Precision measurement of the matrix elements for $\eta\to\pi^+\pi^-\pi^0$ and $\eta\to\pi^0\pi^0\pi^0$ decays

TL;DR

This study provides a high-precision measurement of the matrix elements for eta decays into three pions, confirming some theoretical predictions and exploring asymmetries and cusp effects with a large data sample.

Contribution

It offers the first high-statistics measurement of eta decay matrix elements and investigates decay asymmetries and cusp effects with improved precision.

Findings

Matrix elements agree with previous measurements

Confirmation of non-zero $gX^2Y$ term in $ o ext{pi}^+ ext{pi}^- ext{pi}^0$ decay

No significant cusp effect observed in $ o ext{pi}^0 ext{pi}^0 ext{pi}^0$ decay

Abstract

A precision measurement of the matrix elements for $\eta\to\pi^+\pi^-\pi^0$ and $\eta\to\pi^0\pi^0\pi^0$ decays is performed using a sample of $(10087\pm44)\times10^6$ $J/\psi$ decays collected with the BESIII detector. The decay $J/\psi \to \gamma \eta$ is used to select clean samples of 631,686 $\eta\to\pi^+\pi^-\pi^0$ decays and 272,322 $\eta\to\pi^0\pi^0\pi^0$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The non-zero $gX^2Y$ term for the decay mode $\eta\to\pi^+\pi^-\pi^0$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\eta\to\pi^+\pi^-\pi^0$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\eta\to\pi^0\pi^0\pi^0$ decay, and no obvious structure around the $\pi^+\pi^-$ mass threshold is observed.