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

TL;DR

This study models the $Z_c(3900)$ channel using coupled meson and quark interactions, revealing quark exchanges dominate the scattering process, aligning with lattice simulation results.

Contribution

It introduces an effective coupled channel model combining meson and quark exchanges, highlighting the importance of quark exchanges in $Z_c(3900)$ scattering.

Findings

Meson exchange potential is small.

Quark exchanges at short distances are strong.

Quark exchanges are key for scattering amplitudes.

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.