Charm fragmentation functions in the Nambu-Jona-Lasinio model

TL;DR

This paper develops a model-based calculation of charm quark fragmentation functions into D mesons using the NJL model, matching it to QCD results, and compares it with experimental data from CLEO.

Contribution

It introduces a novel approach to derive charm fragmentation functions within the NJL model and matches it to QCD for realistic D meson production predictions.

Findings

The derived FF agrees with CLEO data.

Finite momentum effects significantly impact the FF.

The model provides a consistent framework for charm fragmentation analysis.

Abstract

We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF including the finite momentum effects leads to theoretical results in agreement with the CLEO data.