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Using $X(3823)\to J/ψπ^+π^-$ 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 $ψ(1^3D_2)$. Because the $X(3823)$ is just near the $D\bar{D}^*$ threshold, the decay $X(3823)\to J/ψπ^+π^-$ 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 $\mathrm{d}Γ[X(3823)\to J/ψπ^+π^-]/\mathrm{d}m_{π^+π^-}$, and the corresponding $\mathrm{d}Γ[X(3823)\to J/ψπ^+π^-]/\mathrm{d}\cosθ$ 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.