Observation of $\psi (3686)\to e^{+}{e}^{-}{\chi }_{cJ}$ and ${\chi }_{cJ}\to e^{+}{e}^{-}J/\psi$

Using $4.479\times 10^8\psi (3686)$ events collected with the BESIII detector, we search for the decays $\psi (3686)\to e^{+}{e}^{-}{\chi }_{cJ}$ and ${\chi }_{cJ}\to e^{+}{e}^{-}J/\psi$, where $J=0$, 1, 2. The decays $\psi (3686)\to e^{+}{e}^{-}{\chi }_{cJ}$ and ${\chi }_{cJ}\to e^{+}{e}^{-}J/\psi$ are observed for the first time. The measured branching fractions are $\mathcal{B}\mathbf{(}\psi (3686)\to e^{+}{e}^{-}{\chi }_{cJ}\mathbf{)}=(11.7\pm 2.5\pm 1.0)\times {10}^{-4}$, $(8.6\pm 0.3\pm 0.6)\times {10}^{-4}$, $(6.9\pm 0.5\pm 0.6)\times {10}^{-4}$ for $J=0$, 1, 2, and $\mathcal{B}({\chi }_{cJ}\to e^{+}{e}^{-}J/\psi )=(1.51\pm 0.30\pm 0.13)\times {10}^{-4}$, $(3.73\pm 0.09\pm 0.25)\times {10}^{-3}$, $(2.48\pm 0.08\pm 0.16)\times {10}^{-3}$ for $J=0$, 1, 2, respectively. The ratios of the branching fractions $\mathcal{B}\mathbf{(}\psi (3686)\to e^{+}{e}^{-}{\chi }_{cJ}\mathbf{)}/\mathcal{B}\mathbf{(}\psi (3686)\to \gamma {\chi }_{cJ}\mathbf{)}$ and $\mathcal{B}\mathbf{(}{\chi }_{cJ}\to e^{+}{e}^{-}J/\psi \mathbf{)}/\mathcal{B}\mathbf{(}{\chi }_{cJ}\to \gamma J/\psi \mathbf{)}$ are also reported. Also, the $\alpha$ values of helicity angular distributions of the $e^{+}{e}^{-}$ pair are determined for $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c1,2}$ and ${\chi }_{c1,2}\to e^{+}{e}^{-}J/\psi$.

Figure 1

Scatter plot of $M(\gamma J/\psi )$ versus $M(e^{+}{e}^{-}J/\psi )$ for data. The horizontal red dashed lines and vertical blue dashed lines indicate the positions of the ${\chi }_{cJ}$ masses in the $M(\gamma J/\psi )$ and $M(e^{+}{e}^{-}J/\psi )$ distributions, respectively.

Figure 2

Data (points with error bars) distributions of (left) $M(\gamma J/\psi )$ and (right) $M(e^{+}{e}^{-}J/\psi )$. The red solid curve is the overall fit result, the green long-dashed curve is for the background (left) $\psi (3686)\to \gamma {\chi }_{c0}$, ${\chi }_{c0}\to e^{+}{e}^{-}J/\psi$ and (right) $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c0}$, ${\chi }_{c0}\to \gamma J/\psi$, the blue dashed curve is for QED background, and the pink dashed-dotted curve in right plot is for the backgrounds from $\psi (3686)$ decays.

Figure 3

Data to MC simulation comparisons of $q$ distribution for the decays (a) $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c1}$, (b) $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c2}$, (c) ${\chi }_{c1}\to e^{+}{e}^{-}J/\psi$, and (d) ${\chi }_{c2}\to e^{+}{e}^{-}J/\psi$. The points with error bars are data and the red histograms are for the signal MC simulation.

Figure 4

Distributions of efficiency corrected $\cos {\theta }_{e^{+}{e}^{-}}$ for the decays (a) $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c1}$, (b) $\psi (3686)\to e^{+}{e}^{-}{\chi }_{c2}$, (c) ${\chi }_{c1}\to e^{+}{e}^{-}J/\psi$, and (d) ${\chi }_{c2}\to e^{+}{e}^{-}J/\psi$. The red line is the fit to $1+\alpha {\cos }^2{\theta }_{e^{+}{e}^{-}}$.