Gluon Generalized TMDs and Wigner Distributions in boost invariant longitudinal space

TL;DR

This paper introduces gluon generalized TMDs and Wigner distributions in boost-invariant longitudinal space for non-zero skewness, using a dressed quark model to explore polarization effects and Fourier transformations.

Contribution

It derives the first gluon Wigner distributions with non-zero skewness in a dressed quark model, expanding the understanding of gluon and quark polarization effects.

Findings

Derived gluon Wigner distributions for the first time with non-zero skewness.

Analyzed polarization contributions in the dressed quark model.

Established Fourier transform relations for generalized TMDs.

Abstract

We present the gluon generalized TMDs for non-zero skewness and Wigner distributions in the boost invariant longitudinal space. The boost-invariant longitudinal space is defined as $\sigma=\frac{1}{2}b^-\Delta^+$ and is conjugate to the skewness variable $\xi$. We use the dressed quark model, where a high-energetic quark is dressed by a gluon. This two-particle system has the advantage of addressing both the gluon and the quark sectors. The different contributions in Wigner distributions coming from different polarization of gluon and the dressed quark system are investigated. The Wigner distributions are obtained by taking the Fourier transformation of generalized TMDs, which we derive for the first time for non-zero skewness in dressed quark model.