Productions of $X(3872)$/$Z_c(3900)$ and $X_2(4013)$/$Z_c(4020)$ in $Y(4220)$ and $Y(4360)$ decays

Abstract

The two excited vector charmonium states $Y(4220)$ and $Y(4360)$ are difficult to be understood as pure $c\bar{c}$ charmonium states. Since they are located close to the mass thresholds of $\bar{D}{D}_1$ and ${\bar{D}}^{\ast }{D}_1$, they can be viewed as $\bar{D}{D}_1$ and ${\bar{D}}^{\ast }{D}_1$ molecules. Furthermore, recent studies indicated that the exotic states $X(3872)$/$Z_c(3900)$ and $X_2(4013)$/$Z_c(4020)$ are the isoscalar/isovector $\bar{D}{D}^{\ast }$ and isoscalar/isovector ${\bar{D}}^{\ast }{D}^{\ast }$ molecules, respectively. In this work, in the molecular picture, we employ the triangle diagram mechanism to study the productions of $Z_c(3900)$ and $X(3872)$ in the pionic and radiative decays of $Y(4220)$, as well as their heavy-quark spin symmetry (HQSS) partners, i.e., the productions of $Z_c(4020)$ and $X_2(4013)$ in the pionic and radiative decays of $Y(4360)$. Using the effective Lagrangian approach, we obtain the ratios of the branching fractions $\mathcal{B}[Y(4360)\to Z_c(4020)\ddot{I}€]/\mathcal{B}[Y(4220)\to Z_c(3900)\ddot{I}€]=1.2$ and $\mathcal{B}[Y(4360)\to X_2(4013){\hat{I}}^3]/\mathcal{B}[Y(4220)\to X(3872){\hat{I}}^3]=0.5$, almost independent of model parameters, which indicate that the productions of $X_2(4013)$ and $Z_c(4020)$ in the radiative and pionic decays of $Y(4360)$ are likely to be measured in the future. The experimental studies of the predicted decay modes will help verify the molecular nature of $X(3872)$, $Z_c(3900)$, and $Y(4220)$. We hope the present work can stimulate experimental and further theoretical studies on these decay modes.

This version is to be published in Phys. Rev. D