Transverse Momentum Dependent Fragmentation and Quark Distribution Functions from the NJL-jet Model

TL;DR

This paper employs the NJL-jet model to analyze the transverse momentum dependence of quark distributions and fragmentation functions, revealing flavor and hadron type differences and their impact on SIDIS observables.

Contribution

It introduces a microscopic NJL-jet model approach to compute transverse momentum dependent functions and their flavor and hadron type dependencies.

Findings

Kaons have larger average transverse momentum squared than pions.

The transverse momentum dependence shows a significant z dependence, deviating from naive Gaussian models.

Flavor and diquark correlations influence the transverse momentum distributions in the nucleon.

Abstract

Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\perp^2>$ has a sizable $z$ dependence, in contrast with the naive Gaussian ansatz for the fragmentation functions. Diquark correlations in the nucleon give rise to a non-trivial flavor dependence in the unpolarized transverse momentum dependent quark distribution functions. The $<k_T^2>$ of the quarks in the nucleon are also found to have a sizable $x$ dependence. Finally, these results are used as input to a Monte Carlo event generator for semi-inclusive deep inelastic scattering (SIDIS), which is used to determine the average transverse momentum squared of the produced hadrons measured in SIDIS, namely $<P_T^2>$. Again we find that the average $P_T^2$ of the produced kaons in SIDIS is significantly larger than that of the pions and in each case $\la P_T^2 \ra$ has a sizable $z$ dependence.