The structure of the tetraquark candidate $Z_{ c}(3900)$, which was experimentally reported in $e^+ e^-$ collisions, is studied by the s-wave meson-meson coupled-channel scattering on the lattice. The s-wave interactions among the $\pi J/\psi$, $\rho \eta_{ c}$ and $D \bar{ D}^{ *}$ channels are derived from (2+1)-flavor dynamical QCD simulations at $m_{ \pi}=410$--$700$ MeV. It is found that the interactions are dominated by the off-diagonal $\pi J/\psi$-$D \bar{ D}^{ *}$ and $\rho \eta_{ c}$-$D \bar{ D}^{ *}$ couplings. With the interactions obtained, the s-wave two-body amplitudes and the pole position in the $\pi J/\psi$-$\rho \eta_{ c}$-$D \bar{ D}^{ *}$ coupled-channel scattering are calculated. The results show that the $Z_{ c}(3900)$ is not a conventional resonance but a threshold cusp. A semiphenomenological analysis with the coupled-channel interaction to the experimentally observed decay mode is also presented to confirm the conclusion.
Categories: hep-lat hep-ph nucl-th