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In this paper we propose to investigate the transverse single spin asymmetryin the inelastic $J/\Psi$ photoproduction in $p^\uparrow p$ and $p^\uparrow A$collisions at RHIC energies. At leading order this process probes the gluonSivers function. We predict large values for the cross sections, whichindicates that its experimental analysis is, in principle, feasible. Therapidity dependence of the single spin asymmetry is presented. We obtain thatthe asymmetry is strongly dependent on the model used for the gluon Siversfunction and that it can be probed by the analysis of the $J/\Psi$ productionat forward rapidities. Our results indicate that a future experimental analysisof this process can be useful to constrain the gluon Sivers function.

Investigating the Transverse Single Spin Asymmetry in the Inelastic $J/\Psi$ photoproduction in $p^\uparrow p$ and $p^\uparrow A$ collisions