  The polarization of $\Lambda_b$ baryon has been measured in ALEPH, OPAL and
DELPHI experiments. A significant loss on the transfer of the $b$ quark
polarization to the $\Lambda_b$ baryon polarization has been noticed. This
implies that the hadronization effects can not be neglected. Therefore, we may
make use of the polarization measurements to look for suitable model for the
$\Lambda_b$ distribution function. To investigate nonperturbative effects
implied in the $\Lambda_b$ polarization, we construct four models based on a
perturbative QCD factorization formula. The models are the quark model (QM),
the modified quark model (MQM), the parton model (PM), and the modified parton
model (MPM). The modified models mean the models having transverse degrees of
freedom and the associated soft radiative corrections having been resummed. The
quark and parton models can not describe all experiments in the same time. On
the other hand, the modified models can have the power to explain all data in
the same formalism.
