Transverse-momentum-dependent fragmentation and quark distribution functions from the Nambu–Jona-Lasinio–jet model

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 ${P}_{\ensuremath{\perp}}^{2}$ of the produced kaons is significantly larger than that of the pions. We also find that $⟨{P}_{\ensuremath{\perp}}^{2}⟩$ 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 nontrivial 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 $⟨{P}_{T}^{2}⟩$ has a sizable $z$ dependence.