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

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-perpendicular to(2) of the produced kaons is significantly larger than that of the pions. We also find that < P-perpendicular to(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 transversemomentum- dependent quark distribution functions. The < k(perpendicular to)(2)> Ti 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-perpendicular to(2)>. Again, we find that the average P-perpendicular to(2) of the produced kaons in SIDIS is significantly larger than that of the pions and in each case < P-perpendicular to(2)> Ti has a sizable z dependence.