Study of Dalitz-Plot Distributions of the Decays η→π+π−π0 and η→π+π−γ

Abstract

Based on 80 884 events, we obtained the matrix element squared for the decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0:{\left|M\mathrm{}\right(x,y\left)\right|}^2=1-(1.08\mathrm{}\pm 0.014)y+(0.03\pm 0.03)y^2+(0.05\mathrm{}\pm 0.03)x^2$ where $x$ and $y$ are the usual Dalitz-plot coordinates. The $\gamma$-ray energy spectrum was measured for 18 150 $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ events. $\rho$ dominance of the ${\pi }^{+}{\pi }^{-}$ final state is strongly favored over a simple gauge-invariant matrix element.