tt Top++}, enhancing computational precision.

Theoretical and Practical Implications

From a theoretical perspective, the findings demonstrate the importance of including even phenomenologically small channels at NNLO for improving precision. Numerically, these corrections, though minor, refine theoretical predictions and provide a more precise baseline for comparisons with experimental results. This completeness is crucial for validating QCD predictions as experiments at the LHC push to higher precision and energies, potentially probing the corrections highlighted here. Additionally, these computations could become relevant in scenarios involving lighter quark pairs or future collider energies where partonic luminosities emphasize higher $\beta$ values.

Future Scope and Developments

While this paper explores all-fermionic channels, the authors indicate ongoing work on the remaining partonic reactions $qg\to t\bar t+X$ and $gg\to t\bar t+X$. Completion of these calculations will culminate in a comprehensive NNLO theoretical foundation for top-quark pair production cross-sections at hadron colliders. Such work is vital as it provides a robust theoretical framework against which experimental findings at evolving collider energies can be benchmarked.

Overall, this paper underlines a key principle in perturbative QCD studies: smaller corrections must be evaluated with precision for a holistic understanding of hadron collider physics. The intricate subtleties associated with higher-order corrections demand attention, especially as experimental data continues to improve in precision. The work is a step forward in a sequence of calculations that aim to entirely encapsulate NNLO contributions, thereby fostering a deeper understanding of top-quark dynamics in QCD.