Effective Lagrangian induced by the anomalous Wess-Zumino action and the exotic resonance state with $I^G(J^{PC})=1^-(1^{-+})$ in the $\rho\pi$, $\eta\pi$, $\eta'\pi$, and $K^*\bar K+\bar K^*K$ 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 $\rho\pi$, $\eta\pi$, $\eta'\pi$, and $K^*\bar K+\bar K^*K$. The possibility of the resonancelike behavior of the $I^G(J^{PC})=1^-(1^{-+})$ amplitudes belonging to the $\{10\}- \{\bar{10}\}$ 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.