Updated measurements of the M1 transition $ψ(3686) \to γη_{c}(2S)$ with $η_{c}(2S) \to K \bar{K} π$

Based on a data sample of $(27.08 \pm 0.14 ) \times 10^8~ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, the M1 transition $ψ(3686) \to γη_{c}(2S)$ with $η_{c}(2S) \to K\bar{K}π$ is studied, where $K\bar{K}π$ is $K^{+} K^{-} π^{0}$ or $K_{S}^{0}K^{\pm}π^{\mp}$. The mass and width of the $η_{c}(2S)$ are measured to be $(3637.8 \pm 0.8 (\rm {stat}) \pm 0.2 (\rm {syst}))$ MeV/$c^{2}$ and $(10.5 \pm 1.7 (\rm {stat}) \pm 3.5 (\rm {syst}))$ MeV, respectively. The product branching fraction $\mathcal{B}\left(ψ(3686) \rightarrow γη_{c}(2 S)\right) \times \mathcal{B}(η_{c}(2 S) \rightarrow K \bar{K} π)$ is determined to be $(0.97 \pm 0.06 (\rm {stat}) \pm 0.09 (\rm {syst})) \times 10^{-5}$. Using $\mathcal{BR}(η_{c}(2S)\to K\bar{K}π)=(1.86^{+0.68}_{-0.49})\%$, we obtain the branching fraction of the radiative transition to be $\mathcal{BR}(ψ(3686) \to γη_{c}(2S)) = (5.2 \pm 0.3 (\rm {stat}) \pm 0.5 (\rm {syst}) ^{+1.9}_{-1.4} (extr)) \times 10^{-4}$, where the third uncertainty is due to the quoted $\mathcal{BR}(η_{c}(2S) \to K\bar{K}π)$.