Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T

TL;DR

This paper introduces fully-unintegrated parton distribution and fragmentation functions, providing one-loop calculations and clarifying measurement subtleties, which enhance the understanding of transverse momentum effects in high-energy processes.

Contribution

It defines and analyzes generalized beam and fragmenting jet functions for perturbative k_T, correcting previous results and enabling momentum-space renormalization.

Findings

Calculated one-loop matching coefficients for generalized BFs and FJFs.

Corrected previous literature results for beam functions.

Demonstrated the importance of these functions in specific factorization theorems.

Abstract

We define and study the properties of generalized beam functions (BFs) and fragmenting jet functions (FJFs), which are fully-unintegrated parton distribution functions (PDFs) and fragmentation functions (FFs) for perturbative k_T. We calculate at one loop the coefficients for matching them onto standard PDFs and FFs, correcting previous results for the BFs in the literature. Technical subtleties when measuring transverse momentum in dimensional regularization are clarified, and this enables us to renormalize in momentum space. Generalized BFs describe the distribution in the full four-momentum k_mu of a colliding parton taken out of an initial-state hadron, and therefore characterize the collinear initial-state radiation. We illustrate their importance through a factorization theorem for pp -> l^+ l^- + 0 jets, where the transverse momentum of the lepton pair is measured. Generalized FJFs are relevant for the analysis of semi-inclusive processes where the full momentum of a hadron, fragmenting from a jet with constrained invariant mass, is measured. Their significance is shown for the example of e^+ e^- -> dijet+h, where the perpendicular momentum of the fragmenting hadron with respect to the thrust axis is measured.