The Zc structures in a coupled-channels model

The Z(3900) / Z(3885) and Z(4020) are two charmonium-like structures discovered in the πJ/ ψ and DD¯ + h. c. invariant mass spectra. Their nature is puzzling due to their charge, which forces its minimal quark content to be cc¯ ud¯ (cc¯ du¯). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as πJ/ ψ and the closeness of their mass to DD¯ -thresholds stimulates both a molecular interpretation or a coupled-channels threshold effect. In this work we perform a coupled-channels calculation of the I(J) = 1 (1 ) sector including DD¯ + h. c., πJ/ ψ and ρη channels in the framework of a constituent quark model which satisfactorily describes a wide range of properties of (non-)conventional hadrons containing heavy quarks. The meson-meson interactions are dominated by the non-diagonal πJ/ ψ- DD¯ and ρη- DD¯ couplings which indicates that the Z(3900) / Z(3885) and Z(4020) are unusual structures. The study of the analytic structure of the S-matrix allows us to conclude that the point-wise behavior of the line shapes in the πJ/ ψ and DD¯ invariant mass distributions is due to the presence of two virtual states that produce the Z peaks