Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the s¯ quark and the ud diquark

Abstract

We investigate the weak decays of ${\overline{B}}_{s}^{0}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}$ to charm hadrons based on the dynamical supersymmetry between the $\overline{s}$ quark and the $ud$ diquark. We derive a new sum rule relating the decay rates of the processes ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}{P}^{\ensuremath{-}}$, ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{*+}{P}^{\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{P}^{\ensuremath{-}}$, where ${P}^{\ensuremath{-}}$ is a negatively charged meson, such as ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{\ensuremath{-}}$. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the $\overline{s}$ quark and the $ud$ diquark is also seen in the wave functions of the heavy hadrons and suggests that the $ud$ diquark can be regarded as a valid effective constituent for heavy hadrons.