Ghost contributions to charmonium production in polarized high-energy collisions

Abstract

In a previous paper [Phys. Rev. D 68, 034017 (2003)], we investigated 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 providing compact analytic results for the double longitudinal-spin asymmetry ${\mathcal{A}}_{LL}$. For convenience, we adopted a simplified expression for the tensor product of the gluon polarization four-vector with its charge conjugate, at the expense of allowing for ghosts and antighosts to appear as external particles. While such ghost contributions cancel in the cross section asymmetry ${\mathcal{A}}_{LL}$ and thus were not listed in our previous paper, they do contribute to the absolute cross sections. Evaluating the latter from those formulas thus leads to erroneous results. For completeness and the reader's convenience, they are provided in this addendum. This fully reconciles our results with those obtained by M. M. Meijer, J. Smith, and W. L. van Neerven [Phys. Rev. D 77, 034014 (2008)].