T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton

TL;DR

This paper explores the structure of T-odd GTMDs and spin-momentum correlations in protons using boost-invariant longitudinal position space, revealing diffraction-like patterns and interference effects.

Contribution

It introduces the analysis of T-odd GTMDs in $\sigma$-space, highlighting diffraction patterns and interference effects in proton structure functions.

Findings

Oscillatory diffraction patterns in $\sigma$-space sensitive to momentum transfer $-t$

Interference effects between transverse momentum transfer and quark momentum

Correlation of proton spin with quark transverse momentum via Wigner distributions

Abstract

The boost invariant longitudinal position space variable $\sigma$, which is the Fourier conjugate to skewness $\xi$, unravels the longitudinal impact parameter information in a proton. Here, we investigate the skewness sensitivity of T-odd leading twist GTMDs within the Dokshitzer Gribov Lipatov Altarelli Parisi (DGLAP) region, considering a momentum transfer to longitudinal as well as transverse direction. The $\sigma$-space distributions of the T-odd sector show oscillatory patterns that are sensitive to the square of the total momentum transfer $-t$, which is analogous to the diffraction scattering of waves 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. We also present the correlation of proton spin to the transverse momentum of constituents through Sivers and Boer-Mulders Wigner Distributions in boost invariant longitudinal position space.