Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation (1111.5869v2)

Abstract: Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total $t\bar t$ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framework of Mellin $N$-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to the NLL approximation, and a small shift in the central value, consistent with the quoted uncertainties. These numerical predictions agree with the currently available measurements from the Tevatron and LHC and have uncertainty of similar size. We conclude that significant improvements in the $t\bar t$ cross-sections can potentially be expected only upon inclusion of the complete NNLO corrections.

• The paper demonstrates that NNLL soft-gluon resummation significantly reduces perturbative uncertainties in top-pair production cross-sections compared to lower order methods.
• It employs Mellin-N space resummation techniques to precisely incorporate soft-gluon corrections, yielding predictions that align well with Tevatron and LHC data.
• The refined framework sets the stage for future NNLO calculations and enhances high-precision tests of the Standard Model in collider experiments.

Soft-Gluon Resummation in Top-Pair Production at Hadron Colliders

The paper "Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation" provides a meticulous analysis of the total top-pair ($t\bar{t}$) production cross-section with an emphasis on soft-gluon resummation up to next-to-next-to-leading logarithmic (NNLL) accuracy. This work builds upon established methods in perturbative QCD, particularly within the framework of Mellin-$N$ space resummation—an approach that has proven effective for studying processes sensitive to soft-gluon emissions near the production threshold.

Overview of Methods and Results

The authors have incorporated recent theoretical advancements to address soft-gluon corrections meticulously. They conducted the soft-gluon resummation at NNLL, an endeavor that hones in on reducing the perturbative uncertainty typical at lower orders like NLL (next-to-leading logarithmic) and NLO (next-to-leading order). The intrinsic stability of such predictions is particularly remarkable when considering the precision required to compare theoretical predictions accurately against experimental data from facilities like the Tevatron and the LHC.

The precise inclusion and treatment of systematic uncertainties, such as the variation of renormalization and factorization scales, the significance of unknown power-suppressed effects, and the missing two-loop corrections, are key highlights of this paper. Intriguingly, the NNLL correction introduces only minor adjustments to central values for the total cross-section with leaps in predictive stability notwithstanding the small quantum of change.

Numerical Implications

The authors report a nominal decrease in perturbative uncertainty when transitioning from NLL to NNLL resummation. Numerical results juxtaposing the theoretical predictions with experimental observations from current collider data indicate consistent findings, reinforcing the accuracy of the NNLL framework. Importantly, they suggest significant improvement can only be realized with the computation of complete next-to-next-to-leading order (NNLO) corrections.

Theoretical and Practical Implications

This paper bears substantial implications both practically and theoretically. By refining predictive uncertainties, it enhances high-precision tests of the Standard Model under the collider-based tests, offering a more reliable comparison with experimental outcomes. This precision is crucial as collider experiments venture into regimes of higher luminosity where statistical errors are minimal relative to systematic and theoretical uncertainties.

Theoretically, the paper sets a foundation for future explorations into even higher-order corrections, potentially guiding refinements in parton distribution functions (PDFs) and in the understanding of higher-mass states. Moreover, the precision at high-energy scales might serve as a litmus test for emerging physics beyond the Standard Model, wherein accurate $t\bar{t}$ cross-sections could manifest as early indicators of new particles or forces.

Future Directions

While this paper paves the way for refined QCD predictions regarding $t\bar{t}$ production, future improvements hinge on a comprehensive calculation of NNLO contributions. Such endeavors may leverage contemporary computational advancements and collaborative efforts within the theoretical physics community. Furthermore, this research could prompt similar analyses in other processes where soft-gluon effects play a pivotal role, enhancing the broader landscape of collider phenomenology.

In conclusion, this rigorous exposition on NNLL resummation elevates the precision in top-quark physics, aligning theoretical predictions closely with empirical data. The nuanced understanding yielded herein may well serve as a cornerstone for ensuing calculations in perturbative QCD and reinforce the predictive framework upon which particle physics heavily relies.