$SU(3)$ Classification of $p$-Wave $\eta \pi$ and ${\eta }^{\mathrm{\prime }}\pi$ Systems

An exotic meson, the ${\pi }_1(1400)$ with $J^{PC}=1^{-+}$, has been seen to decay into a p-wave $\eta \pi$ system. If this decay conserves flavor SU(3), then it can be shown that this exotic meson must be a four-quark state ($q\bar q+q\bar q$)belongingtoaflavor${\bf10}\oplus{\bf\bar{10}}$ representation of SU(3). In contrast, the ${\pi }_1(1600)$ with a substantial decay mode into ${\eta }^{\mathrm{\prime }}\pi$ is likely to be a member of a flavor octet.