Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions

TL;DR

This paper develops a next-to-leading order calculation of unpolarized gluon-induced deep inelastic scattering using fully unintegrated parton distribution functions, maintaining exact momentum conservation and providing a new framework for factorization.

Contribution

It introduces a fully unintegrated factorization formalism with a non-trivial hard scattering coefficient, advancing beyond collinear approaches by incorporating all momentum components.

Findings

Derived the NLO fully unintegrated hard scattering coefficient.

Maintained exact four-momentum conservation throughout.

Provided a parameterization for the fully unintegrated gluon distribution.

Abstract

We calculate the next-to-leading order fully unintegrated hard scattering coefficient for unpolarized gluon-induced deep inelastic scattering using the logical framework of parton correlation functions developed in previous work. In our approach, exact four-momentum conservation is maintained throughout the calculation. Hence, all non-perturbative functions, like parton distribution functions, depend on all components of parton four-momentum. In contrast to the usual collinear factorization approach where the hard scattering coefficient involves generalized functions (such as Dirac $\delta$-functions), the fully unintegrated hard scattering coefficient is an ordinary function. Gluon-induced deep inelastic scattering provides a simple illustration of the application of the fully unintegrated factorization formalism with a non-trivial hard scattering coefficient, applied to a phenomenologically interesting case. Furthermore, the gluon-induced process allows for a parameterization of the fully unintegrated gluon distribution function.