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 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 χ (h=0) c1 : D χ (|h|=1) c1 ≃ 1 : 1, D χ (h=0) c2 : D χ (|h|=1) c2 : D χ (|h|=2) c2 ≃ 1 : 2.9 : 6.0 and DJ/Ψ(h=0) : DJ/Ψ(|h|=1) ≃ 1 : 3.4. We also speculate that gluon fragmentation to the radially excited χc2(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. 8/94 1 Work supported in part by an SSC Fellowship and by the U.S. Dept. of Energy under DOE Grant no. DE-FG03-92-ER40701. 2 Work supported in part by the U.S. Dept. of Energy under DOE Grant no. DE-FG03-92ER40701. 3 Work supported in part by DOE Contract no. DE-AC02-76CHO3000. The production of the J/Ψ charmonium bound state is currently under active study at Fermilab [1]. Until recently, the dominant sources of J/Ψ’s at a hadron collider were believed to be parton fusion and B meson decay. These two processes respectively produce prompt and delayed J/Ψ’s which can be distinguished via B meson vertex displacement measurements. Comparison between the theoretical prediction and experimental measurement of the transverse momentum differential cross section dσ(pp → J/Ψ +X)/dp⊥ section reveals that parton fusion alone underestimates the prompt J/Ψ production rate at high transverse momenta by approximately an order of magnitude [2,3]. Such a large discrepancy between theory and data clearly indicates that another prompt production mechanism must be at work. Within the past few years, parton fragmentation has been examined as an alternate source of J/Ψ’s [4]. Although fragmentation takes place at higher order in perturbative QCD than quark or gluon fusion, the falloff of the former with increasing transverse momentum is much slower than that of the latter. So for p⊥>∼6 GeV, parton fragmentation represents the dominant source of prompt J/Ψ’s. The first charmonium fragmentation functions to be calculated were Dg→J/Ψ(z) and Dc→J/Ψ(z) which specify the probability for gluons and charm quarks to hadronize into J/Ψ as a function of its longitudinal momentum fraction z [4–6]. The only nonperturbative piece of information which enters into the lowest order computation of these S-wave fragmentation functions is the square of the charmonium bound state’s wavefunction at the origin. The remainder of the calculation is based upon perturbative QCD. More recently, the fragmentation functions for gluons and charm quarks to hadronize into the lowest lying P -wave charmonium bound states χc0, χc1 and χc2 have been computed [7]. These χcJ states radiatively decay down to J/Ψ with the branching ratios 0.7%, 27% and 14% for J = 0, 1 and 2 respectively. After folding together these branching ratios with the P -wave fragmentation functions, one finds that gluon fragmentation to χcJ followed by single photon emission to J/Ψ dominates at high p⊥ over all other prompt mechanisms by more than an order of magnitude. When this J/Ψ source is included, the theoretical prediction for dσ(pp → J/Ψ +X)/dp⊥ at √ s = 1.8 TeV moves to within a factor of two of recent CDF data. Most of the fragmentation functions which have been calculated to date describe the production of unpolarized quarkonium. However, it is straightforward to compute polarized fragmentation functions as well. Charm fragmentation into transverse and longitudinal J/Ψ’s was considered in refs. [6] and [8] and found to yield essentially no polarization.