$\psi'$ Polarization due to Color-Octet Quarkonia Production

We calculated the polarization of \psi' due to gg \to Q\bar{Q}[^3P_J^(8)]g \to \psi^\lambda color-octet quarkonia production. We find that at low transverse momenta the \psi' is unpolarized due to the contributions proportional to the L=S=0 and L=S=1 color-octet matrix elements. As p_\perp increases, the \psi' mesons become 100% polarized, as predicted by fragmentation calculations. Polarization due to lowest order color-singlet production is also considered, which qualitatively has a similar shape to the color-octet production.