Search for ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c$ and ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp }$ decays

Based on $(27.12\pm 0.14)\times {10}^8\psi (2S)$ events collected by the BESIII detector, we search for the decay ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c$ via $\psi (2S)\to \gamma {\eta }_c(2S)$. No significant signal is observed, and the upper limit on the product branching fraction $\mathcal{B}(\psi (2S)\to \gamma {\eta }_c(2S))\times \mathcal{B}({\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c$) is determined to be $2.21\times {10}^{-5}$ at the 90% confidence level. In addition, the ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp }$ decay is studied via $\psi (2S)\to \gamma {\eta }_c(2S)$ and is observed with a statistical significance of $10\sigma$ for the first time. The branching fraction of ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp }$ is determined to be ($1.33\pm 0.11\pm 0.40\pm 0.95$)$\times {10}^{-2}$, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is due to the quoted $\mathcal{B}(\psi (2S)\to \gamma {\eta }_c(2S))$.

Figure 1

The Feynman diagram for the process of ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c$.

Figure 2

Distributions of $M({\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp })$ for ${\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c,{\eta }_c\to K_S^0{K}^{\pm }{\pi }^{\mp }$ with 3C kinematic fit (black solid line), $\psi (2S)\to {\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp }$ with 3C kinematic fit (blue solid line) and 4C kinematic fit (blue dashed line) based on MC simulation.

Figure 3

The simultaneous fit to the distributions of (a) $M^{3\mathrm{C}}({\pi }^{+}{\pi }^{-}{K}^{+}{K}^{-}{\pi }^0)$ and (b) $M^{3\mathrm{C}}({\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp })$, and the magnified view of the signal region on a logarithmic scale. The black dots with error bars are data, the red dotted lines are the signal, the green solid lines are the background I, the blue solid lines are the background II, the purple solid lines are the background III, the brown solid lines are other backgrounds $\mathrm{IV}+\mathrm{V}$ in the left figure and IV in the right figure. The red solid lines are the total fit curves.

Figure 4

Normalized likelihood versus $\mathcal{B}(\psi (2S)\to \gamma {\eta }_c(2S))\times \mathcal{B}({\eta }_c(2S)\to {\pi }^{+}{\pi }^{-}{\eta }_c)$ after incorporating the systematic uncertainties. The black arrow corresponds to the upper limit on the product branching fraction at the 90% CL.

Figure 5

(a) Fit to the distribution of $M^{3\mathrm{C}}({\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp })$ and the relative pull distribution. (b) Zoomed $M^{3\mathrm{C}}({\pi }^{+}{\pi }^{-}{K}_S^0{K}^{\pm }{\pi }^{\mp })$ distribution and background residuals. The black dots with error bars are data, the red dotted lines are the signal, the blue solid lines are the background I, the green solid lines are the background II, the purple solid lines are the background III, the brown solid lines are the background IV, the gray solid lines are for the remaining background $\mathrm{V}+\mathrm{VI}+\mathrm{VII}$, and the red solid lines are the total fit curves.