Amplitude Analysis of the Isospin-Violating Decay $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$

Abstract

Using $(10087\pm 44)\times 10^6$ $J/\ddot{I}ˆ$ events collected with the BESIII detector, we perform the first amplitude analysis of the process $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$. The decay is dominated by the intermediate processes $J/\ddot{I}ˆ\to \ddot{I}{€}^0{b}_1(1235{)}^0\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$, $J/\ddot{I}ˆ\to \ddot{I}{€}^0\ddot{I}(1450{)}^0\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$ and $J/\ddot{I}ˆ\to \hat{I}\cdot h_1(1170)\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$. Contributions from $J/\ddot{I}ˆ\to {\hat{I}}^3{a}_0(980{)}^0\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$, $J/\ddot{I}ˆ\to {\hat{I}}^3{a}_2(1320{)}^0\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$ and $J/\ddot{I}ˆ\to {\hat{I}}^3{a}_2(1700{)}^0\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$ are observed with a statistical significance exceeding $5\ddot{I}ƒ$, constituting the first observation of radiative transitions of $J/\ddot{I}ˆ$ to isospin-triplet scalar mesons. The total branching fraction of $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot \ddot{I}{€}^0$ is measured to be $(25.7\pm 0.3\pm 1.5)\times 10^{-6}$, where the first uncertainty is statistical and the second systematic. This result is consistent with the previous measurement, with the precision improved by more than a factor of two.

12 pages, 2 figures