The NJL-jet model for quark fragmentation functions

A description of fragmentation functions which satisfy the momentum and isospin sum rules is presented in an effective quark theory. Concentrating on the pion fragmentation function, we first explain why the elementary (lowest order) fragmentation process q --> q \pi is completely inadequate to describe the empirical data, although the "crossed" process \pi --> q \bar{q} describes the quark distribution functions in the pion reasonably well. Taking into account cascade-like processes in a generalized jet-model approach, we then show that the momentum and isospin sum rules can be satisfied naturally, without the introduction of ad hoc parameters. We present results for the Nambu--Jona-Lasinio (NJL) model in the invariant mass regularization scheme and compare them with the empirical parametrizations. We argue that the NJL-jet model, developed herein, provides a useful framework with which to calculate the fragmentation functions in an effective chiral quark theory.