Improved measurement of the decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+(0)}\ddot{I}{€}^{-(0)}$ and search for the rare decay $\hat{I}{\cdot }^{\prime }\to 4\ddot{I}{€}^0$

Abstract

Using a sample of 10 billion $J/\ddot{I}ˆ$ events collected with the BESIII detector, the decays $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0\ddot{I}{€}^0$ and $\hat{I}{\cdot }^{\prime }\to 4\ddot{I}{€}^0$ are studied via the process $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }^{\prime }$. The branching fractions of $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ $\ddot{I}{€}^0$ are measured to be $(8.56\pm 0.25(stat.)\pm 0.23(syst.))\times 10^{-5}$ and $(2.12\pm 0.12(stat.)\pm 0.10(syst.))\times 10^{-4}$, respectively, which are consistent with previous measurements but with improved precision. No significant $\hat{I}{\cdot }^{\prime }\to 4\ddot{I}{€}^0$ signal is observed, and the upper limit on the branching fraction of this decay is determined to be less than $1.24\times 10^{-5}$ at the $90\%$ confidence level. In addition, an amplitude analysis of $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ is performed to extract the doubly virtual isovector form factor $\hat{I}\pm$ for the first time. The measured value of $\hat{I}\pm =1.22\pm 0.33(stat.)\pm 0.04(syst.)$, is in agreement with the prediction of the VMD model.