On the Determination of the $b \rightarrow c$ Handedness Using Nonleptonic $\Lambda_c$-Decays

We consider possibilities to determine the handedness of $b \ra c$ current transitions using semileptonic baryonic $\Lambda_{b} \rightarrow \Lambda_{c}$ transitions. We propose to analyze the longitudinal polarization of the daughter baryon $\Lambda_c$ by using momentum-spin correlation measurements in the form of forward-backward (FB) asymmetry measures involving its nonleptonic decay products. We use an explicit form factor model to determine the longitudinal polarization of the $\Lambda_c$ in the semileptonic decay $\Lambda_b \ra \Lambda_c + l^- + \bar \nu_l$. The mean longitudinal polarization of the $\Lambda_c$ is negative (positive) for left-chiral (right-chiral) $b \ra c$ current transitions. The frame dependent longitudinal polarization of the $\Lambda_c$ is large ($\cong 80\%$) in the $\Lambda_b$ rest frame and somewhat smaller (30\% - 40\%) in the lab frame when the $\Lambda_b$'s are produced on the $Z_0$ peak. We suggest to use nonleptonic decay modes of the $\Lambda_c$ to analyze its polarization and thereby to determine the chirality of the $b \ra c$ transition. Since the $\Lambda_b$'s produced on the $Z_0$ are expected to be polarized we discuss issues of the polarization transfer in $\Lambda_b \ra \Lambda_c$ transitions. We also investigate the $p_\perp$- and $p$-cut sensitivity of our predictions for the polarization of the $\Lambda_c$.