We analyze the role of final state interactions (FSI) in decay of the lightest exotic meson, with $J^{PC}=1^{-+}{\pi }_1$. We use the relativistic Lippmann-Schwinger equation for two coupled $\pi b_1$ and $\pi \rho$ channels. The first one is the predicted dominant decay mode of the ${\pi }_1$, whereas in the other a narrow ${\pi }_1(1600)$ exotic signal has been reported by the E852 collaboration. The FSI potential is constructed, based on the $\omega$ meson exchange between the two channels. We find that this process introduces corrections to the ${\pi }_1$ widths of the order of only a few MeV. Therefore, we conclude that a substantial $\pi \rho$ mode cannot be generated through level mixing.

• Received 8 January 2005

DOI:https://doi.org/10.1103/PhysRevD.71.056003