Measurement of the matrix elements for the decays $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^0\ddot{I}{€}^0$

Abstract

Based on a sample of $1.31\times 10^9$ $J/\ddot{I}ˆ$ events collected with the BESIII detector, the matrix elements for the decays $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^0\ddot{I}{€}^0$ are determined using 351,016 $\hat{I}{\cdot }^{\prime }\to (\hat{I}\cdot \to {\hat{I}}^3{\hat{I}}^3)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and 56,249 $\hat{I}{\cdot }^{\prime }\to (\hat{I}\cdot \to {\hat{I}}^3{\hat{I}}^3)\ddot{I}{€}^0\ddot{I}{€}^0$ 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 $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^0\ddot{I}{€}^0$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in $\hat{I}{\cdot }^{\prime }\to \hat{I}\cdot \ddot{I}{€}^0\ddot{I}{€}^0$ is observed.

11 pages, 7 figures