Enhancement of the ${\Lambda }_b$ decay rate

Abstract

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, $|\Psi (0){|}_{bu}^2$, is obtained in terms of the ${\Sigma }_b^{\ast }-{\Sigma }_b$ hyperfine splitting, the $B^{\ast }-B$ hyperfine splitting, and the $B$ meson decay constant $f_B$. For $M({\Sigma }_b^{\ast })-M({\Sigma }_b)=56\pm 16$ MeV, $M(B^{\ast })-M(B)=46$ 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 $|\Psi (0){|}_{bu}^2$ considerably larger than the corresponding value of $|\Psi (0){|}_{cd}^2$ in the ${\Lambda }_c$ baryon.

Comments: 7 pages, latex, no figures