Quark generalized TMDs at skewness and Wigner Distribution in boost invariant longitudinal space

Abstract: The boost-invariant longitudinal space, defined by the parameter $\sigma=\frac{1}{2}b^-P^+$ can be studied from the Fourier transformation of distributions over the conjugate variable skewness $\xi$. We investigate quark Wigner distributions in the $\sigma$ space in dressed quark model and found diffraction patterns that are analogous to the single slit experiment of light in optics. The width of the central maxima varies with energy transfer to the system and essentially $\xi$ behaves like a slit-width. Qualitatively similar diffraction pattern is reported recently in other models. In this model, we compute all the leading twist GTMDs with non-zero skewness for quarks which provides Wigner distributions under Fourier transformation.