Study of $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ decays to $\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\cdot }^{\prime }$

Abstract

Using the data samples of $1.31\times 10^9$ $J/\ddot{I}ˆ$ events and $4.48\times 10^8$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, partial wave analyses on the decays $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\cdot }^{\prime }$ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ decays to $\ddot{I}\hat{I}{\cdot }^{\prime }$. In the $J/\ddot{I}ˆ$ decay, the branching fraction $\mathcal{B}(J/\ddot{I}ˆ\to \ddot{I}\hat{I}{\cdot }^{\prime })$ is determined to be $(7.90\pm 0.19(\mathrm{stat})\pm 0.49(\mathrm{sys}))\times 10^{-5}$. Two solutions are found in the $\ddot{I}ˆ(3686)$ decay, and the corresponding branching fraction $\mathcal{B}(\ddot{I}ˆ(3686)\to \ddot{I}\hat{I}{\cdot }^{\prime })$ is $(1.02\pm 0.11(\mathrm{stat})\pm 0.24(\mathrm{sys}))\times 10^{-5}$ for the case of constructive interference, and $(5.69\pm 1.28(\mathrm{stat})\pm 2.36(\mathrm{sys}))\times 10^{-6}$ for destructive interference. As a consequence, the ratios of branching fractions between $\ddot{I}ˆ(3686)$ and $J/\ddot{I}ˆ$ decays to $\ddot{I}\hat{I}{\cdot }^{\prime }$ are calculated to be $(12.9\pm 1.4(\mathrm{stat})\pm 3.1(\mathrm{sys}))$\% and $(7.2\pm 1.6(\mathrm{stat})\pm 3.0(\mathrm{sys}))$\%, respectively. We also determine the inclusive branching fractions of $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ decays to $\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\cdot }^{\prime }$ to be $(1.36\pm 0.02(\mathrm{stat})\pm 0.08(\mathrm{sys}))\times 10^{-4}$ and $(1.51\pm 0.14(\mathrm{stat})\pm 0.23(\mathrm{sys}))\times 10^{-5}$, respectively.

13 pages, 5 figures, 6 tables