The Zc structures in a coupled-channels model

Abstract

The Zc(3900) ±/ Zc(3885) ± and Zc(4020) ± are two charmonium-like structures discovered in the πJ/ ψ and D∗D¯ (∗)+ 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 D∗D¯ (∗)-thresholds stimulates both a molecular interpretation or a coupled-channels threshold effect. In this work we perform a coupled-channels calculation of the IG(JPC) = 1 +(1 + -) sector including D(∗)D¯ ∗+ h. c. , πJ/ ψ and ρηc 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- D∗D¯ (∗) and ρηc- D∗D¯ (∗) couplings which indicates that the Zc(3900) ±/ Zc(3885) ± and Zc(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 Zc peaks.