Comparison of the Parton and Light-Cone Analyses of Highly Inelastic Leptonic Processes

Abstract

We study the relationship between the parton model and the analysis of light-cone singularities for highly inelastic leptonic processes. For deep-inelastic lepton scattering the parton model is found to be a momentum-space representation of any model in which free-field singularities on the light cone are dominant. Scaling laws and sum rules derived in one approach are shown to obtain in the other with equivalent assumptions. For massive-muonpair production the two approaches are found to differ fundamentally. In the parton model the leading singularity is dominated in the high-mass limit by the nonsingular annihilation diagram. The scaling law which is obtained in the parton model is not obtained from a lightcone analysis without additional, seemingly arbitrary assumptions. Massive-muon-pair production therefore tests the parton model in a region where it is not equivalent to the lightcone approach. Several other processes are studied including one-particle inclusive $e^{+}{e}^{-}$ annihilation and photoproduction of muon pairs.