Polarized fragmenting jet functions in Inclusive and Exclusive Jet Production

TL;DR

This paper develops a theoretical framework using SCET to analyze polarized hadron distributions within jets, enabling new measurements of parton distribution and fragmentation functions in polarized collisions.

Contribution

It introduces polarized fragmenting jet functions for both inclusive and exclusive jets, providing a basis for extracting TMD PDFs and FFs with numerical examples for RHIC and EIC.

Findings

Numerical results for spin asymmetries in polarized $pp$ and $ep$ collisions.

Demonstrates potential for new TMD PDF and FF measurements.

Provides a comprehensive SCET-based factorization framework.

Abstract

In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry $A_{TU,T}^{\cos(\phi _S - \hat{\phi}_{S_h})}$ from polarized semi-inclusive hadron-in-jet production in polarized $pp$ collisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry, $A_{TU, L}^{\cos(\phi _q - \phi _{S})}$ from polarized exclusive hadron-in-jet production in polarized $ep$ collisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements.