Determination of the $Z_c(3900)$ and the $Z_{cs}(3985)$ states from joint analysis of experimental and lattice data

Abstract

We present a unified analysis of the $Z_c(3900)$ and $Z_{cs}(3985)$ states considering both experimental and lattice data. The study simultaneously includes the processes $e^+e^- \rightarrow J/\psi \pi^+\pi^-, J/\psi K^+ K^-, D^0 D^{\ast-} \pi^+, (D^{\ast 0} D_s^{-}+D^0 D_s^{\ast -}) K^+$, together with finite-volume energy levels from recent lattice QCD simulations. Open-charm meson loops with triangle singularities, the $J/\psi\pi(J/\psi \bar{K})$-$\bar{D}D^*(\bar{D}D^*_s)$ coupled-channel interactions, and the $\pi\pi$-$K\bar K$ final-state interaction are all taken into account. We find that pole contributions associated with the $Z_c(3900)$ and $Z_{cs}(3985)$ are indispensable for describing the data. The successful joint description of the experimental and lattice data supports the interpretation that the $Z_c(3900)$ and $Z_{cs}(3985)$ are SU(3) flavor partners within the same octet multiplet and indicates that both are resonance states. The extracted pole masses and half-widths of the $Z_c(3900)$ and the $Z_{cs}(3985)$ are $(3879.6 \pm 4.8)$ MeV and $(32.2 \pm 4.7)$ MeV, and $(3976.9 \pm 5.1)$ MeV and $(28.8 \pm 5.9)$ MeV, respectively. The ratios of the $Z_c(Z_{cs})$ couplings to the $D\bar D^*(D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ and $J/\psi \pi(J/\psi K)$ channels are also determined. A compositeness analysis indicates that, although the $D\bar D^* (D_s\bar{D}^\ast+D\bar{D}_s^\ast)$ component in the $Z_c(3900) (Z_{cs}(3985))$ state is sizable, additional components are still needed to form these exotic states.