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

Alexei Prokudin, Peng Sun, Feng Yuan

TL;DR

The paper analyzes scheme dependence in Collins-Soper-Sterman resummation within the TMD framework, showing that a universal C-coefficient makes different TMD schemes equivalent up to perturbative corrections. By applying three schemes to Drell-Yan processes and using the b*-prescription with SIYY non-perturbative factors, it demonstrates consistent non-perturbative extractions and phenomenology across schemes. The results support a unified, TMD-based interpretation of CSS resummation and provide a pathway to compare schemes in both unpolarized and future polarized contexts. This work clarifies how scheme choices affect hard factors and non-perturbative inputs, facilitating cross-process TMD analyses and global fits.

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.

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

TL;DR

The paper analyzes scheme dependence in Collins-Soper-Sterman resummation within the TMD framework, showing that a universal C-coefficient makes different TMD schemes equivalent up to perturbative corrections. By applying three schemes to Drell-Yan processes and using the b*-prescription with SIYY non-perturbative factors, it demonstrates consistent non-perturbative extractions and phenomenology across schemes. The results support a unified, TMD-based interpretation of CSS resummation and provide a pathway to compare schemes in both unpolarized and future polarized contexts. This work clarifies how scheme choices affect hard factors and non-perturbative inputs, facilitating cross-process TMD analyses and global fits.

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 -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.

Paper Structure

This paper contains 5 sections, 19 equations, 2 figures.

Table of Contents

  1. Introduction
  2. TMD Schemes
  3. Non-perturbative Form Factors and TMD Interpretation
  4. Conclusion
  5. Acknowledgments

Figures (2)

  • Figure 1: TMD up-quark distributions $\tilde{f}_u^{(sub.)}(x=0.1,b)$ as functions of $b$ at different scale $Q^2 = 2.4$, $10$, $90$ (GeV$^2$) for three different schemes, from the top to the bottom: JCC Collins:2011zzd, Lattice Ji:2014hxa, JMY Ji:2004wuJi:2004xq ($\ln\rho=1$).
  • Figure 2: TMD up-quark distributions ${f}_u^{(sub.)}(x=0.1,k_\perp)$ as functions of the transverse momentum $k_\perp$ (GeV) at three different scales $Q^2 = 2.4$, $10$, $90$ (GeV$^2$) for three different schemes, from the top to the bottom: JCC Collins:2011zzd, Lattice Ji:2014hxa, JMY Ji:2004wuJi:2004xq ($\ln\rho=1$).