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Gluon Wigner distributions with transverse polarization at non-zero skewness

Sujit Jana, Kenil Solanki, Vikash Kumar Ojha

TL;DR

This work addresses the three-dimensional imaging of gluons at non-zero skewness by computing gluon Wigner distributions within a dressed quark model using two-particle light-front wavefunctions. It derives analytic expressions for the boost-invariant $\sigma$-space distributions under transverse polarization configurations, and confirms consistency with the zero-skewness limit. A key finding is the emergence of diffraction-like oscillations in $\sigma$-space that persist across gluon and target polarization choices and exhibit explicit dependence on the momentum transfer $-t$. These results advance the GTMD/Wigner framework for gluons and provide groundwork for phenomenology related to gluon spin–orbital correlations in upcoming EIC-era measurements.

Abstract

We investigate the gluon Wigner distributions at non-zero skewness using light-front wave functions (LFWFs) in the dressed quark model, where the target state is a quark dressed with a gluon in the leading-order Fock space expansion. Our analysis focuses on the configurations in which the gluon, the target, or both are transversely polarized. We derive analytical expressions for the Wigner distributions in the boost-invariant longitudinal space ($σ$) for transversely polarized configurations and observe a diffraction-like oscillatory pattern in $σ$-space, analogous to that reported earlier for unpolarized and longitudinally polarized gluons.

Gluon Wigner distributions with transverse polarization at non-zero skewness

TL;DR

This work addresses the three-dimensional imaging of gluons at non-zero skewness by computing gluon Wigner distributions within a dressed quark model using two-particle light-front wavefunctions. It derives analytic expressions for the boost-invariant -space distributions under transverse polarization configurations, and confirms consistency with the zero-skewness limit. A key finding is the emergence of diffraction-like oscillations in -space that persist across gluon and target polarization choices and exhibit explicit dependence on the momentum transfer . These results advance the GTMD/Wigner framework for gluons and provide groundwork for phenomenology related to gluon spin–orbital correlations in upcoming EIC-era measurements.

Abstract

We investigate the gluon Wigner distributions at non-zero skewness using light-front wave functions (LFWFs) in the dressed quark model, where the target state is a quark dressed with a gluon in the leading-order Fock space expansion. Our analysis focuses on the configurations in which the gluon, the target, or both are transversely polarized. We derive analytical expressions for the Wigner distributions in the boost-invariant longitudinal space () for transversely polarized configurations and observe a diffraction-like oscillatory pattern in -space, analogous to that reported earlier for unpolarized and longitudinally polarized gluons.

Paper Structure

This paper contains 6 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dressed Quark Model and Kinematics
  3. Gluon Wigner distribution at non-zero skewness
  4. Transverse Polarization Case
  5. Numerical Analysis and Discussion
  6. Conclusion

Figures (2)

  • Figure 1: The first moment of the gluon Wigner distribution $\rho^g_{UU}$ for various values of $-t$, corresponding to the unpolarized gluon in an unpolarized target.
  • Figure 2: The first moment of the gluon Wigner distribution for a) transversely polarized gluon in unplolarized target $\rho^{gR}_{UT}$ b) transversely polarized gluon in longitudinally polarized target $\rho^{gR}_{LT}$ c) $\rho^{g(R)x}_{TT}$ both the gluon and the target are transversely polarized d) $\rho^{gx}_{TL}$ longitudinally polarized gluon and transversely polarized target