Two body non-leptonic $\Lambda_b$ decays in quark model with factorization ansatz

The two body non-leptonic $\Lambda_b$ decays are analyzed in factorization approximation, using quark model, $\xi = 1 / N_c$ as a free parameter. It is shown that the experimental branching ratio for $\Lambda_b \longrightarrow \Lambda {J/\psi}$ restricts $\xi$ and this ratio can be understood for a value of $\xi$ which lies in the range $0 \leq \xi \leq 0.5$ suggested by two body B meson decays. The branching ratios for $\Lambda_b \longrightarrow \Lambda_{c} D^*_s(D_s)$ are predicted to be larger than the previous estimates. Finally it is pointed that CKM-Wolfenstein parameter $\rho^2 + \eta^2$, where $\eta$ is CP phase, can be determined from the ratio of widths of $\Lambda_b \longrightarrow \Lambda \bar{D}$ and $\Lambda_b \longrightarrow \Lambda {J/\psi}$ or that of $\Lambda_b \longrightarrow p D_s$ and $\Lambda_b \longrightarrow \Lambda_c D_s$ independent of the parameter $\xi$.