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

Abstract

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 correlation 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.

44 pages, 69 figures typos fixed, clarifications and second appendix added

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Cited by in corpus (8)

• Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum
• Renormalization, Wilson lines, and transverse-momentum dependent parton distribution functions
• Spectral analysis of gluonic pole matrix elements for fragmentation
• Angular correlations in multi-jet final states from kt-dependent parton showers
• Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions
• Gauge invariance and renormalization-group effects in transverse-momentum dependent parton distribution functions
• Parton correlation functions and factorization in deep inelastic scattering
• Unintegrated parton distributions and correlation functions