First observation of the $M1$ transition $\psi(3686) \rightarrow \gamma\eta_c (2S)$

Abstract

Using a sample of $106×10^6$ $\psi(3686)$ 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: $\psi(3686)→\gamma\eta_c (2S)$. Analyses of the processes $\psi(3686)→\gamma\eta_c (2S)$ with $\eta_c (2S)→K^{0}_{S} K^{±}\pi^∓$ 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 $(M(\eta_c (2S))=3637.6±2.9_{\text{stat}}±1.6_{\text{syst}} MeV/c^2)$, width $(\Gamma(\eta_c (2S))=16.9±6.4_{\text{stat}}±4.8_{\text{syst}} MeV)$, and the product branching-fraction $(\mathscr{B}(\psi(3686)→\gamma\eta_c (2S))×\mathscr{B}(\eta_c (2S)→K\overline{K}_π)=(1.30±0.20_{stat}±0.30_{\text{syst}})×10^{−5})$. Combining our result with a BABAR measurement of $\mathscr{B}(\eta_c (2S)→K\overline{K}_π)$, we find the branching fraction of the $M1$ transition to be $\mathscr{B}(\psi(3686)→\gamma\eta_c (2S))=(6.8±1.1_{\text{stat}}±4.5_{\text{syst}})×10^{−4}$.