Search

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., Comment: 5 pages, 1 figure, 1 table

Speculating that the $ud$ diquark with spin 0 has a similar mass to the constituent $s$ quark, we introduce a symmetry between the $s$ quark and the $\overline{ud}$ diquark. Constructing an algebra for this symmetry, we regard a triplet of the $s$ quarks with spin up and down and the $\overline{ud}$ diquark with spin 0 as a fundamental representation of this algebra. We further build higher representations constructed by direct products of the fundamental representations. We propose assignments of hadrons to the multiples of this algebra. We find in particular that $\{D_{s}, D_{s}^{*}, \Lambda_{c}\}$, $\{\eta_{s}, \phi, \Lambda, f_{0}(1370)\}$ and $\{\Omega_{c}, T_{sc}\}$ form a triplet, a nonet and a quintet, respectively, where $T_{sc}$ is a genuine tetraquark meson composed of $\overline{ud}sc$. We also find a mass relation between them by introducing the symmetry breaking due to the mass difference between the $s$ quark and the $\overline{ud}$ diquark. The masses of possible tetraquarks $\overline{ud}sc$ and $\overline{ud}sb$ are estimated from the symmetry breaking and the masses of $\Omega_{c}$ and $\Omega_{b}$ to be 2.942 GeV and 6.261 GeV, respectively., Comment: 22 pages