Measurement of the matrix elements for the decays $\eta^{\prime}\rightarrow\eta\pi^+\pi^-$ and $\eta^{\prime}\rightarrow\eta\pi^0\pi^0$

TL;DR

This study measures the matrix elements for specific eta prime decays using a large data sample, revealing deviations from simple models and no cusp structure, thereby providing detailed insights into decay dynamics.

Contribution

First precise determination of matrix elements for eta prime decays with detailed Dalitz plot analysis using BESIII data.

Findings

Linear amplitude assumption does not fit data well

Small deviation in matrix elements between charged and neutral decay modes

No cusp structure observed in eta prime to eta pi0 pi0 decay

Abstract

Based on a sample of $1.31\times10^9$ $J/\psi$ events collected with the BESIII detector, the matrix elements for the decays $\eta^{\prime}\to\eta\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ are determined using 351,016 $\eta^{\prime}\to(\eta\to\gamma\gamma)\pi^+\pi^-$ and 56,249 $\eta^{\prime}\to(\eta\to\gamma\gamma)\pi^0\pi^0$ events with background levels less than 1\%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between $\eta^{\prime}\to\eta\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ is observed.