The Tetraquark Candidate Zc(3900) from Dynamical Lattice QCD Simulations

Abstract

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 $D{\bar{D}}^{\ast }$ 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 $\pi J/\psi$-$D{\bar{D}}^{\ast }$ and $\rho {\eta }_c$-$D{\bar{D}}^{\ast }$ couplings. With the interactions obtained, the s-wave two-body amplitudes and the pole position in the $\pi J/\psi$-$\rho {\eta }_c$-$D{\bar{D}}^{\ast }$ 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.

Comments: 19 pages, 12 figures. arXiv admin note: text overlap with arXiv:1602.03465