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

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.

arXiv comment19 pages, 10 figures

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• Deciphering Twist-3 Chiral-Even GPDs in the Light-Front Quark-Diquark Model
• T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton