Multipole decomposition of the nucleon transverse phase space

TL;DR

This paper provides a comprehensive multipole decomposition of the leading-twist quark Wigner distributions in the nucleon, revealing the underlying spin and orbital correlations in transverse phase space.

Contribution

It introduces a complete multipole framework for Wigner distributions, linking them to GPDs and TMDs, and offers visual representations of these complex structures.

Findings

Identification of basic multipole structures in transverse phase space

Connection established between Wigner functions, GPDs, and TMDs

Visualization method for multipole structures in position and momentum spaces

Abstract

We present a complete study of the leading-twist quark Wigner distributions in the nucleon, discussing both the $\mathsf T$-even and $\mathsf T$-odd sector, along with all the possible configurations of the quark and nucleon polarizations. We identify the basic multipole structures associated with each distribution in the transverse phase space, providing a transparent interpretation of the spin-spin and spin-orbit correlations of quarks and nucleon encoded in these functions. Projecting the multipole parametrization of the Wigner functions onto the transverse-position and the transverse-momentum spaces, we find a natural link with the corresponding multipole parametrizations for the generalized parton distributions and transverse-momentum dependent parton distributions, respectively. Finally, we show results for all the distributions in the transverse phase space, introducing a representation that allows one to visualize simultaneously the multipole structures in both the transverse-position and transverse-momentum spaces.