Productions of $X(3872)$/Zc(3900) and X₂(4013)/Zc(4020) in $Y(4220)$ and $Y(4360)$ decays

The two excited vector charmonium states $Y(4220)$ and $Y(4360)$ are difficult to be understood as pure cc̄ charmonium states. Since they are located close to the mass thresholds of D̄D₁ and D̄^*D₁, they can be viewed as D̄D₁ and D̄^*D₁ molecules. Furthermore, recent studies indicated that the exotic states $X(3872)$/Zc(3900) and X₂(4013)/Zc(4020) are the isoscalar/isovector D̄D* and isoscalar/isovector D̄^*D* molecules, respectively. In this work, in the molecular picture, we employ the triangle diagram mechanism to study the productions of Zc(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 Zc(4020) and X₂(4013) in the pionic and radiative decays of $Y(4360)$. Using the effective Lagrangian approach, we obtain the ratios of the branching fractions B[Y(4360) → Zc(4020)π]/B[Y(4220)→ Zc(3900)π]=1.2 and B[Y(4360)→ X₂(4013) γ]/B[Y(4220)→ X(3872)γ]=0.5, almost independent of model parameters, which indicate that the productions of X₂(4013) and Zc(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 $X(3872)$, Zc(3900), and $Y(4220)$. We hope the present work can stimulate experimental and further theoretical studies on these decay modes.