Sivers and Boer-Mulders distributions in boost-invariant longitudinal position space

Abstract: The boost invariant longitudinal position space variable $\sigma$, the Fourier conjugate to skewness $\xi$, unravels the longitudinal impact parameter information in a proton. Here, we investigate skewness sensitivity of T-odd leading twist GTMDs considering a momentum transfer to longitudinal as well as transverse direction and present a detailed study of the spin-transverse momentum correlation through Sivers and Boer-Mulders Wigner Distributions in boost invariant longitudinal position space. The $\sigma$-space distributions of T-odd sector show oscillatory patterns sensitive to square of the total momentum transfer $-t$, analogous to the diffraction scattering of wave in Optics. An additional effect on the diffraction pattern is reported caused by interference between transverse momentum transfer $\bfd$ to the transverse momentum $\bfp$ of quarks.