Pion fragmentation functions from a quark-jet model in a functional approach

TL;DR

This paper develops a quark-jet model using a functional approach to predict pion fragmentation functions, incorporating crossing symmetry, charge symmetry, and Bethe-Salpeter wave functions, and compares results with NJL model predictions.

Contribution

It introduces a self-consistent method to calculate pion fragmentation functions from a quark-jet model using a functional approach with Bethe-Salpeter wave functions.

Findings

Fragmentation function is enhanced for z < 0.8 compared to NJL model.

Full fragmentation function exceeds elementary one below z ≈ 0.6.

Qualitative agreement with previous models in certain z ranges.

Abstract

The elementary fragmentation function that describes the process $q\to \pi$ is predicted applying crossing and charge symmetry to the cut diagram of the pion valence quark distribution function. This elementary probability distribution defines the ladder-kernel of a quark jet fragmentation equation, which is solved self-consistently to obtain the full pion fragmentation function. The hadronization into a pion employs the complete Poincar\'e invariant Bethe-Salpeter wave function, though the overwhelming contribution to the fragmentation function is due the leading Bethe-Salpeter amplitude. Compared to a Nambu--Jona-Lasinio model prediction, the fragmentation function we obtain is enhanced in the range $z \lesssim 0.8$ but otherwise in good qualitative agreement. The full pion fragmentation function is overall greater than the elementary fragmentation function below $z\lesssim 0.6$.