Two body nonleptonicΛbdecays in the quark model with a factorization ansatz

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