Study of the $\eta {\pi }^0$ spectrum and search for a $J^{\mathrm{PC}}{=1\mathrm{}}^{-+}$ exotic meson

A partial wave analysis (PWA) of the $\eta {\pi }^0$ system (where $\overrightarrow{\eta }\gamma \gamma )$ produced in the charge exchange reaction ${\pi }^{-}\overrightarrow{p}\eta {\pi }^{0}n$ at an incident momentum of $18\mathrm{GeV}/c$ is presented as a function of the $\eta {\pi }^0$ invariant mass $m_{\eta {\pi }^0}$ and momentum transfer squared $t_{{\pi }^{-}\to \eta \pi },$ from the incident ${\pi }^{-}$ to the outgoing $\eta {\pi }^0$ system. S, P, and D waves were included in the PWA. The $a_0\mathrm{}\left(980\right)\mathrm{}$ and $a_2\mathrm{}\left(1320\right)\mathrm{}$ states are clearly observed in the overall $\eta {\pi }^0$ effective mass distribution as well as in the amplitudes associated with S wave and D waves, respectively, after partial wave decomposition. The observed distributions in moments (averages of spherical harmonics) were compared to the results from the PWA and the two are consistent. The distribution in $t_{{\pi }^{-}\to \eta \pi }$ for individual D waves associated with natural and unnatural parity exchange in the t channel are consistent with Regge phenomenology. Of particular interest in this study is the P wave since this leads to an exotic $J^{\mathrm{PC}}{=1\mathrm{}}^{-+}$ for the $\eta \pi$ system. A P wave is present in the data; however, attempts to describe the mass dependence of the amplitude and phase motion with respect to the D wave as a Breit-Wigner resonance are problematic. This has implications regarding the existence of a reported exotic $J^{\mathrm{PC}}{=1\mathrm{}}^{-+}$ meson decaying into $\eta {\pi }^0$ with a mass near $1.4\mathrm{GeV}{/c}^2.$