Improved measurement of the branching fractions for $J/\ddot{I}ˆ\to {\hat{I}}^3\ddot{I}{€}^0$, ${\hat{I}}^3\hat{I}\cdot$ and ${\hat{I}}^3\hat{I}{\cdot }^{\prime }$

Abstract

Using a data sample of $(1.0087\pm 0.0044)\times 10^{10}$ $J/\ddot{I}ˆ$ events collected with the BESIII detector, the decays of $J/\ddot{I}ˆ\to {\hat{I}}^3\ddot{I}{€}^0(\hat{I}\cdot ,\hat{I}{\cdot }^{\prime })\to {\hat{I}}^3{\hat{I}}^3{\hat{I}}^3$ are studied. Newly measured branching fractions are $\mathcal{B}$$(J/\ddot{I}ˆ\to {\hat{I}}^3\ddot{I}{€}^0)$=$(3.34\pm 0.02\pm 0.09)\times 10^{-5}$, $\mathcal{B}$$(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot )$=$(1.096\pm 0.001\pm 0.019)\times 10^{-3}$ and $\mathcal{B}$$(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }^{\prime })$=$(5.40\pm 0.01\pm 0.11)\times 10^{-3}$, where the first uncertainties are statistical and the second are systematic. These results are consistent with the world average values within two standard deviations. The ratio of partial widths $\hat{I}“(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }^{\prime })/\hat{I}“(J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot )$ is measured to be $4.93\pm 0.13$. The singlet-octet pseudoscalar mixing angle $\hat{I}{¸}_P$ is determined to be $\hat{I}{¸}_P=-(22.11\pm 0.26{)}^{\circ }$ or $-(19.34\pm 0.34{)}^{\circ }$ with two different phenomenological models.