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The recently developed quantum mechanical string+${}^3P_0$ model of polarized quark fragmentation with pseudoscalar and vector meson production has been implemented in a stand alone Monte Carlo program. The simulation enables the detailed study of the quark spin dependent effects in the fragmentation process such as the transverse spin asymmetries. In particular, it allows to investigate the effects of the production and decay of vector mesons on the Collins and dihadron asymmetries of the observed hadrons, and to study the still unknown Collins effect for vector mesons. The main results of the Monte Carlo simulations obtained so far are summarized and the comparison with the existing experimental data on SIDIS and $e^+e^-$ annihilation to hadrons processes are presented., 5 pages, 3 figures, Contribution to The 24th International Spin Symposium (SPIN2021)

We present the main theoretical aspects of the quantum mechanical string+${}^3P_0$ model of polarized quark fragmentation for pseudoscalar and vector meson production. The model is an extension of the Lund string fragmentation model that systematically includes the quark spin degree of freedom assuming the ${}^3P_0$ mechanism of quark pair production at string breaking. The recently achieved introduction of vector mesons accounts for the spin correlations between the latter and the quark of the fragmentation chain. The string+${}^3P_0$ model reproduces transverse spin effects such as the Collins effect and the dihadron asymmetry, and longitudinal spin effects such as the jet handedness., Comment: 5 pages, 3 figures, Contribution to the 24th International Spin Symposium (SPIN-2021)