Gluon fragmentation into polarized charmonium

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

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