Z0 decay into charmonium via charm quark fragmentation.

In decays of the Z, the dominant mechanism for the direct production of charmonium states is the decay of the Z into a charm quark or antiquark followed by its fragmentation into the charmonium state. We calculate the fragmentation functions describing the splitting of charm quarks into S-wave charmonium states to leading order in the QCD coupling constant. Leading logarithms of MZ/mc are summed up using Altarelli-Parisi evolution equations. Our analytic result agrees with the complete leading order calculation of the rate for Z → ψcc̄. We also use our fragmentation functions to calculate the production rate of heavy quarkonium states in W, top quark, and Higgs decays. Introduction Among the rare decay modes of the Z predicted by the Standard Gauge Theory are ones whose final states include charmonium. Of particular importance are the S1 charmonium states J/ψ and ψ, since their decays into lepton pairs provide easily identifiable experimental signatures. The dominant production mechanism for ψ and ψ is the decay of B hadrons; in fact, this serves as a signature for B hadron production in Z decay. The direct production of ψ and ψ is therefore important in Z decays as a background to B physics. It is also of interest in its own right, since it involves both short distance and long distance aspects of quantum chromodynamics (QCD). The production of a charm quark and antiquark with small relative momentum in Z decay is a short distance process with a characteristic length scale that can range from 1/MZ to as large as 1/mc. The subsequent formation of a bound state from the cc̄ pair is a long distance process involving all the complications of nonperturbative QCD. The methods of perturbative QCD can be used to calculate the production rates provided that it is possible to systematically separate the short distance effects from the long distance effects. Most previous work on charmonium production in Z decay [1, 2, 3] has focused on short distance processes in which the cc̄ pair that form the ψ is produced with a transverse separation of order 1/MZ . Long distance effects involved in the formation of the bound state are factored into the nonrelativistic radial wavefunction at the origin R(0). The best example of a short distance process is Z → ψgg, which has a branching fraction of about 10. This small branching fraction can be partly attributed to a factor of |R(0)|/(mcM Z), which represents the probability for a cc̄ pair that is produced in a region of size 1/(mcM 2 Z) to form a bound state. This probability factor suppresses the branching fractions for short distance processes by m2c/M 2 Z , so that they can be neglected in the limit MZ/mc → ∞. As pointed out by Kühn and Schneider [4], the direct production of charmonium in Z decay will be dominated not by short distance processes but by fragmentation processes. The fragmentation mechanism is the decay of the Z into a final state that includes a high energy quark or gluon, followed by the splitting of that parton into the charmonium state plus other partons. In the fragmentation mechanism, the c and c̄ that form the charmonium