Evidence for the Direct Two-Photon Transition from $\psi (3686)$ to $J/\psi$

The two-photon transition $\psi (3686)\to \gamma \gamma J/\psi$ is studied in a sample of $1.06\times {10}^8$ $\psi (3686)$ decays collected by the BESIII detector. The branching fraction is measured to be $\mathbf{(}3.1\pm 0.6(\mathrm{stat}{)}_{-1.0}^{+0.8}(\mathrm{syst})\mathbf{)}\times {10}^{-4}$ using $J/\psi \to e^{+}{e}^{-}$ and $J/\psi \to {\mu }^{+}{\mu }^{-}$ decays, and its upper limit is estimated to be $4.5\times {10}^{-4}$ at the $90\%$ confidence level. This work represents the first measurement of a two-photon transition among charmonium states. The orientation of the $\psi (3686)$ decay plane and the $J/\psi$ polarization in this decay are also studied. In addition, the product branching fractions of sequential $E1$ transitions $\psi (3686)\to \gamma {\chi }_{cJ}$ and ${\chi }_{cJ}\to \gamma J/\psi (J=0,1,2)$ are reported.

Figure 1

Top: (a) distributions of $M_{\gamma \gamma \mathrm{\text{−}}\mathrm{recoil}}$ in data (points) and in the combined data set (solid line) of MC simulation of $\psi (3686)$ decays (shaded histogram) and continuum backgrounds (dashed line), before the KF is applied. The arrows indicate the window to select a $J/\psi$ candidate. Bottom: scatter plots of $M_{{\gamma }_{\mathrm{sm}}\mathrm{\text{−}}\mathrm{recoil}}$ versus $M_{\gamma \gamma }$ for the $\gamma \gamma e^{+}{e}^{-}$ channel, in (b) data, (c) continuum data, and (d) MC simulated signal, after applying the KF constraint and the $M_{\gamma \gamma \mathrm{\text{−}}\mathrm{recoil}}$ window. The corresponding plots for the $\gamma \gamma {\mu }^{+}{\mu }^{-}$ channel are very similar.

Figure 2

(a) Unbinned maximum likelihood fit to the distribution of $M_{{\gamma }_{\mathrm{sm}}\mathrm{\text{−}}\mathrm{recoil}}$ in data with combination of the two $J/\psi$ decay modes. Thick lines are the sum of the fitting models, and long-dashed lines are the ${\chi }_{cJ}$ shapes. Short-dashed lines represent the two-photon signal processes. The light shaded histogram is $\psi (3686)$ decay backgrounds (yellow), and the dark shaded histogram is non-$\psi (3686)$ backgrounds (green), with the fixed amplitude and shape taken from MC simulation and continuum data. (b) The number of standard deviations, $n_{\sigma }$, of data points from the fitted curves in (a). The rates of the signal process and sequential ${\chi }_{cJ}$ processes are derived from these fits. (c) Distributions of $M_{\gamma \gamma \mathrm{\text{−}}\mathrm{recoil}}$ in data (signals and known backgrounds) with the kinematic requirement $3.44\mathrm{GeV}/c^2<M_{{\gamma }_{\mathrm{sm}}\mathrm{\text{−}}\mathrm{recoil}}<3.48\mathrm{GeV}/c^2$ and with the removal of ${\chi }_{\mathrm{KF}}^2$ and $M_{\gamma \gamma \mathrm{\text{−}}\mathrm{recoil}}$ restrictions. (d) Stacked histograms of the three ${\chi }_{cJ}$ components in (c).

Figure 3

(a) The corrected distribution of the normal angle $\beta$ of the $\psi (3686)$ decay plane, and (b) the helicity angle ${\theta }_{\ell }$ of $J/\psi$ decays. The curves in (a) and (b) present the fits of functions $P_0(1+a{cos}^2\beta )$ and $P_0(1+\alpha {cos}^2{\theta }_{\ell })$, respectively.