Improved measurement of the branching fraction of $h_c\to {\hat{I}}^3\hat{I}{\cdot }^{\prime }/\hat{I}\cdot$ and search for $h_c\to {\hat{I}}^3\ddot{I}{€}^0$

Abstract

The processes $h_c\to {\hat{I}}^{3}P(P=\hat{I}{\cdot }^{\prime },\hat{I}\cdot ,\ddot{I}{€}^0)$ are studied with a sample of $(27.12\pm 0.14)\times 10^8$ $\ddot{I}ˆ(3686)$ events collected by the BESIII detector at the BEPCII collider. The decay $h_c\to {\hat{I}}^3\hat{I}\cdot$ is observed for the first time with the significance of $9.0\ddot{I}ƒ$, and the branching fraction is determined to be $(3.77\pm 0.55\pm 0.13\pm 0.26)\times 10^{-4}$, while $\mathcal{B}(h_c\to {\hat{I}}^3\hat{I}{\cdot }^{\prime })$ is measured to be $(1.40\pm 0.11\pm 0.04\pm 0.10)\times 10^{-3}$, where the first uncertainties are statistical, the second systematic, and the third from the branching fraction of $\ddot{I}ˆ(3686)\to \ddot{I}{€}^0{h}_c$. The combination of these results allows for a precise determination of $R_{h_c}=\frac{\mathcal{B}(h_c\to {\hat{I}}^3\hat{I}\cdot )}{\mathcal{B}(h_c\to {\hat{I}}^3\hat{I}{\cdot }^{\prime })}$, which is calculated to be $(27.0\pm 4.4\pm 1.0)\%$. The results are valuable for gaining a deeper understanding of $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing, and its manifestation within quantum chromodynamics. No significant signal is found for the decay $h_c\to {\hat{I}}^3\ddot{I}{€}^0$, and an upper limit is placed on its branching fraction of $\mathcal{B}(h_c\to {\hat{I}}^3\ddot{I}{€}^0)<5.0\times 10^{-5}$, at the 90$\%$ confidence level.