Measurement of the Matrix Elements for the Decays $\eta \rightarrow \pi^{+}\pi^{-}\pi^0$ and $\eta/\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$

TL;DR

This study measures the decay matrix elements of eta and eta prime particles into three pions using a large data sample, providing more precise Dalitz plot parameters and confirming the significance of final state interactions.

Contribution

It presents the first detailed Dalitz plot analysis of eta and eta prime decays with significantly improved precision, confirming the role of final state interactions.

Findings

Measured Dalitz plot slope parameters with improved precision.

Confirmed the importance of final state interactions.

Results are consistent with previous measurements.

Abstract

Based on a sample of $1.31 \times 10^9$ $J/\psi$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $\eta\rightarrow\pi^{+}\pi^{-}\pi^0$ events, 33,908 $\eta\rightarrow\pi^0\pi^0\pi^0$ events and 1,888 $\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$ events are performed. The measured matrix elements of $\eta\rightarrow\pi^+\pi^-\pi^0$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $\eta\rightarrow\pi^0\pi^0\pi^0$ and $\eta^{\prime}\rightarrow\pi^0\pi^0\pi^0$ are determined to be $-0.055 \pm 0.014 \pm 0.004$ and $-0.640 \pm 0.046 \pm 0.047$, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of three. Final state interactions are found to have an important role in those decays.