Vector boson production in joint resummation

TL;DR

This paper advances the joint resummation formalism to NNLL accuracy for vector boson production, comparing it with standard methods and analyzing its benefits and limitations across different collider scenarios.

Contribution

It extends joint resummation to NNLL accuracy and evaluates its performance for vector boson production at colliders.

Findings

Joint resummation provides moderate corrections over $Q_T$ resummation.

It reduces scale dependence of the results.

Limitations include increased power correction dependence for processes away from threshold.

Abstract

We study the transverse momentum ($Q_T$) distribution of an electro-weak vector boson produced via the Drell-Yan mechanism, in the context of joint resummation. This formalism allows for the simultaneous resummation of logarithmic contributions that are enhanced at small $Q_T$ and at partonic threshold. We extend joint resummation to next-to-next-to leading logarithmic accuracy and we present resummed and matched results for three different phenomenological setups. In particular, we study the production of a $Z$ boson at the Tevatron and at the Large Hadron Collider (LHC), as well as the production of a heavier $Z^\prime$ at the LHC. We compare our findings to standard $Q_T$ resummation, as well as to fixed-order perturbation theory. We find that joint resummation provides a moderate (but not flat) correction with respect to $Q_T$ resummation and it leads to a reduction of the scale dependence of the results. However, our study also shows some limitations of this formalism. While the use of joint resummation for $Z$ production at the Tevatron and $Z^\prime$ production at the LHC appears to be justified, our implementation suffers from a stronger dependence on power corrections for processes which are further away from threshold, such as $Z$ production at the LHC, for which we cannot claim an improvement over standard $Q_T$ resummation.