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

Abstract

A precision measurement of the matrix elements for $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ and $\hat{I}\cdot \to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$ decays is performed using a sample of $(10087\pm 44)\times 10^6$ $J/\ddot{I}ˆ$ decays collected with the BESIII detector. The decay $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot$ is used to select clean samples of 631,686 $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decays and 272,322 $\hat{I}\cdot \to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The non-zero $g{X}^{2}Y$ term for the decay mode $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\hat{I}\cdot \to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\hat{I}\cdot \to \ddot{I}{€}^0\ddot{I}{€}^0\ddot{I}{€}^0$ decay, and no obvious structure around the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ mass threshold is observed.

13 pages, 6 figures