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Motivated by the need to correct the potentially large kinematic errors inapproximations used in the standard formulation of perturbative QCD, wereformulate deeply inelastic lepton-proton scattering in terms of gaugeinvariant, universal parton correlation functions which depend on allcomponents of parton four-momentum. Currently, different hard QCD processes aredescribed by very different perturbative formalisms, each relying on its ownset of kinematical approximations. In this paper we show how to set upformalism that avoids approximations on final-state momenta, and thus has avery general domain of applicability. The use of exact kinematics introduces anumber of significant conceptual shifts already at leading order, and tightlyconstrains the formalism. We show how to define parton correlation functionsthat generalize the concepts of parton density, fragmentation function, andsoft factor. After setting up a general subtraction formalism, we obtain afactorization theorem. To avoid complications with Ward identities the fullderivation is restricted to abelian gauge theories; even so the resultingstructure is highly suggestive of a similar treatment for non-abelian gaugetheories.

Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering