Amplitude Analysis of the Decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$

Abstract

Based on a sample of $1.31\times 10^9$ $J/\ddot{I}ˆ$ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$ is performed. A significant $P$-wave contribution from $\hat{I}{\cdot }^{\prime }\to \ddot{I}{}^{\pm }\ddot{I}{€}^{\mp }$ is observed for the first time in $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$. The branching fraction is determined to be $\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{}^{\pm }\ddot{I}{€}^{\mp })=(7.44\pm 0.60\pm 1.26\pm 1.84)\times 10^{-4}$, where the first uncertainty is statistical, the second systematic, and the third model dependent. In addition to the nonresonant $S$-wave component, there is a significant $\ddot{I}ƒ$ meson component. The branching fractions of the combined $S$-wave components are determined to be $\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0{)}_S=(37.63\pm 0.77\pm 2.22\pm 4.48)\times 10^{-4}$ and $\mathcal{B}(\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0)=(35.22\pm 0.82\pm 2.54)\times 10^{-4}$, respectively. The latter one is consistent with previous BESIII measurements.

7 pages, 3 figures