Recursive fragmentation of a polarized quark

This thesis is devoted to the study of the fragmentation process of polarized quarks, which cannot be described in the framework of perturbative QCD and is a very interesting topic per se. The work is motivated by the study of the Collins effect which is used as a polarimeter to measure the quark transversity distribution, the third collinear parton distribution function necessary for the description of the nucleon at leading order. The present phenomenological extractions of the transversity distribution make use of the Collins asymmetry measured in SIDIS of leptons on transversely polarized nucleons and of the corresponding asymmetries in e+e- annihilation into hadrons, which both give access to the Collins function. A useful tool, not only for the extraction of the quark transversity distribution but also for the extraction of other still unknown chiral odd parton distribution functions like the Boer-Mulders function, will be the Monte Carlo (MC) simulation of the Collins effect. Furthermore, a MC event generator including the quark spin degree of freedom in the fragmentation process will be helpful for the interpretation and for the analysis of the experimental data as well as for the design of future experiments. Up to now such an event generator based on a consistent model for this process is not available. The aim of this work is to fill this shortcoming by including the spin degree of freedom in the hadronization part of MC event generators, even if it does not constitute a complete study of spin effects in the quark fragmentation process. The main emphasis here lies on the fragmentation of transversely polarized quarks but longitudinal spin effects like jet-handedness are included as well. The model utilized is based on the Lund Model (LM) of string fragmentation supplemented with the 3P0 model of quark pair production at string breaking. The quark spin is encoded in 2x2 density matrices and propagated using transition matrix amplitudes inspired by the 3P0 model. In this work, two variants of the model for pseudoscalar meson production are formulated. The first variant (M18) includes the so called spin independent correlations between the transverse momenta of successive quarks created at string breakings. The second variant (M19) is free from such correlations, is simpler from the analytical and numerical points of view, and it is more suitable for further extensions and for the implementation in event generators where the hadronization part is based on the LM. Both variants are written in a form suitable for numerical simulations and have been implemented in stand alone MC programs. After tuning one single parameter, the MC results are compared with the measured Collins and dihadron transverse spin asymmetries showing a satisfactory agreement. Also, it is shown that both variants give practically the same results, in spite of the simplicity of M19. Given the encouraging results, M19 has been interfaced with the PYTHIA event generator. The quark transversity distribution has been implemented in the generator allowing to simulate for the first time the polarized SIDIS process. The comparison of the simulated transverse spin asymmetries with the experimental data is found to be very promising. As final development, M19 is extended by introducing vector meson production and decays. The spin density matrix of the vector meson is calculated and utilized for the generation of the angular distribution of the decay hadrons. The quantum mechanical correlations between the relative orientation of the decay products and the next quark in the recursive process are taken into account. The effect of vector meson production on observables like the Collins and the dihadron asymmetries has been studied in detail. The model M20 is shown to be a promising and powerful model to describe the polarized quark fragmentation. The thesis ends with a summary and an overview of possible future studies which can be performed with this model.