Kinematical Constraints on QCD Factorization in the Drell-Yan Process

We study factorization schemes for parton shower models in hadron-hadron collisions. As an example, we calculate lepton pair production mediated by a virtual photon in quark--anti-quark annihilation, and we compare factorized cross sections obtained in the conventional $\bar{\rm MS}$ scheme with those obtained in a factorization scheme in which a kinematical constraint due to parton radiation is taken into account. We discuss some properties of factorized cross sections.