Determination of $\eta\to\pi^+\pi^-\pi^0$ Dalitz plot slopes and asymmetries with the KLOE detector

TL;DR

This study uses the KLOE detector to precisely measure the Dalitz plot slopes and asymmetries in the decay ta, confirming $C$-invariance and demonstrating consistency across decay channels.

Contribution

The paper provides the most precise measurements of ta Dalitz plot parameters and confirms $C$-invariance in this decay mode.

Findings

Precise Dalitz plot slope parameters obtained.

Confirmed $C$-invariance in ta decay.

Demonstrated consistency between ta and ta decay channels.

Abstract

We have studied, with the KLOE detector at the DA$\Phi$NE $\Phi$-Factory, the dynamics of the decay $\eta\to\pi^+\pi^-\pi^0$ using $\eta$ mesons from the decay $\phi\to\eta\gamma$ for an integrated luminosity ${\mathcal L}$ = 450 pb$^{-1}$. From a fit to the Dalitz plot density distribution we obtain a precise measurement of the slope parameters. An alternative parametrization relates the $\pi^+\pi^-\pi^0$ slopes to that for $\eta\to 3\pi^0$ showing the consistency of KLOE results for both channels. We also obtain the best confirmation of the $C$-invariance in the $\eta\to\pi^+\pi^-\pi^0$ decay.