A Study of the \eta \pi^{0} Spectrum and Search for a J^{PC} = 1^{-+} Exotic Meson

TL;DR

This study performs a partial wave analysis of the $ ext{eta} ext{pi}^0$ system produced in $ ext{pi}^- ext{p}$ reactions at 18 GeV/c, investigating the presence of an exotic $J^{PC}=1^{-+}$ meson and analyzing the observed waves and resonances.

Contribution

It provides the first detailed partial wave analysis of the $ ext{eta} ext{pi}^0$ system at high energy, examining the existence of an exotic meson with $J^{PC}=1^{-+}$ and comparing results with Regge phenomenology.

Findings

Clear observation of $a_0(980)$ and $a_2(1320)$ resonances.

Presence of a $P$ wave compatible with an exotic $J^{PC}=1^{-+}$ state.

Difficulty in modeling the $P$ wave as a Breit-Wigner resonance.

Abstract

A partial wave analysis (PWA) of the of the $\eta \pi ^0$ system (where $\eta \to \gamma \gamma$) produced in the charge exchange reaction $\pi ^-p\to \eta \pi ^0n$ at an incident momentum of 18 GeV$/c$ is presented as a function of ${\eta \pi ^0}$ 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 $a_0(980)$ and $a_2(1320)$ 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 $J^{PC}=1^{-+}$ 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 $J^{PC} = 1^{-+}$ meson decaying into $\eta \pi^0$ with a mass near 1.4 GeV$/c^2$.