Gluon fragmentation to 1D2 quarkonia.

Gluon fragmentation to heavy J C = 2 quarkonia is studied herein. We compute these D-wave states’ polarized fragmentation functions and find that they are enhanced by large numerical prefactors. The prospects for detecting the lowest lying D2 charmonium state at the Tevatron are discussed. 10/94 1 Work supported in part by a DuBridge 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. One of the outstanding challenges in QCD is to understand the process whereby colored quarks and gluons hadronize into colorless mesons and baryons. Until recently, the only basis for parton fragmentation intuition came from simple models and empirical observations. However within the past two years, important progress has been made in understanding hadronization from first principles [1–5]. It is now possible to calculate the fragmentation functions which specify the probability for heavy quarks and gluons to hadronize into quarkonium bound states starting from perturbative QCD. These functions involve nonperturbative matrix elements whose values must still be extracted from experiment or the lattice. But their dependence upon the quarkonium longitudinal momentum fraction z can be calculated to lowest order in the strong interaction fine structure constant αs(mQ) and the velocity v of the heavy constituent quark inside the bound state. In principle, higher order corrections associated with these two small expansion parameters may be systematically evaluated as well. These developments have allowed a range of hadronization issues to be explored in a limited but model independent context. The first fragmentation functions to be computed from perturbative QCD described the hadronization of gluons and heavy quarks into S-wave quarkonium bound states [1,2]. These O(v) functions can be used to predict the direct production of ηc and J/Ψ charmonia as well as ηb and Υ bottomonia at lepton and hadron colliders. More recently, O(v ) P-wave fragmentation functions have also been calculated [3–5]. In this paper, we extend the ideas and methods developed in refs. [1–5] to the D-wave sector. As L = 2 fragmentation functions start at O(v), they are generally less important than those for L = 0 and L = 1 quarkonia. P-wave contributions to Q → χQ have been found to be quite suppressed compared to S-wave terms [5], and D-wave effects should be even smaller still. On the other hand, gluon fragmentation to χQ is known to be phenomenologically significant at hadron machines where the number of gluons in the initial state is large. Indeed, the dominant source of high p⊥ prompt J/Ψ’s at the Tevatron is gluon fragmentation to χc’s followed by single photon emission [6–8]. This prompt J/Ψ mechanism beats all others by almost two orders of magnitude. It is therefore interesting to examine the rate at which gluon fragmentation to D-wave quarkonia occurs as well. We will focus in particular upon the production of the lowest lying charmonium state with the quantum numbers n = 1, L = 2 and S = 0. This J C = 2 meson has not yet been observed. Quark model predictions for its mass fall within the range 3.81 GeV ≤ M ≤ 3.84 GeV which lies above the DD threshold [9–12]. But since its parity is odd, 1D2 cannot decay to DD, for the two spinless mesons would have to emerge in an even parity