Generalized Parton Distributions of proton for non zero skewness in transverse and longitudinal position spaces

Abstract: We investigate the Generalized Parton Distributions(GPDs) of proton by expressing them in terms of overlaps of light front wave functions (LFWFs) using a simulated model which is able to qualitatively improve the convergence near the end points of $x$. We study the spin non-flip $H(x, \zeta, t)$ and spin flip $E(x, \zeta, t)$ part of GPDs for the particle conserving $n \rightarrow n$ overlap in the DGLAP region $(\zeta<x<1)$. The Fourier transform (FT) of the GPDs w.r.t. to the transverse momentum transfer as well the FT of the GPDs w.r.t. $\zeta$ have also been obtained giving the distribution of partons in the transverse position space and the distribution in the longitudinal position space respectively. Diffraction pattern is obtained for both $ \mathcal{H}(x,\sigma,t)$ and $ \mathcal{E}(x,\sigma,t)$ in the longitudinal position space.