Updated measurements of the M1 transition $\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)$ with ${\eta }_{c}\left(2S\right)\to K\overline{K}\pi $

Based on a data sample of $\left(2712.4±14.3\right)×{10}^{6}\psi \left(3686\right)$ events collected with the BESIII detector at the BEPCII collider, the M1 transition $\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)$ with ${\eta }_{c}\left(2S\right)\to K\overline{K}\pi $ is studied, where $K\overline{K}\pi $ is ${K}^{+}{K}^{-}{\pi }^{0}$ or ${K}_{S}^{0}{K}^{±}{\pi }^{\mp }$. The mass and width of the ${\eta }_{c}\left(2S\right)$ are measured to be $\left(3637.8±0.8\left(\mathrm{stat}\right)±0.2\left(\mathrm{syst}\right)\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left(10.5±1.7\left(\mathrm{stat}\right)±3.5\left(\mathrm{syst}\right)\right)\text{}\text{}\mathrm{MeV}$, respectively. The product branching fraction $B\left(\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)\right)×B\left({\eta }_{c}\left(2S\right)\to K\overline{K}\pi \right)$ is determined to be $\left(0.97±0.06\left(\mathrm{stat}\right)±0.09\left(\mathrm{syst}\right)\right)×{10}^{-5}$. Using $B\left({\eta }_{c}\left(2S\right)\to K\overline{K}\pi \right)=\left(1.8{6}_{-0.49}^{+0.68}\right)%$, we obtain the branching fraction of the radiative transition to be $B\left(\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)\right)=\left(5.2±0.3\left(\mathrm{stat}\right)±0.5\left(\mathrm{syst}{\right)}_{-1.4}^{+1.9}\left(\mathrm{extr}\right)\right)×{10}^{-4}$, where the third uncertainty is due to the quoted $B\left({\eta }_{c}\left(2S\right)\to K\overline{K}\pi \right)$.