Gluon fragmentation into heavy quarkonium.

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions D(z, μ) describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of μ/mQ, where μ is the factorization scale and mQ is the heavy quark mass, are summed up using AltarelliParisi evolution equations. Quantitative evidence for quantum chromodynamics (QCD) as the fundamental field theory describing the strong interactions has come primarily from high energy processes involving leptons and the electroweak gauge bosons. Such processes are simpler than most purely hadronic processes, because leptons and electroweak gauge bosons do not have strong interactions. The next simplest particles as far as the strong interactions are concerned are heavy quarkonia, the bound states of a heavy quark and antiquark. While not pointlike, the lowest states in the charmonium and bottomonium systems have typical radii that are significantly smaller than those of hadrons containing light quarks. They have simple internal structure, consisting primarily of a nonrelativistic quark and antiquark only. The charmonium and bottomonium systems exhibit a rich spectrum of orbital and angular excitations. Thus in addition to being simple enough to be used as probes of the strong interactions, heavy quarkonia are also a potentially much richer source of information than leptons and electroweak gauge bosons. In most previous studies of the production of heavy quarkonia in high energy processes, it was implicitly assumed that they are produced by short distance mechanisms, in which the heavy quark and antiquark are created with transverse separations of order 1/E, where E is the characteristic energy scale of the process. In this paper, we point out that the dominant mechanism at very high energies is fragmentation, the production of a high energy parton followed by its splitting into the quarkonium state and other partons. The QQ̄ pair are created with a separation of order 1/mQ, where mQ is the mass of the heavy quark Q. The fragmentation mechanism is often of higher order in the QCD coupling constant αs than the short distance mechanism, but it is enhanced by a factor of (E/mQ) 2 and thus dominates at high energies E >> mQ. The fragmentation of a parton into a quarkonium state is described by a fragmentation function D(z, μ), where z is the longitudinal momentum fraction of the quarkonium state and μ is a factorization scale. We calculate to leading order in αs the fragmentation functions D(z,mQ) for gluons to split into S-wave quarkonium states at energy scales μ of order mQ. The fragmentation functions at larger scales μ are then determined by Altarelli-Parisi evolution equations which sum up the leading logarithms of μ/mQ. One of the quarkonium processes that is important in hadron collider physics is the