Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Transverse momentum dependence in gluon distribution and fragmentation functions

P. J. Mulders, J. Rodrigues

TL;DR

The paper develops a comprehensive framework for twist-two, transverse-momentum dependent gluon distributions and fragmentation functions for spin-1/2 hadrons, clarifying their gauge-invariant definitions via gluon-gluon correlators and gauge links. It derives the Lorentz structures, performs a twist expansion, connects twist-two functions to parton-density interpretations, and extends the formalism to fragmentation, including T-odd components. Positivity and related bounds are established for both distributions and fragmentation functions, providing constraints for phenomenology. The results illuminate how gluon soft parts contribute to azimuthal asymmetries in processes with at least two hadrons and set the stage for quantitative estimates of single-spin effects in hadronic collisions.

Abstract

We investigate the twist two gluon distribution functions for spin 1/2 hadrons, emphasizing intrinsic transverse momentum of the gluons. These functions are relevant in leading order in the inverse hard scale in scattering processes such as inclusive leptoproduction or Drell-Yan scattering, or more general in hard processes in which at least two hadrons are involved. They show up in azimuthal asymmetries. For future estimates of such observables, we discuss specific bounds on these functions.

Transverse momentum dependence in gluon distribution and fragmentation functions

TL;DR

The paper develops a comprehensive framework for twist-two, transverse-momentum dependent gluon distributions and fragmentation functions for spin-1/2 hadrons, clarifying their gauge-invariant definitions via gluon-gluon correlators and gauge links. It derives the Lorentz structures, performs a twist expansion, connects twist-two functions to parton-density interpretations, and extends the formalism to fragmentation, including T-odd components. Positivity and related bounds are established for both distributions and fragmentation functions, providing constraints for phenomenology. The results illuminate how gluon soft parts contribute to azimuthal asymmetries in processes with at least two hadrons and set the stage for quantitative estimates of single-spin effects in hadronic collisions.

Abstract

We investigate the twist two gluon distribution functions for spin 1/2 hadrons, emphasizing intrinsic transverse momentum of the gluons. These functions are relevant in leading order in the inverse hard scale in scattering processes such as inclusive leptoproduction or Drell-Yan scattering, or more general in hard processes in which at least two hadrons are involved. They show up in azimuthal asymmetries. For future estimates of such observables, we discuss specific bounds on these functions.

Paper Structure

This paper contains 11 sections, 48 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Gluon Correlation Functions
  3. The Lorentz structure of the gluon correlator
  4. Twist expansion
  5. Sum rules
  6. Gauge Invariance
  7. The Twist Two Functions as densities
  8. Gluon Fragmentation Functions
  9. Bounds on the distribution and fragmentation functions
  10. Conclusions
  11. Gluon Distributions

Figures (4)

  • Figure 1: The gluon correlator
  • Figure 2: Some contributions to the fictitious highly virtual fermion-nucleon cross section
  • Figure 3: The gluon correlator
  • Figure 4: Gluon distribution and fragmentation functions contributing to the single spin asymmetry in $p^\uparrow p \rightarrow \pi X$ scattering cross section.