Quark fragmentation functions in a diquark model for $\Lambda$ production

Using a simple quark-diquark model, we extract a set of unpolarized and polarized fragmentation functions for the $\Lambda$ based on the available unpolarized $\Lambda$ production data in $e^{+}{e}^{-}$ annihilation. It was found that there is a strong $\mathrm{SU}\left(3\right)\mathrm{}$ flavor symmetry breaking in the unpolarized $\Lambda$ fragmentation functions and that the polarized u and d quark contributions to the polarized $\Lambda$ fragmentation are positive in the medium and large z regions. The predictions of $\Lambda$ polarization with the obtained quark fragmentation functions are compatible with the available data on the longitudinally polarized $\Lambda$ produced in $e^{+}{e}^{-}$ annihilation, polarized charged lepton deep inelastic scattering (DIS), and neutrino DIS. The spin asymmetry for the $\Lambda$ production in $p\overrightarrow{p}$ collisions is also predicted for a future test in experiments at BNL RHIC.