Threshold resummation of the rapidity distribution for Drell-Yan production at NNLO+NNLL

TL;DR

This paper improves the precision of Drell-Yan lepton pair production predictions at the LHC by incorporating threshold resummation at NNLL accuracy, enhancing the understanding of perturbative stability and uncertainties.

Contribution

The authors develop a formalism for threshold resummation in the rapidity distribution of Drell-Yan production at NNLL accuracy, providing more accurate predictions compared to previous fixed order calculations.

Findings

Resummed predictions are close to other approaches at NNLL level.

Resummation improves perturbative convergence despite unchanged scale dependence.

Uncertainties from parton distribution functions are quantified.

Abstract

We consider the production of pairs of lepton through the Drell-Yan process at the LHC and present the most accurate prediction on their rapidity distribution. While the fixed order prediction is already known to next-to-next-to-leading order in perturbative QCD, the resummed contribution coming from threshold region of phase space up to next-to-next-to-leading logarithmic (NNLL) accuracy has been computed in this article. The formalism developed in [1-3] has been used to resum large threshold logarithms in the two dimensional Mellin space to all orders in perturbation theory. We have done a detailed numerical comparison against other approaches that resum certain threshold logarithms in Mellin-Fourier space. Our predictions at NNLL level are close to theirs even though at leading logarithmic and next-to-leading logarithmic level we differ. We have also investigated the impact of these threshold logarithms on the stability of perturbation theory against factorisation and renormalisation scales. While the dependence on these scales does not get better with resummed results, the convergence of the perturbative series shows a better trend compared to the fixed order predictions. This is evident from the reduction in the K-factor for the resummed case compared to fixed order. We also present the uncertainties on the predictions resulting from parton distribution functions.