Proton 3D reconstruction with T-odd TMD gluon densities

We present studies aimed at probing the 3D gluon content of the proton through spin-dependent TMD gluon densities, computed by means of the spectator-model approach. Our formalism incorporates a fit-based modulation function for the spectator mass, designed to capture longitudinal-momentum effects across a broad kinematic range. Special emphasis is placed on the time-reversal even Boer-Mulders and the time-reversal odd Sivers functions. Accurate understanding of these functions is crucial for conducting precise 3D analyses of nucleons, highlighting the importance of collaborative efforts between the LHC and EIC Communities.