Need for fully unintegrated parton densities

TL;DR

Integrated PDFs impose kinematic approximations by integrating over transverse momentum and virtuality, leading to unphysical distributions in semi-inclusive observables. The paper advocates reformulating perturbative QCD factorization around fully unintegrated parton densities differential in all momentum components, known as doubly unintegrated densities or parton correlation functions, as an extension of $k_T$-factorization. This framework aims to provide a unified methodology applicable to Monte Carlo event generators and detailed final-state kinematics across processes. By highlighting inadequacies of conventional PDFs and outlining a path to systematic adoption of unintegrated densities, the work lays the groundwork for more accurate and consistent predictions in high-energy hadronic processes.

Abstract

Associated with the use of conventional integrated parton densities are kinematic approximations on parton momenta which result in unphysical differential distributions for final-state particles. We argue that it is important to reformulate perturbative QCD results in terms of fully unintegrated parton densities, differential in all components of the parton momentum.

Figures (2)

• Figure 1: (a) and (b): Comparison between use of simple LO parton model approximation and of the use of $k_{T}$ densities for the $p_{T}$ of $c\bar{c}$ pairs in photoproduction, and for the $x_\gamma$. (c) and (d): Comparison of use of $k_{T}$ densities and full simulation.
• Figure 2: Photon-gluon fusion.