Effective Lagrangian induced by the anomalous Wess-Zumino action and the exotic resonance state with $I^G(J^{PC})=1^{-}(1^{-+})$ in the $\rho \pi$, $\eta \pi$, ${\eta }^{\prime }\pi$, and $K^{\ast }\bar{K}+{\bar{K}}^{\ast }K$ channels

Abstract

A simple model for the exotic waves with $I^G(J^{PC})=1^{-}(1^{-+})$ in the reactions $VP\to VP$, $VP\to PP$, and $PP\to PP$ is constructed beyond the scope of the quark-gluon approach. The model satisfies unitarity and analyticity and uses as a "priming" the "anomalous" nondiagonal $VPPP$ interaction which couples together the four channels $\rho \pi$, $\eta \pi$, ${\eta }^{\prime }\pi$, and $K^{\ast }\bar{K}+{\bar{K}}^{\ast }K$. The possibility of the resonancelike behavior of the $I^G(J^{PC})=1^{-}(1^{-+})$ amplitudes belonging to the $\{10\}-\{\overline{10}\}$ and $\{8\}$ representations of SU(3) as well as their mixing is demonstrated explicitly in the $1.3-1.6$ GeV mass range which, according to the current experimental evidence, is really rich in exotics.

Comments: LaTex, 17 pages including 4 figures, version published in Phys. Rev. D