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Single spin asymmetries in hadron-hadron collisions

A. Bacchetta, C. J. Bomhof, P. J. Mulders, F. Pijlman

TL;DR

The paper develops a diagrammatic, LO framework to analyze weighted single-spin asymmetries in hadron-hadron collisions, incorporating intrinsic transverse momentum and gauge-link–induced T-odd effects. By decomposing correlators into gauge-link–dependent gluonic-pole components, it shows how Sivers- and Collins-type functions enter hadron-hadron, hadron-jet, and jet-jet processes via gluonic-pole cross sections, enabling a universal folding with hard parts that depend on the subprocess. It highlights process-dependent signs and combinations of T-odd fragmentation and distribution functions, discusses the potential universality of the Collins effect, and provides explicit expressions for several back-to-back final states. The findings clarify the role of gauge-links in TMD factorization for hadronic collisions and offer a practical framework for interpreting SSA measurements in upcoming experiments. The work also sets the stage for including gluon contributions and exploring subleading effects in future analyses.

Abstract

We study weighted azimuthal single spin asymmetries in hadron-hadron scattering using the diagrammatic approach at leading order and assuming factorization. The effects of the intrinsic transverse momenta of the partons are taken into account. We show that the way in which $T$-odd functions, such as the Sivers function, appear in these processes does not merely involve a sign flip when compared with semi-inclusive deep inelastic scattering, such as in the case of the Drell-Yan process. Expressions for the weighted scattering cross sections in terms of distribution and fragmentation functions folded with hard cross sections are obtained by introducing modified hard cross sections, referred to as gluonic pole cross sections.

Single spin asymmetries in hadron-hadron collisions

TL;DR

The paper develops a diagrammatic, LO framework to analyze weighted single-spin asymmetries in hadron-hadron collisions, incorporating intrinsic transverse momentum and gauge-link–induced T-odd effects. By decomposing correlators into gauge-link–dependent gluonic-pole components, it shows how Sivers- and Collins-type functions enter hadron-hadron, hadron-jet, and jet-jet processes via gluonic-pole cross sections, enabling a universal folding with hard parts that depend on the subprocess. It highlights process-dependent signs and combinations of T-odd fragmentation and distribution functions, discusses the potential universality of the Collins effect, and provides explicit expressions for several back-to-back final states. The findings clarify the role of gauge-links in TMD factorization for hadronic collisions and offer a practical framework for interpreting SSA measurements in upcoming experiments. The work also sets the stage for including gluon contributions and exploring subleading effects in future analyses.

Abstract

We study weighted azimuthal single spin asymmetries in hadron-hadron scattering using the diagrammatic approach at leading order and assuming factorization. The effects of the intrinsic transverse momenta of the partons are taken into account. We show that the way in which -odd functions, such as the Sivers function, appear in these processes does not merely involve a sign flip when compared with semi-inclusive deep inelastic scattering, such as in the case of the Drell-Yan process. Expressions for the weighted scattering cross sections in terms of distribution and fragmentation functions folded with hard cross sections are obtained by introducing modified hard cross sections, referred to as gluonic pole cross sections.

Paper Structure

This paper contains 13 sections, 89 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. kinematics
  3. cross sections
  4. Single-spin asymmetries in inclusive hadron-hadron scattering
  5. Hadron-hadron production in $p^\uparrow p$ scattering: $p^\uparrow{+}p\rightarrow\pi{+}\pi{+}X$
  6. Hadron-jet production in $p^\uparrow p$ scattering: $p^\uparrow{+}p\rightarrow\pi{+}\text{Jet}{+}X$
  7. Jet-jet production in $p^\uparrow p$ scattering: $p^\uparrow{+}p\rightarrow\text{Jet}{+}\text{Jet}{+}X$
  8. Summary and conclusions
  9. quark correlators and gauge-links
  10. consequences of gauge-links for distribution functions
  11. consequences of gauge-links for fragmentation functions
  12. Results in the diagrammatic approach
  13. Partonic cross sections

Figures (4)

  • Figure 1: The leading order contribution to the cross section of $H_1{+}H_2\rightarrow h_1{+}h_2{+}X$.
  • Figure 2: Plane perpendicular to the incoming hadronic momenta.
  • Figure 3: Hard scattering amplitudes for quark-quark scattering: (a) $t$-diagram, (b) $u$-diagram; quark-antiquark scattering: (c) $s$-diagram, (d) $t$-diagram.
  • Figure 4: Gauge-links entering in the correlator for the lower-left incoming quark for a hard two-fermion scattering process without exchange of charge. Top: quark-quark scattering; bottom: quark-antiquark scattering.