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.
Highlights
We investigate the weak decays of B 0s and Λb to charm hadrons based on the dynamical supersymmetry between the squark and the ud diquark
It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the squark and the ud diquark is 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
Both objects have the same color charge 3 ̄ and same electric charge. They are known to have a similar mass around 500 MeV. This is a supersymmetry between a boson and a fermion, but not a symmetry for fundamental particles, rather a dynamical symmetry for quasiparticles which are regarded as effective elements of the dynamics like the constituent quarks
Summary
AMANO, JIDO, and LEUPOLD stemming from the mass difference among the light constituent quarks. The symmetry of the wave functions can be seen in the decay of the heavy hadrons, where the decay rates are expressed by the matrix elements of the parent and daughter particles with the wave functions of the initial and final states For this purpose, we compare the weak decays of B 0s into Dþs and DÃsþ with those of Λb into Λc. In the former process, the squark or the ud diquark is a spectator in the weak decay, and the weak transition of the b quark commonly contributes to the decays of B 0s and Λb and the wave functions of the squark in B 0s and of the ud diquark in Λb are responsible for the difference of their decay rates The latter process involves two particles in the initial state. For the decay rate of an unpolarized Λb to Λc, we take a spin average of the initial Λb and sum up all of the spin states of the final Λc, XðMμ ÞÃMν 1⁄4 1 ðMμÃMν þ MμÃMν
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