Within the framework of the nonrelativistic QCD (NRQCD) factorization approach, we compute the polarization of prompt $J/\psi$ produced at the Brookhaven’s Relativistic Heavy-Ion Collider from proton-proton collisions at the center-of-momentum energy $\sqrt{s}=200\mathrm{GeV}$. The perturbative contributions are computed at leading order in the strong coupling constant. The prediction reveals that the color-singlet contribution severely underestimates the PHENIX preliminary data for the differential cross section integrated over the rapidity range $|y|<0.35$ and its contribution is strongly transversely polarized, which disagrees with the PHENIX preliminary data. After including the color-octet contributions, we find that the NRQCD predictions for both the cross section and polarization over the transverse-momentum range $1.5\mathrm{GeV}<p_T<5\mathrm{GeV}$ ($1.5\mathrm{GeV}<p_T<2\mathrm{GeV}$) integrated over the rapidity range $|y|<0.35$ ($1.2<|y|<2.2$) agree with the data within errors.

• Received 11 November 2009

DOI:https://doi.org/10.1103/PhysRevD.81.014020