<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math> polarization in large- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> semi-inclusive deep-inelastic scattering at the EIC

We present a detailed phenomenological study of $J/\ensuremath{\psi}$ polarization in semi-inclusive deep-inelastic scattering processes, focusing on the kinematics accessible at future Electron-Ion Collider. show theoretical estimates for standard parameters different frames usually adopted literature, large ${P}_{T}$ region, namely ${P}_{T}\ensuremath{\gg}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$, where collinear factorization is expected to hold. adopt both color singlet model and nonrelativistic QCD approach, paying special attention role sets long distance matrix elements. Finally we preliminary analysis some frame independent invariants.