First Observation of the $M1$ Transition $\psi (3686)\to \gamma {\eta }_c(2S)$

Using a sample of $106\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector at the BEPCII storage ring, we have made the first measurement of the $M1$ transition between the radially excited charmonium $S$-wave spin-triplet and the radially excited $S$-wave spin-singlet states: $\psi (3686)\to \gamma {\eta }_c(2S)$. Analyses of the processes $\psi (3686)\to \gamma {\eta }_c(2S)$ with ${\eta }_c(2S)\to K_S^0{K}^{\pm }{\pi }^{\mp }$ and $K^{+}{K}^{-}{\pi }^0$ give an ${\eta }_c(2S)$ signal with a statistical significance of greater than 10 standard deviations under a wide range of assumptions about the signal and background properties. The data are used to obtain measurements of the ${\eta }_c(2S)$ mass ($M\mathbf{(}{\eta }_c(2S)\mathbf{)}=3637.6\pm {2.9}_{\mathrm{stat}}\pm {1.6}_{\mathrm{syst}}\mathrm{MeV}/c^2$), width ($\Gamma \mathbf{(}{\eta }_c(2S)\mathbf{)}=16.9\pm {6.4}_{\mathrm{stat}}\pm {4.8}_{\mathrm{syst}}\mathrm{MeV}$), and the product branching-fraction ($\mathcal{B}\mathbf{(}\psi (3686)\to \gamma {\eta }_c(2S)\mathbf{)}\times \mathcal{B}\mathbf{(}{\eta }_c(2S)\to K\overline{K}\pi \mathbf{)}=(1.30\pm {0.20}_{\mathrm{stat}}\pm {0.30}_{\mathrm{syst}})\times {10}^{-5}$). Combining our result with a BABAR measurement of $\mathcal{B}\mathbf{(}{\eta }_c(2S)\to K\overline{K}\pi \mathbf{)}$, we find the branching fraction of the $M1$ transition to be $\mathcal{B}\mathbf{(}\psi (3686)\to \gamma {\eta }_c(2S)\mathbf{)}=(6.8\pm {1.1}_{\mathrm{stat}}\pm {4.5}_{\mathrm{syst}})\times {10}^{-4}$.

Figure 1

The invariant-mass spectrum for $K_S^0{K}^{\pm }{\pi }^{\mp }$ (left panel), $K^{+}{K}^{-}{\pi }^0$ (right panel), and the simultaneous likelihood fit to the three resonances and combined background sources as described in the text.