Measurements of the branching fractions of the $P$-wave charmonium spin-singlet state $h_c{(}^1{P}_1)\to h^{+}{h}^{-}\ddot{I}{€}^0/\hat{I}\cdot$

Abstract

Based on $(2712.4\pm 14.3)\times 10^6$ $\ddot{I}ˆ(3686)$ events, we investigate four hadronic decay modes of the $P$-wave charmonium spin-singlet state $h_c{(}^1{P}_1)\to h^{+}{h}^{-}\ddot{I}{€}^0/\hat{I}\cdot$ ($h=\ddot{I}€$ or $K$) via the process $\ddot{I}ˆ(3686)\to \ddot{I}{€}^0{h}_c$ at BESIII. The $h_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ decay is observed with a significance of 9.6$\ddot{I}ƒ$ after taking into account systematic uncertainties. Evidences for $h_c\to K^{+}{K}^{-}\ddot{I}{€}^0$ and $h_c\to K^{+}{K}^{-}\hat{I}\cdot$ are found with significances of $3.5\ddot{I}ƒ$ and $3.3\ddot{I}ƒ$, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be $\mathcal{B}(h_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)=(1.36\pm 0.16\pm 0.14)\times 10^{-3}$, $\mathcal{B}(h_c\to K^{+}{K}^{-}\ddot{I}{€}^0)=(3.26\pm 0.84\pm 0.36)\times 10^{-4}$, and $\mathcal{B}(h_c\to K^{+}{K}^{-}\hat{I}\cdot )=(3.13\pm 1.08\pm 0.38)\times 10^{-4}$, where the first uncertainties are statistical and the second are systematic. No significant signal of $h_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot$ is found, and the upper limit of its decay branching fraction is determined to be $\mathcal{B}(h_c\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}\cdot )<4.0\times 10^{-4}$ at 90% confidence level.

9 pages, 7 figures