Observation of the $\psi (1\hspace{0.17em}{}^3{D}_2)$ State in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma {\chi }_{c1}$ at BESIII

We report the observation of the $X(3823)$ state in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}X(3823)\to {\pi }^{+}{\pi }^{-}\gamma {\chi }_{c1}$ with a statistical significance of $6.2\sigma$, in data samples at center-of-mass energies $\sqrt{s}=4.230$, 4.260, 4.360, 4.420, and 4.600 GeV collected with the BESIII detector at the BEPCII electron positron collider. The measured mass of the $X(3823)$ state is $(3821.7\pm 1.3\pm 0.7)\mathrm{MeV}/c^2$, where the first error is statistical and the second systematic, and the width is less than 16 MeV at the 90% confidence level. The products of the Born cross sections for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}X(3823)$ and the branching ratio $\mathcal{B}[X(3823)\to \gamma {\chi }_{c1,c2}]$ are also measured. These measurements are in good agreement with the assignment of the $X(3823)$ state as the $\psi (1\hspace{0.17em}{}^3{D}_2)$ charmonium state.

Figure 1

Scatter plots of $M_{\text{recoil}}({\pi }^{+}{\pi }^{-})$ vs $M({\gamma }_{H}J/\psi )$ at (a) $\sqrt{s}=4.230$, (b) 4.260, (c) 4.360, (d) 4.420, and (e) 4.600 GeV. The sum of all the data sets is shown in (f). In each plot, the vertical dashed red lines represent ${\chi }_{c1}$ (left two lines) and ${\chi }_{c2}$ (right two lines) signal regions, and the horizontal lines represent the ${\psi }^{\prime }$ mass range (bottom two lines) and 3.82 GeV (top line), respectively.

Figure 2

Simultaneous fit to the $M_{\text{recoil}}({\pi }^{+}{\pi }^{-})$ distribution of $\gamma {\chi }_{c1}$ events (left) and $\gamma {\chi }_{c2}$ events (right), respectively. Dots with error bars are data, red solid curves are total fit, dashed blue curves are background, and the green shaded histograms are $J/\psi$ mass sideband events.

Figure 3

(a) The $X(3823)$ scattering angle distribution for $X(3823)$ signal events, the inset shows the corresponding $M({\pi }^{+}{\pi }^{-})$ invariant mass distribution per $20\mathrm{MeV}/c^2$ bin; and (b) fit to the energy-dependent cross section of ${\sigma }^B[e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}X(3823)]\mathcal{B}[X(3823)\to \gamma {\chi }_{c1}]$ with the $Y(4360)$ (red solid curve) and the $\psi (4415)$ (blue dashed curve) line shapes. Dots with error bars are data. The red solid (blue dashed) histogram in (a) is MC simulation with a $D$ wave ($S$ wave).