Borel resummation of transverse momentum distributions

TL;DR

This paper introduces a Borel resummation method for transverse momentum distributions in processes like Drell-Yan, addressing divergence issues in the perturbative series and providing a stable, ambiguity-aware resummation prescription.

Contribution

It develops a novel Borel resummation approach for transverse momentum distributions, overcoming divergence problems and improving stability over existing methods.

Findings

Resummation series are divergent and require Borel resummation.

The new method removes numerical instabilities in resummation.

Results are consistent with alternative prescriptions and include ambiguity analysis.

Abstract

We present a new prescription for the resummation of contributions due to soft gluon emission to the trasverse momentum distribution of processes such as Drell-Yan production in hadronic collisions. We show that familiar difficulties in obtaining resummed results as a function of transverse momentum starting from impact-parameter space resummation are related to the divergence of the perturbative expansion of the momentum-space result. We construct a resummed expression by Borel resummation of this divergent series, removing the divergence in the Borel inversion through the inclusion of a suitable higher twist term. The ensuing resummation prescription is free of numerical instabilities, is stable upon the inclusion of subleading terms, and the original divergent perturbative series is asymptotic to it. We compare our results to those obtained using alternative prescriptions, and discuss the ambiguities related to the resummation procedure.