Quark-Jet model for transverse momentum dependent fragmentation functions

Understand

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.