Scheme dependence and Transverse Momentum Distribution interpretation of Collins-Soper-Sterman resummation

TL;DR

This paper explores the scheme dependence in the CSS resummation formalism for TMDs, demonstrating that different schemes yield consistent non-perturbative form factors in Drell-Yan processes.

Contribution

It clarifies the scheme dependence of TMDs using a universal C-coefficient and shows the consistency of non-perturbative factors across schemes in Drell-Yan processes.

Findings

Different TMD schemes produce consistent non-perturbative form factors.

The scheme dependence can be attributed to a perturbative calculable function.

Universal C-coefficient function links various TMD schemes.

Abstract

Following an earlier derivation by Catani-de Florian-Grazzini (2000) on the scheme dependence in the Collins-Soper-Sterman (CSS) resummation formalism in hard scattering processes, we investigate the scheme dependence of the Transverse Momentum Distributions (TMDs) and their applications. By adopting a universal $C$-coefficient function associated with the integrated parton distributions, the difference between various TMD schemes can be attributed to a perturbative calculable function depending on the hard momentum scale. We further apply several TMD schemes to the Drell-Yan process of lepton pair production in hadronic collisions, and find that the constrained non-perturbative form factors in different schemes are remarkably consistent with each other and with that of the standard CSS formalism.