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

Very recently, the Belle and BESIII experiments observed a new charmonium-like state $X(3823)$, which is a good candidate for the $D$-wave charmonium $\psi(1^3D_2)$. Because the $X(3823)$ is just near 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 quantum chromodynamics multipole expansion (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, so the results depend mainly only on one unknown phase between the QCDME and hidden-charm dipion amplitudes.