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

Abstract

We perform coupled channel analysis for $D{\bar{D}}^{\ast }$, $J/\psi \pi$ 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 $D^{(\ast )}$ 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 $D{\bar{D}}^{\ast }$-$J/\psi \pi$ 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.

15 pages, 8 figures

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