Reconciling experimental and lattice data of $Z_c(3900)$ in a $J/\psi \pi$-$D{\bar{D}}^{\ast }$ coupled-channel analysis

Abstract

We study the $J/\psi \pi$ and $D{\bar{D}}^{\ast }$ coupled-channel system within a covariant framework. The $J/\psi \pi$ and $D{\bar{D}}^{\ast }$ invariant-mass distributions measured at 4.23~GeV and 4.26~GeV by BESIII and the finite-volume energy levels from recent lattice QCD simulations are simultaneously fitted. Phase shifts and inelasticities of the $J/\psi \pi$ and $D{\bar{D}}^{\ast }$ scattering are predicted using the resulting amplitudes. Poles corresponding to the $Z_c(3900)$ state are found in the complex energy plane and their couplings with $J/\psi \pi$ and $D{\bar{D}}^{\ast }$ are determined. Our results indicate that the current lattice data do not preclude the existence of a physical $Z_c(3900)$ state.

Comments: 22 pages, 4 figures