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

We perform a study on the struck quark to the $Λ$-hyperon fragmentation processes by taking into account the anti-quark fragmentations and intermediate decays from other hyperons. We concentrate on how the longitudinally polarized quark fragments to the longitudinally polarized $Λ$, how unpolarized quark and anti-quark fragment to the unpolarized $Λ$, and how quark and anti-quark fragment to the $Λ$ 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 the Melosh-Wigner rotation effect also included. The calculated results are in reasonable agreement with the HERMES semi-inclusive $ep$ experimental data and the OPAL and ALEPH $e^{+}e^{-}$ annihilation experimental data.