Enhancement of the $\Lambda_b$ decay rate

The enhancement $\Delta \Gamma (\Lambda_b)$ of the $\Lambda_b$ decay rate due to four-fermion processes of weak scattering and Pauli interference is calculated within the quark model. An estimate of the relative $bu$ wave function at zero separation, $|\Psi(0)|^2_{bu}$, is obtained in terms of the $\Sigma_b^* - \Sigma_b$ hyperfine splitting, the $B^* - B$ hyperfine splitting, and the $B$ meson decay constant $f_B$. For $M(\Sigma_b^*) - M(\Sigma_b) = 56 \pm 16$ MeV, $M(B^*) - M(B) = 46$ MeV, and $f_B = 190 \pm 40$ MeV, we find $\Delta \Gamma(\Lambda_b) = (0.025 \pm 0.013)$ ps$^{-1}$, to be compared with the observed enhancement $\Gamma(\Lambda_b) - \Gamma(B^0) = 0.20 \pm 0.05$ ps$^{-1}$. Even such a meager enhancement entails a value of $|\Psi(0)|^2_{bu}$ considerably larger than the corresponding value of $|\Psi(0)|^2_{cd}$ in the $\Lambda_c$ baryon.