ρ′(1600)and approximate helicity selection rules for the meson transitionsB→ωπ, etc., in chiralSU(3)⊗SU(3)charge algebra
Abstract
The possible existence of approximate helicity selection rules for some meson transitions such as $B\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$ and ${K}_{B}\ensuremath{\rightarrow}K^{*}\ensuremath{\pi}$, etc., is discussed. The argument is based on the approximate saturation of the charge algebra, $[{A}_{i},{A}_{j}]=i{f}_{\mathrm{ijk}}{V}_{k}$. A remark is made on the role of ${\ensuremath{\rho}}^{\ensuremath{'}}(1600)$ for this saturation and also on some constraints imposed on the ${\ensuremath{\rho}}^{\ensuremath{'}}$ coupling. The over-all consistency of the approximate saturation considered [in the theoretical framework of asymptotic SU(3) and the full chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ charge algebra supplemented by the presence of the exotic commutators which characterize the chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ symmetry breaking] is also demonstrated.
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