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

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

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