Proton GTMDs and Wigner Distributions in the Chiral Quark Soliton Model: Orbital Angular Momentum and Spin-Orbit Correlation with Sea Quarks

We calculate the leading-twist vector and axial-vector quark generalized transverse-momentum-dependent distributions (GTMDs) of the proton in the chiral quark soliton model, including both the discrete valence level and the regularized Dirac sea. We consider the isosinglet and isotriplet combinations of GTMDs at zero and nonzero skewness. At zero skewness, we construct Wigner distributions and resolve the orbital angular momentum (OAM) and spin-orbit correlation (SOC) densities in transverse position and momentum space, separately for quarks and antiquarks. This provides a phase-space picture of the sea-quark and sea-antiquark contributions, displaying OAM aligned with the proton spin and anti-aligned with the partons' own spin.