Gluon fragmentation into polarized charmonium

Gluon fragmentation to χcJ(1P) followed by single photon emission represents the dominant source of prompt J/{ψ}'s at the Fermilab Tevatron for p_⊥{}6 GeV. Since fragmenting gluons are approximately transverse, their products are significantly polarized. We find that gluon fragmentation populates the helicity levels of χc1, χc2, and J/{ψ} according to D_χc1⁽ʰ⁼⁰⁾:D_χc1^(h=1) {}1:1, D_χc2⁽ʰ⁼⁰⁾: D_χc2^(h=1):D_χc2^(h=2) {}1:2.8:6.0, and D_J/ψ⁽ʰ⁼⁰⁾:D_J/ψ^(h=1){}1:3.4. We also speculate that gluon fragmentation to the radially excited χc2(2P) state followed by radiative decay could represent a large source of {ψ}'(2S)'s. A measurement of these states' polarizations would test this idea.