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Investigating the origins of transverse spin asymmetries at RHIC

Daniel Boer

TL;DR

The paper investigates the origins of transverse spin asymmetries in hadron-hadron collisions, proposing a chiral-odd T-odd distribution with intrinsic transverse momentum (h1^⊥) as a mechanism that links quark transverse spin and momentum inside an unpolarized hadron. It argues that conventional perturbative and higher-twist explanations are insufficient and develops a TMD framework incorporating f1^⊥ and h1^⊥ to describe both polarized and unpolarized Drell-Yan processes, including the cos 2φ modulation. Using NA10 data, it constructs a crude h1^⊥ model and shows how such a function could relate unpolarized azimuthal asymmetries to polarized observables, offering a path to access the transversity distribution h1 at RHIC. The work also discusses the theoretical challenges of time-reversal constraints, factorization, and universality, and outlines experimental tests at RHIC to validate the proposed mechanism and extract h1.

Abstract

We discuss possible origins of transverse spin asymmetries in hadron-hadron collisions and propose an explanation in terms of a chiral-odd T-odd distribution function with intrinsic transverse momentum dependence, which would signal a correlation between the transverse spin and the transverse momentum of quarks inside an unpolarized hadron. We will argue that despite its conceptual problems, it can account for single spin asymmetries, for example in p + p(transversely polarized) -> pion + X, and at the same time for the large cos(2 phi) asymmetry in the unpolarized Drell-Yan cross section, which still lacks understanding. We use the latter asymmetry to arrive at a crude model for this function and show explicitly how it relates unpolarized and polarized observables in the Drell-Yan process, as could be measured with the proton-proton collisions at RHIC. Moreover, it would provide an alternative method of accessing the transversity distribution function h_1. For future reference we also list the complete set of azimuthal asymmetries in the unpolarized and polarized Drell-Yan process at leading order involving T-odd distribution functions with intrinsic transverse momentum dependence.

Investigating the origins of transverse spin asymmetries at RHIC

TL;DR

The paper investigates the origins of transverse spin asymmetries in hadron-hadron collisions, proposing a chiral-odd T-odd distribution with intrinsic transverse momentum (h1^⊥) as a mechanism that links quark transverse spin and momentum inside an unpolarized hadron. It argues that conventional perturbative and higher-twist explanations are insufficient and develops a TMD framework incorporating f1^⊥ and h1^⊥ to describe both polarized and unpolarized Drell-Yan processes, including the cos 2φ modulation. Using NA10 data, it constructs a crude h1^⊥ model and shows how such a function could relate unpolarized azimuthal asymmetries to polarized observables, offering a path to access the transversity distribution h1 at RHIC. The work also discusses the theoretical challenges of time-reversal constraints, factorization, and universality, and outlines experimental tests at RHIC to validate the proposed mechanism and extract h1.

Abstract

We discuss possible origins of transverse spin asymmetries in hadron-hadron collisions and propose an explanation in terms of a chiral-odd T-odd distribution function with intrinsic transverse momentum dependence, which would signal a correlation between the transverse spin and the transverse momentum of quarks inside an unpolarized hadron. We will argue that despite its conceptual problems, it can account for single spin asymmetries, for example in p + p(transversely polarized) -> pion + X, and at the same time for the large cos(2 phi) asymmetry in the unpolarized Drell-Yan cross section, which still lacks understanding. We use the latter asymmetry to arrive at a crude model for this function and show explicitly how it relates unpolarized and polarized observables in the Drell-Yan process, as could be measured with the proton-proton collisions at RHIC. Moreover, it would provide an alternative method of accessing the transversity distribution function h_1. For future reference we also list the complete set of azimuthal asymmetries in the unpolarized and polarized Drell-Yan process at leading order involving T-odd distribution functions with intrinsic transverse momentum dependence.

Paper Structure

This paper contains 11 sections, 35 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Origins of transverse spin asymmetries
  3. The polarized Drell-Yan process
  4. Pion production in $p \, p^{\uparrow}$ scattering
  5. The unpolarized Drell-Yan process
  6. Transverse momentum dependent distribution functions
  7. Unpolarized and single spin dependent cross sections
  8. Quark spin correlations
  9. Implications for RHIC
  10. Discussion
  11. Conclusions

Figures (4)

  • Figure 1: The leading order contribution to the Drell-Yan process
  • Figure 2: A contribution to the process $p \, p^{\uparrow} \rightarrow \pi \, X$
  • Figure 3: Kinematics of the Drell-Yan process in the lepton center of mass frame.
  • Figure 4: Data from NA10 at 194 GeV and fit (using Eq. (\ref{['kappa2']})) to $\nu=2\kappa$ as a function of the transverse momentum $Q_T$ of the lepton pair. The fitted parameters are $M_C=2.3 \pm 0.5 \, \text{GeV}$ and $16 \, \kappa_1 = 7 \pm 2$.