Using $X(3823)\to J/ψπ^+π^-$ to identify coupled-channel effects

Very recently, a new charmonium-like state $X(3823)$ was observed by the Belle and BESIII experiments, which is a good candidate of $D$-wave charmonium $\psi(1^3D_2)$. Since the $X(3823)$ is just below the $D\bar{D}^*$ threshold, the decay $X(3823)\to J/\psi\pi^+\pi^-$ can be a golden channel to test the significance of coupled-channel effects. In this work, this decay is considered including both the hidden-charm dipion and the usual QCDME contributions. The partial decay width, the dipion invariant mass spectrum distribution $\mathrm{d}\Gamma[X(3823)\to J/\psi\pi^+\pi^-]/\mathrm{d}m_{\pi^+\pi^-}$, and the corresponding $\mathrm{d}\Gamma[X(3823)\to J/\psi\pi^+\pi^-]/\mathrm{d}\cos\theta$ distribution are computed. Many parameters are determined from existing experimental data, leaving the results mainly dependent on only one unknown phase between the QCDME and hidden-charm dipion amplitudes.