Effective Lagrangians Induced by the Anomalous Wess-Zumino Action and $I^G(J^{PC})=1^{-}(1^{-+})$ Exotic States

Abstract

A simple dynamical model for the exotic waves with $I^G(J^{PC})=1^{-}(1^{-+})$ in the reactions $\rho \pi \to \rho \pi$, $\rho \pi \to \eta \pi$, $\rho \pi \to {\eta }^{\prime }\pi$, $\rho \pi \to (K^{\ast }\bar{K}+{\bar{K}}^{\ast }K)$, and in the related ones, is constructed beyond the scope of the quark-gluon approach. The model satisfies unitarity and analyticity and uses as a "priming" the anomalous non-diagonal $VPPP$ 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 resonance-like 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 experiments, is really rich in exotics.

Comments: Parallel session talk given at HADRON 2001, Protvino, Russia, August 28, 2001. LaTex, 5 pages, 1 figure