Investigation of the $X(4020)$ peak in the $D^*\bar D^*$ and $πh_c$ channels

Abstract: In this paper, the nature of $X(4020)$ observed in the vicinity of the $D^*\bar D^*$ threshold of the $\pi h_c$ and $D^*\bar D^*$ distributions is studied. Using a model containing one bare-particle state with the $\pi h_c$ and $D^*\bar D^*$ one-loop self energies, we make a fit to the $\pi h_c$ and $D^*\bar D^*$ distributions of the $e^+e^-\to\pi^+\pi^-h_c$ and $e^+e^-\to\pi^- D^{*+}\bar D^{*0}$ reactions reported by the BESIII Collaboration. It is found that both structures seen in the $\pi h_c$ and $D^*\bar D^*$ channels are described well with one resonant state which can be associated with $X(4020)$ while the obtained $X(4020)$ mass and width are found to be larger than those in the latest PDG. We evaluate the scattering length and effective range of the $S$-wave $D^*\bar D^*$ pair with spin $J=1$ related to the $X(4020)$ properties which can be tested with model calculations or future lattice QCD study. Our analysis suggests that a large part of $X(4020)$ may come from a bare-particle state originating from some short-range dynamics other than the $D^*\bar D^*$ channel.