  We present a detailed phenomenological study of $J/\psi$ polarization in
semi-inclusive deep inelastic scattering processes, focusing on the kinematics
accessible at the future Electron-Ion Collider. We show theoretical estimates
for the standard polarization parameters for different frames usually adopted
in the literature, in the large $P_T$ region, namely $P_T\gg
\Lambda_\text{QCD}$, where collinear factorization is expected to hold. We
adopt both the Color Singlet Model and the Nonrelativistic QCD approach, paying
special attention to the role of different sets of Long Distance Matrix
Elements. Finally we present a preliminary analysis of some frame independent
polarization invariants.
