Quark-Jet model for transverse momentum dependent fragmentation functions

TL;DR

This paper extends the quark-jet model to include transverse momentum dependent fragmentation functions, providing a framework for describing polarized quark hadronization with detailed sum rules and numerical applicability.

Contribution

It introduces a novel extension of the quark-jet model to TMD fragmentation functions, enabling detailed calculations and simulations of polarized quark hadronization.

Findings

The model satisfies 3D momentum sum rules naturally.

The approach is suitable for numerical calculations in effective quark theories.

Can be implemented in Monte-Carlo simulations of polarized processes.

Abstract

In order to describe the hadronization of polarized quarks, we discuss an extension of the quark-jet model to transverse momentum dependent fragmentation functions. The description is based on a product ansatz, where each factor in the product represents one of the transverse momentum dependent splitting functions, which can be calculated by using effective quark theories. The resulting integral equations and sum rules are discussed in detail for the case of inclusive pion production. In particular, we demonstrate that the 3-dimensional momentum sum rules are satisfied naturally in this transverse momentum dependent quark-jet model. Our results are well suited for numerical calculations in effective quark theories, and can be implemented in Monte-Carlo simulations of polarized quark hadronization processes.