Gluon Fragmentation into Heavy Quarkonium

TL;DR

The fragmentation functions for a gluon to split into [ital S]-wave quarkonium states to leading order in the QCD coupling constant are calculated using perturbative QCD.

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