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We perform a study on the struck quark to the $\Lambda$-hyperon fragmentationprocesses by taking into account the anti-quark fragmentations and intermediatedecays from other hyperons. We concentrate on how the longitudinally polarizedquark fragments to the longitudinally polarized $\Lambda$, how unpolarizedquark and anti-quark fragment to the unpolarized $\Lambda$, and how quark andanti-quark fragment to the $\Lambda$ through the intermediate decay processes.We calculate the effective fragmentation functions in the light-cone SU(6)quark-spectator-diquark model via the Gribov-Lipatov relation, with theMelosh-Wigner rotation effect also included. The calculated results are inreasonable agreement with the HERMES semi-inclusive $ep$ experimental data andthe OPAL and ALEPH $e^{+}e^{-}$ annihilation experimental data.

Quark to $\Lambda$-hyperon spin transfers in the current-fragmentation region