Influence of threshold effects induced by charmed meson rescattering

We investigate the processes $e^+e^-$ annihilating to $J/\psi\pi\pi$, $\psi^\prime\pi\pi$ and $h_c\pi\pi$. The coupled-channel effects induced by the couplings between the widely accepted $D$-wave charmonium $\psi(4160)$ and $D_1D$, $D_1D^*$ and $D_2D^*$ charmed meson pairs in the $S$-wave state with couplings given by heavy quark spin symmetry are analyzed. The line shapes show the presence of cusps that result from the singularities of the rescattering loops, which could be helpful in understanding the nature of $Y(4260)$, $Y(4360)$, $Z_c(3900)$/$Z_c(3885)$ and $Z_c(4020)$/$Z_c(4025)$.