$D\bar{D}^\ast$-$\pi J/\psi$ scatterings of coupled channels for $Z_c(3900)$ channel

Abstract

We perform coupled channel analysis for $D \bar D^*$, $J/\psi \pi$ and related meson pairs for the $Z_c(3900)$ channel in an effective model of hadrons and quarks. The model incorporates meson exchange potential such as one pion and $D^{(*)}$ meson exchanges, and quark exchanges. It turns out that the meson exchange potential is small, while the off-diagonal interactions by the quark exchanges at short distances, particularly for transitions between $D\bar D^*$-$J/\psi \pi$ are strong, which plays a main role for the scattering amplitudes for the $Z_c(3900)$ channel, in consistent with the results of the lattice simulations of the HALQCD group.