Gluon Wigner distributions with transverse polarization at non-zero skewness

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 ($\sigma$) for transversely polarized configurations and observe a diffraction-like oscillatory pattern in $\sigma$-space, analogous to that reported earlier for unpolarized and longitudinally polarized gluons.