Fate of the Tetraquark Candidate Zc(3900) from Lattice QCD

Abstract

The possible exotic meson $Z_c(3900)$, found in $e^{+}{e}^{-}$ reactions, is studied by the method of coupled-channel scattering in lattice QCD. The interaction among $\pi J/\psi$, $\rho {\eta }_c$ and $\bar{D}{D}^{\ast }$ channels is derived from (2+1)-flavor QCD simulations at $m_{\pi }=410$-$700$ MeV. The interaction is dominated by the off-diagonal $\pi J/\psi$-$\bar{D}{D}^{\ast }$ and $\rho {\eta }_c$-$\bar{D}{D}^{\ast }$ couplings, which indicates that the $Z_c(3900)$ is not a usual resonance but a threshold cusp. Semi-phenomenological analyses with the coupled-channel interaction are presented to confirm this conclusion.

5 pages, 6 figures

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