Abstract
We investigate the inclusive production of prompt $J/\ensuremath{\psi}$ mesons in polarized hadron-hadron, photon-hadron, and photon-photon collisions in the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) providing all contributing partonic cross sections in analytic form. In the case of photoproduction, we also include the resolved-photon contributions. We present numerical results appropriate for BNL RHIC-Spin, the approved SLAC fixed-target experiment E161, and the ${e}^{+}{e}^{\ensuremath{-}}$ and $\ensuremath{\gamma}\ensuremath{\gamma}$ modes of DESY TESLA. Specifically, we assess the feasibility to access the spin-dependent parton distributions in the polarized proton and photon. We also point out that preliminary data on $J/\ensuremath{\psi}$ inclusive production taken by the PHENIX Collaboration in unpolarized proton-proton collisions at RHIC tend to favor the NRQCD factorization hypothesis, while they significantly overshoot the theoretical prediction of the color-singlet model at large values of transverse momentum.
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