Factorization of the Drell-Yan cross section in perturbation theory

Abstract

We develop, through detailed one- and two-loop examples, a procedure for expressing the leading-twist Drell-Yan cross section in terms of the factored form proposed by Collins, Soper, and Sterman. We then show that this factorization program can be implemented to all orders in perturbation theory. The factored cross section takes the form of an on-shell qq\ifmmode\bar\else\textasciimacron\fi{} annihilation cross section (less certain collinear subtractions) convolved with structure functions for the incoming hadrons. The structure functions contain all the collinear singularities and spectator interactions. They are shown to be simply related to those that occur in deep-inelastic lepton scattering. We also demonstrate that the qq\ifmmode\bar\else\textasciimacron\fi{} cross section minus the collinear subtractions is free of infrared singularities if one integrates over the transverse momentum of the lepton pair.