Soft gluon resummation of Drell-Yan rapidity distributions: theory and phenomenology

TL;DR

This paper critically examines the theoretical basis and phenomenological impact of soft gluon resummation on Drell-Yan rapidity distributions at colliders, providing tools and methods to assess and implement resummation effects.

Contribution

It introduces a fast, accurate method for resummation implementation and compares different prescriptions, highlighting ambiguities and their phenomenological significance.

Findings

Resummation is necessary near partonic threshold energies.

Resummation effects are comparable to NNLO corrections.

Substantial ambiguities can affect resummation results.

Abstract

We examine critically the theoretical underpinnings and phenomenological implications of soft gluon (threshold) resummation of rapidity distributions at a hadron collider, taking Drell-Yan production at the Tevatron and the LHC as a reference test case. First, we show that in perturbative QCD soft gluon resummation is necessary whenever the partonic (rather the hadronic) center-of-mass energy is close enough to threshold, and we provide tools to assess when resummation is relevant for a given process. Then, we compare different prescriptions for handling the divergent nature of the series of resummed perturbative corrections, specifically the minimal and Borel prescriptions. We assess the intrinsic ambiguities of resummed results, both due to the asymptotic nature of their perturbative expansion, and to the treatment of subleading terms. Turning to phenomenology, we introduce a fast and accurate method for the implementation of resummation with the minimal and Borel prescriptions using an expansion on a basis of Chebyshev polynomials. We then present results for W and Z production as well as both high- and low-mass dilepton pairs at the LHC, and show that soft gluon resummation effects are generally comparable in size to NNLO corrections, but sometimes affected by substantial ambiguities.