Leading twist GTMDs at nonzero skewness and Wigner distributions in boost-invariant longitudinal position space

TL;DR

This paper explores the structure of quark distributions within the nucleon using a light-front model, revealing how GTMDs relate to Wigner distributions and exhibit diffraction patterns in longitudinal position space.

Contribution

It introduces a novel analysis of leading twist GTMDs at nonzero skewness and connects them to Wigner distributions in boost-invariant longitudinal position space.

Findings

Wigner distributions show diffraction patterns in longitudinal space

Fourier transform of GTMDs relates to Wigner distributions

Model is motivated by soft-wall AdS/QCD

Abstract

We investigate the leading twist quark generalized transverse momentum distributions (GTMDs) at nonzero skewness in a light-front quark-diquark model for the nucleon motivated by soft-wall AdS/QCD. The boost-invariant longitudinal coordinate, $\sigma=\frac{1}{2} b^- P^+$, is identified as the Fourier conjugate of the skewness. The Fourier transform of the GTMDs with respect to the skewness variable $\xi$ can be employed to provide the Wigner distributions in the boost-invariant longitudinal position space $\sigma$, the coordinate conjugate to light-front time, $\tau=t+z/c$. The Wigner distributions in the longitudinal position space exhibit diffraction patterns, which are analogous to the diffractive scattering of a wave in optics.