Enhancement of the $Λ_b$ decay rate

Abstract

The enhancement $ΔΓ(Λ_b)$ of the $Λ_b$ 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, $|Ψ(0)|^2_{bu}$, is obtained in terms of the $Σ_b^* - Σ_b$ hyperfine splitting, the $B^* - B$ hyperfine splitting, and the $B$ meson decay constant $f_B$. For $M(Σ_b^*) - M(Σ_b) = 56 \pm 16$ MeV, $M(B^*) - M(B) = 46$ MeV, and $f_B = 190 \pm 40$ MeV, we find $ΔΓ(Λ_b) = (0.025 \pm 0.013)$ ps$^{-1}$, to be compared with the observed enhancement $Γ(Λ_b) - Γ(B^0) = 0.20 \pm 0.05$ ps$^{-1}$. Even such a meager enhancement entails a value of $|Ψ(0)|^2_{bu}$ considerably larger than the corresponding value of $|Ψ(0)|^2_{cd}$ in the $Λ_c$ baryon.