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We present novel analyses on accessing the 3D gluon content of the proton viaspin-dependent TMD gluon densities, calculated through the spectator-modelapproach. Our formalism embodies a fit-based spectator-mass modulationfunction, suited to catch longitudinal-momentum effects in a wide kinematicrange. Particular attention is paid to the time-reversal even Boer--Mulders andthe time-reversal odd Sivers functions, whose accurate knowledge, needed toperform precise 3D analyses of nucleons, motivates synergies between LHC andEIC Communities.

Spectator-model studies for spin-dependent gluon TMD PDFs at the LHC and EIC