${\psi }^{\mathrm{\prime }}$ productions as a test of color-octet mechanism

To test the color-octet model of heavy quarkonium productions, we propose ${\psi }^{\mathrm{\prime }}$-productions at small-$p_T$ regions in polarized $pp$ collisions for the forthcoming RHIC polarized experiments, whose experimental test at $\sqrt s=50$ GeV might be very promising.