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

TL;DR

This paper derives a new sum rule for the decay rates of certain bottom hadrons based on a dynamical supersymmetry between the strange antiquark and the ud diquark, supported by experimental data.

Contribution

It introduces a novel sum rule relating decay rates of bottom hadrons based on supersymmetry, highlighting the diquark as an effective constituent in heavy hadrons.

Findings

Observed decay rates satisfy the sum rule very well.

Supports the view of the ud diquark as an effective constituent.

Indicates supersymmetry is reflected in heavy hadron wavefunctions.

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 $\bar B_{s}^{0} \to D_{s}^{+} P^{-}$, $\bar B_{s}^{0} \to D_{s}^{*+} P^{-}$ 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.