Hadronic top-quark pair production with NNLL threshold resummation (1109.1536v1)

Abstract: We compute the total top-quark pair production cross section at the Tevatron and LHC based on approximate NNLO results, and on the summation of threshold logarithms and Coulomb enhancements to all orders with next-to-next-to-leading logarithmic (NNLL) accuracy, including bound-state effects. We find \sigma_{t\bar t} = 7.22^{+0.31+0.71}_{-0.47-0.55} pb at Tevatron and \sigma_{t\bar t} = 162.6^{+7.4+15.4}_{-7.6-14.7} pb at LHC with 7 TeV c.o.m. energy, for m_t=173.3 GeV. The implementation of joint soft and Coulomb resummation, its ambiguities, and the present theoretical uncertainty are discussed in detail. We further obtain new approximate results at N3LO.

• The paper presents a detailed NNLL resummation method that combines soft-gluon and Coulomb corrections to enhance t-tbar cross section predictions.
• It achieves precise cross section estimates at the Tevatron and LHC, significantly reducing theoretical uncertainties.
• The approach sets a benchmark for future top-quark studies by effectively addressing scale ambiguities and calibrating associated errors.

Resummation of Threshold Logarithms and Coulomb Corrections in $t\bar{t}$ Production

The computation of the total $t\bar{t}$ production cross section is crucial for understanding the properties of the top quark, the heaviest standard model fermion, at hadron colliders like the Tevatron and the LHC. The precision of these measurements, and their corresponding theoretical calculations, can provide insight into the nature of the top quark, as well as potential new physics beyond the Standard Model. This paper focuses on improving the theoretical calculation of the $t\bar{t}$ cross section by incorporating next-to-next-to-leading logarithmic (NNLL) resummation of threshold logarithms and Coulomb enhancements.

The paper begins with a review of the current status of $t\bar{t}$ production calculations, emphasizing the need for precision beyond the next-to-leading order (NLO) accuracy due to the reduced experimental uncertainties in cross section measurements. Given the complex interplay of hard, soft, and Coulombic interactions in $t\bar{t}$ production, the resummation of large threshold logarithms and the inclusion of Coulomb corrections provide significant enhancements to existing higher-order QCD calculations.

The authors implement a combined approach utilizing the momentum-space resummation framework for soft-gluon and Coulomb-gluon effects. They derive the factorization formula for the partonic cross sections, focusing on the threshold region where the top quarks have a small relative velocity, $\beta$. In this domain, they include contributions from virtual Coulomb gluons and soft-gluon emissions, which manifest as significant corrections in the expansion.

To reach NNLL accuracy, the authors calculate the hard, soft, and Coulomb functions at the relevant matching scales and evolve them using renormalization group equations. This detailed resummation approach incorporates contributions from singular logarithms at the near-threshold limit and mixes both soft-gluon and Coulomb resummations, which had previously been studied separately.

Key numerical results presented include precise predictions for the $t\bar{t}$ cross section at the Tevatron and LHC for $m_t = 173.3$ GeV. The authors' meticulous estimation of uncertainties, accounting for both theoretical errors and PDF+α_s uncertainties, showcases their comprehensive treatment of the NNLL cross sections. For instance, the results for LHC with $\sqrt{s}=7$ TeV show a cross section of $$162.6^{+4.2}_{-1.9}{}^{+3.9}_{-5.6}{}^{+4.7}_{-4.7}{}^{+15.4}_{-14.7}$$ pb, indicating a thorough inclusion of errors.

The authors calibrate potential uncertainties arising from missing two-loop hard and soft function constants, handling kinematical ambiguities and offering two methods for the choice of the soft scale in NNLL resummation. They find the choice of the scale $\mu_s$ critical, affecting the convergence of the logarithmic series.

The implications of this work are far-reaching. The inclusion of detailed resummation not only improves the precision of theoretical predictions but also aids in extracting top-quark properties, such as mass, from experimental data with higher accuracy. Future studies might extend such resummations to other heavy-particle processes and explore further resummation effects beyond NNLL accuracy.

In conclusion, this paper advances the methodology for calculating $t\bar{t}$ production cross sections by exploiting joint soft and Coulomb resummation within the NNLL framework. The detailed treatment of theoretical uncertainties and the robust numerical results serve as a benchmark for ongoing and future top quark studies at hadron colliders.