PQCD Analysis of Inclusive Semileptonic Decays of Polarized $\Lambda_b$

We investigate the Lambda_b polarization problem in the inclusive semileptonic decays of a polarized Lambda_b baryon, using the modified perturbative QCD formalism which includes Sudakov suppression. According to HQEFT, we show that, at the leading order in the 1/M_b expansion, the polarized and unpolarized distribution functions become one single universal distribution function. To explore the mechanisms which determine the spin properties of a polarized Lambda_b baryon, we construct four formalisms which are the naive quark model (QM), the modified quark model (MQM), the naive parton model (PM) and the modified parton model (MPM), and calculate their corresponding Lambda_b polarizations, denoted as P's. The modified quark and parton models are with Sudakov suppression. The resulting P's are -0.23 (QM), -0.94 (MQM), -0.37 (PM) and -0.68 (MPM), respectively. We note that P_MQM (equal to -0.94) is very close the b quark polarization asymmetry, A_RL=-0.94, calculated at the Z vertex in Z -> b bar{b} process, and that P_MPM (equal to -0.68) is also very close to the Lambda_b polarization (equal to -0.68) which was estimated from the fragmentation processes under the heavy quark limit. Based on our analysis, there exists no any paradox in the theoretical explanations of the Lambda_b polarization for the experimental data