Multipole decomposition of the nucleon transverse phase space

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.