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 $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-},J/\psi K^{+}{K}^{-},D^0{D}^{\ast -}{\pi }^{+},(D^{\ast 0}{D}_s^{-}+D^0{D}_s^{\ast -})K^{+}$, together with finite-volume energy levels from recent lattice QCD simulations. Open-charm meson loops with triangle singularities, the $J/\psi \pi (J/\psi \bar{K})$-$\bar{D}{D}^{\ast }(\bar{D}{D}_s^{\ast })$ 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 $D{\bar{D}}^{\ast }(D_s{\bar{D}}^{\ast }+D{\bar{D}}_s^{\ast })$ and $J/\psi \pi (J/\psi K)$ channels are also determined. A compositeness analysis indicates that, although the $D{\bar{D}}^{\ast }(D_s{\bar{D}}^{\ast }+D{\bar{D}}_s^{\ast })$ component in the $Z_c(3900)(Z_{cs}(3985))$ state is sizable, additional components are still needed to form these exotic states.

Comments: 13 pages, 9 figures