Updated measurements of the M1 transition $\psi (3686)\to \gamma {\eta }_c(2S)$ with ${\eta }_c(2S)\to K\bar{K}\pi$

Based on a data sample of $(27.08\pm 0.14)\times {10}^8\psi (3686)$ events collected with the BESIII detector at the BEPCII collider, the M1 transition $\psi (3686)\to \gamma {\eta }_c(2S)$ with ${\eta }_c(2S)\to K\bar{K}\pi$ is studied, where $K\bar{K}\pi$ is $K^{+}{K}^{-}{\pi }^0$ or $K_S^0{K}^{\pm }{\pi }^{\mp }$. The mass and width of the ${\eta }_c(2S)$ are measured to be $(3637.8\pm 0.8(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.2(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))$ MeV/$c^2$ and $(10.5\pm 1.7(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 3.5(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))$ MeV, respectively. The product branching fraction $\mathcal{B}(\psi (3686)\to \gamma {\eta }_c(2S))\times \mathcal{B}({\eta }_c(2S)\to K\bar{K}\pi )$ is determined to be $(0.97\pm 0.06(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.09(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\times {10}^{-5}$. Using $\mathcal{B}\mathcal{R}({\eta }_c(2S)\to K\bar{K}\pi )=(1.86_{-0.49}^{+0.68})\mathrm{\%}$, we obtain the branching fraction of the radiative transition to be $\mathcal{B}\mathcal{R}(\psi (3686)\to \gamma {\eta }_c(2S))=(5.2\pm 0.3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.5(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}{)}_{-1.4}^{+1.9}(\mathrm{e}\mathrm{x}\mathrm{t}\mathrm{r}))\times {10}^{-4}$, where the third uncertainty is due to the quoted $\mathcal{B}\mathcal{R}({\eta }_c(2S)\to K\bar{K}\pi )$.