The Heavy Quark Parton Oxymoron -- A mini-review of Heavy Quark Production theory in PQCD

Conventional perturbative QCD calculations on the production of a heavy quark ``$H$'' consist of two contrasting approaches: the usual QCD parton formalism uses the zero-mass approximation ($m_H=0$) once above threshold, and treats $H$ just like the other light partons; on the other hand, most recent ``NLO'' heavy quark calculations treat $m_H$ as a % large parameter and always consider $H$ as a heavy particle, never as a parton, irrespective of the energy scale of the physical process. By their very nature, both these approaches are limited in their regions of applicability. This dichotomy can be resolved in a unified general-mass variable-flavor-number scheme, which retains the $m_H$ dependence at all energies, and which naturally reduces to the two conventional approaches in their respective region of validity. Recent applications to lepto- and hadro-production of heavy quarks are briefly summarized.