Two body nonleptonicΛbdecays in the quark model with a factorization ansatz

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