Gluon Fragmentation into Heavy Quarkonium

Abstract

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 \(D(z,\mu)\) 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 \(\mu/m_Q\), where \(\mu\) is the factorization scale and \(m_Q\) is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.