Final state interactions in decays of the exoticπ1meson

Abstract

We analyze the role of final state interactions (FSI) in decay of the lightest exotic meson, with ${J}^{PC}={1}^{\ensuremath{-}+}{\ensuremath{\pi}}_{1}$. We use the relativistic Lippmann-Schwinger equation for two coupled $\ensuremath{\pi}{b}_{1}$ and $\ensuremath{\pi}\ensuremath{\rho}$ channels. The first one is the predicted dominant decay mode of the ${\ensuremath{\pi}}_{1}$, whereas in the other a narrow ${\ensuremath{\pi}}_{1}(1600)$ exotic signal has been reported by the E852 collaboration. The FSI potential is constructed, based on the $\ensuremath{\omega}$ meson exchange between the two channels. We find that this process introduces corrections to the ${\ensuremath{\pi}}_{1}$ widths of the order of only a few MeV. Therefore, we conclude that a substantial $\ensuremath{\pi}\ensuremath{\rho}$ mode cannot be generated through level mixing.