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 $πJ/ψ$, $ρη_{c}$ and $\bar{D}D^{*}$ channels is derived from (2+1)-flavor QCD simulations at $m_π=410$-$700$ MeV. The interaction is dominated by the off-diagonal $πJ/ψ$-$\bar{D}D^{*}$ and $ρη_{c}$-$\bar{D}D^{*}$ 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