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Chromodynamic Lensing and Transverse Single Spin Asymmetries

Matthias Burkardt

TL;DR

This work links axial asymmetries in impact-parameter dependent PDFs to transverse single-spin asymmetries through final- and initial-state interactions encoded by Wilson lines. By formulating the mean transverse momentum as a correlation between IPD PDFs and a lensing impulse, it provides a physically intuitive, semi-classical mechanism—chromodynamic lensing—for translating spatial spin structure into a pronounced $\sin\phi$ SSA. Using simple abelianized potential models, the authors show that the resulting mean $k_ op$ is typically $0.2$–$0.4$ GeV/$c$, suggesting a sizable, robust Sivers-type effect driven by FSI. The approach clarifies how Wilson-line phases contribute to large SSAs and offers a framework for connecting GPD-based transverse distortions to measurable momentum-space asymmetries, while acknowledging the simplifying assumptions and the need for more detailed dynamical treatments.

Abstract

We illustrate how an axial asymmetry in impact parameter dependent parton distributions can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. The single spin asymmetry arising from the asymmetry of the impact parameter dependent parton distributions is shown to exhibit a pure $\sin φ$ dependence.

Chromodynamic Lensing and Transverse Single Spin Asymmetries

TL;DR

This work links axial asymmetries in impact-parameter dependent PDFs to transverse single-spin asymmetries through final- and initial-state interactions encoded by Wilson lines. By formulating the mean transverse momentum as a correlation between IPD PDFs and a lensing impulse, it provides a physically intuitive, semi-classical mechanism—chromodynamic lensing—for translating spatial spin structure into a pronounced SSA. Using simple abelianized potential models, the authors show that the resulting mean is typically – GeV/, suggesting a sizable, robust Sivers-type effect driven by FSI. The approach clarifies how Wilson-line phases contribute to large SSAs and offers a framework for connecting GPD-based transverse distortions to measurable momentum-space asymmetries, while acknowledging the simplifying assumptions and the need for more detailed dynamical treatments.

Abstract

We illustrate how an axial asymmetry in impact parameter dependent parton distributions can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. The single spin asymmetry arising from the asymmetry of the impact parameter dependent parton distributions is shown to exhibit a pure dependence.

Paper Structure

This paper contains 6 sections, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Initial (final) state interactions and transverse spin asymmetries
  3. Simple Models for the Final State Interactions
  4. Angular and $x$ Dependence of the Asymmetry
  5. Summary
  6. Detailed Derivation

Figures (3)

  • Figure 1: "Lensing function" ${\bf I}_\perp$ for $|{\bf b}_\perp|<1\,fm$ in the three models (\ref{['eq:models']}) for the quark potential. The vector field represents the mean transverse momentum that the ejected quark acquires when it is knocked out at transverse position (relative to the center of momentum) ${\bf b}_\perp$.
  • Figure 2: Transverse momenta resulting from the three models (\ref{['eq:models']}) for the quark potential as a function of the impact parameter ${\bf b}_\perp$.
  • Figure 3: Distribution of $u$ and $d$ quarks in the $\perp$ plane ($x_{Bj}=0.3$ is fixed) for a nucleon that is polarized in the $x$ direction (\ref{['eq:qX']}) in the model from Ref. ijmpa (\ref{['eq:model']}).