Gluon fragmentation into polarized charmonium

Gluon fragmentation to $\text{chicJ}(1P)$ followed by single photon emission represents the dominant source of prompt $J\mathrm{/}\mathrm{\Psi }$’s at the Tevatron for $p_{\perp }\text{gtap}6\text{GeV}$. Since fragmenting gluons are approximately transverse, their products are significantly polarized. We find that gluon fragmentation populates the helicity levels of $\text{chione}$, $\text{chitwo}$ and $J\mathrm{/}\mathrm{\Psi }$ according to $D_{{\text{chione}}^{(h=0)}}:D_{{\text{chione}}^{(\mathrm{\mid }h\mathrm{\mid }=1)}}\simeq 1:1$, $D_{\chitwo^{(h=0)}} : D_{\chitwo^{(|h|=1)}} : D_{\chitwo^{(|h|=2)}} \simeq 1:2.9:6.0$and$D_{\J^{(h=0)}} : D_{\J^{(|h|=1)}} \simeq 1:3.4$. We also speculate that gluon fragmentation to the radially excited $\text{chitwo}(2P)$ state followed by subsequent radiative decay could represent a large source of ${\psi }^{\mathrm{\prime }}(2S)$‘s and potentially resolve the ${\psi }^{\mathrm{\prime }}$ deficit problem. A measurement of these states’ polarizations would test this idea.