Pionic transitions from $Z_c(4020)$ to $D$ wave charmonia

In the present work, we investigate the charmed meson loops contributions to the pionic transitions from $Z_c(4020{)}^{+}$ to the $D$ wave triplets charmonia by using an effective Lagrangian approach. Our estimations indicate that the predicted branching fraction of $Z_c(4020{)}^{+}\to {\pi }^{+}\psi (1^3{D}_J),J=(1,2,3)$ are much smaller than the one of $Z_c(4020{)}^{+}\to {\pi }^{+}{h}_c$. Thus, searching $Z_c(4020{)}^{\pm }$ in the ${\pi }^{\pm }\psi (1^3{D}_J)$ invariant mass distributions is impossible. Thus, the observed peak structures at 4.04 and 4.13 GeV in the ${\pi }^{\pm }\psi (3770)$ invariant mass distributions should not come from the contributions of $Z_c(4020{)}^{\pm }$, and further precise experimental measurements of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (3770)$ process are needed to decode the nature of these two peak structures.