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

The boost-invariant longitudinal space, defined by the parameter sigma 1/4 12 b-P thorn , can be studied from the Fourier transformation of generalized transverse momentum distributions (GTMDs) 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 nonzero skewness for quarks which provides Wigner distributions under Fourier transformation.

Automated summary

This study investigates the boost-invariant longitudinal space, defined by the parameter sigma 1/4 12 b-P thorn, through the Fourier transformation of generalized transverse momentum distributions (GTMDs) over the skewness xi. The presence of diffraction patterns similar to the single slit experiment of light in optics is observed in quark Wigner distributions in the sigma space in a dressed quark model. The computed leading twist GTMDs with nonzero skewness provide Wigner distributions under Fourier transformation.