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

Abstract

We investigate the weak decays of ${\bar{B}}_s^0$ and ${\Lambda }_b$ 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 ${\bar{B}}_s^0\to D_s^{+}{P}^{-}$, ${\bar{B}}_s^0\to D_s^{\ast +}{P}^{-}$ and ${\Lambda }_b\to {\Lambda }_c{P}^{-}$, where $P^{-}$ is a negatively charged meson, such as ${\pi }^{-}$ 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.

Comments: 5 pages, 1 figure, 1 table