The Z_c structures in a coupled-channels model

Abstract

The Z_{c}(3900)^pm /Z_c(3885)^pm and Z_{c}(4020)^pm are two charmonium-like structures discovered in the pi J/psi and D^*bar{D}^{(*)}+h.c. invariant mass spectra. Their nature is puzzling due to their charge, which forces its minimal quark content to be cbar{c} ubar{d} (cbar{c} dbar{u}). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as pi J/psi and the closeness of their mass to D^*bar{D}^{(*)}-thresholds stimulates both a molecular interpretation or a coupled-channels threshold effect. In this work we perform a coupled-channels calculation of the I^G(J^{PC})=1^+(1^{+-}) sector including D^{(*)}bar{D}^{*}+h.c., pi J/psi and rho eta _c 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 pi J/psi -D^*bar{D}^{(*)} and rho eta _c-D^*bar{D}^{(*)} couplings which indicates that the Z_{c}(3900)^pm /Z_c(3885)^pm and Z_{c}(4020)^pm 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 pi J/psi and Dbar{D}^* invariant mass distributions is due to the presence of two virtual states that produce the Z_c peaks.