Motivated by the need to correct the potentially large kinematic errors in approximations used in the standard formulation of perturbative QCD, we reformulate deeply inelastic lepton-proton scattering in terms of gauge invariant, universal parton cor
relation functions which depend on all components of parton four-momentum. Currently, different hard QCD processes are described by very different perturbative formalisms, each relying on its own set of kinematical approximations. In this paper we show how to set up formalism that avoids approximations on final-state momenta, and thus has a very general domain of applicability. The use of exact kinematics introduces a number of significant conceptual shifts already at leading order, and tightly constrains the formalism. We show how to define parton correlation functions that generalize the concepts of parton density, fragmentation function, and soft factor. After setting up a general subtraction formalism, we obtain a factorization theorem. To avoid complications with Ward identities the full derivation is restricted to abelian gauge theories; even so the resulting structure is highly suggestive of a similar treatment for non-abelian gauge theories.
The perturbative QCD formula for minijet production consitutes an important ingredient in models describing the total cross section and multiparticle production in hadron-hadron scattering at high energies. Using arguments based on s-channel unitarit
y we set bounds on the minimum value of p_T for which the leading twist minijet formula can be used. For large impact parameters where correlations between partons appear to be small we find that the minimum value of p_T should be greater than 2.5 GeV for LHC energies and greater than 3.5 GeV for cosmic ray energies of about 50 TeV. We also argue that for collisions with values of impact parameters typical for heavy particle production the values of minimum p_T are likely to be considerably larger. We also analyze and quantify the potential role of saturation effects in the gluon density. We find that although saturation effects alone are not sufficient to restore unitarity, they are likely to play an important role at LHC energies.
