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Universality of T-odd effects in single spin and azimuthal asymmetries

Daniel Boer, P. J. Mulders, F. Pijlman

TL;DR

This work develops a fully color-gauge-invariant framework for transverse momentum dependent distribution and fragmentation functions across SIDIS, Drell–Yan, and e+e− annihilation. By organizing the leading and first subleading 1/Q terms via gauge links and quark–gluon correlators, it clarifies how TMD observables such as the Sivers and Collins effects arise and how they transform between processes. A key result is the direct link between the Sivers effect and the Qiu–Sterman gluonic-pole mechanism, which also explains sign changes between SIDIS and DY, while fragmentation-related T-odd effects involve both gluonic poles and final-state interactions, complicating universality. The findings have important implications for interpreting azimuthal asymmetries and for designing experimental tests of TMD factorization and universality in hadronic physics.

Abstract

We analyze the transverse momentum dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular 1-particle inclusive leptoproduction, the Drell-Yan process and two-particle inclusive hadron production in electron-positron annihilation. As is well-known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color gauge invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu-Sterman mechanism. We also study fragmentation functions, where the process dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

Universality of T-odd effects in single spin and azimuthal asymmetries

TL;DR

This work develops a fully color-gauge-invariant framework for transverse momentum dependent distribution and fragmentation functions across SIDIS, Drell–Yan, and e+e− annihilation. By organizing the leading and first subleading 1/Q terms via gauge links and quark–gluon correlators, it clarifies how TMD observables such as the Sivers and Collins effects arise and how they transform between processes. A key result is the direct link between the Sivers effect and the Qiu–Sterman gluonic-pole mechanism, which also explains sign changes between SIDIS and DY, while fragmentation-related T-odd effects involve both gluonic poles and final-state interactions, complicating universality. The findings have important implications for interpreting azimuthal asymmetries and for designing experimental tests of TMD factorization and universality in hadronic physics.

Abstract

We analyze the transverse momentum dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular 1-particle inclusive leptoproduction, the Drell-Yan process and two-particle inclusive hadron production in electron-positron annihilation. As is well-known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color gauge invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu-Sterman mechanism. We also study fragmentation functions, where the process dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

Paper Structure

This paper contains 24 sections, 108 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Hadron tensor and correlators in SIDIS
  3. SIDIS and DIS cross sections
  4. Integrated SIDIS cross section at leading order
  5. Azimuthal asymmetries in SIDIS at leading order
  6. Integrated SIDIS cross section at ${\cal O}(1/Q)$
  7. Integrated DIS cross section at ${\cal O}(1/Q)$
  8. Azimuthal asymmetries in JET SIDIS at leading order
  9. Other subleading cross sections
  10. The Drell-Yan cross sections
  11. Integrated DY cross section at leading order
  12. Azimuthal asymmetries in DY at leading order
  13. Integrated DY cross section at ${\cal O}(1/Q)$
  14. Back-to-back jet production in electron-positron annihilation
  15. Integrated annihilation cross section at leading order
  16. ...and 9 more sections

Figures (8)

  • Figure 1: Diagrams contributing in inclusive deep inelastic scattering
  • Figure 2: Diagrams contributing in 1-particle inclusive deep inelastic scattering
  • Figure 3: Soft parts representing the quark-quark and quark-quark-gluon matrix elements used in Eqs. \ref{['soft1']} - \ref{['soft4']}
  • Figure 4: Link structure for $\Phi^{[+]}(x,p_{ T})$ (a and b) and for $\Phi(x)$ (c) after integration over transverse momenta.
  • Figure 5: Link structure for $\Phi(x,p_{ T})$ (a and b) and $\Delta(z,k_{ T})$ (c and d).
  • ...and 3 more figures