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 $D^{\ast }{\bar{D}}^{(\ast )}+h.c.$ invariant mass spectra. Their nature is puzzling due to their charge, which forces its minimal quark content to be $c\bar{c}u\bar{d}$ ($c\bar{c}d\bar{u}$). 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 $D^{\ast }{\bar{D}}^{(\ast )}$-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 $D^{(\ast )}{\bar{D}}^{\ast }+h.c.$, $\pi J/\psi$ 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 $\pi J/\psi -D^{\ast }{\bar{D}}^{(\ast )}$ and $\rho {\eta }_c-D^{\ast }{\bar{D}}^{(\ast )}$ 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 $D{\bar{D}}^{\ast }$ invariant mass distributions is due to the presence of two virtual states that produce the $Z_c$ peaks.

10 pages, 5 figures, 2 tables. Accepted for publication in The European Physical Journal C

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Cited by in corpus (26)

• Pentaquark and Tetraquark states
• Triply-heavy baryons in a constituent quark model
• $Z_{cs}(3985{)}^{-}$ as the $U$-spin partner of $Z_c(3900{)}^{-}$ and implication of other states in the ${\text{SU(3)}}_F$ symmetry and heavy quark symmetry
• Spectroscopy of ${\mathbf{B}}_{\mathbf{c}}$ mesons and the possibility of finding exotic ${\mathbf{B}}_{\mathbf{c}}$-like structures
• Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\Lambda }(4338)$ and $P_{cs}(4459)$
• The strange partner of the $Z_c$ structures in a coupled-channels model
• The $Z_{cs}(3985)$ as a threshold effect from the ${\bar{D}}_s^{\ast }D+{\bar{D}}_s{D}^{\ast }$ interaction
• Nature of the doubly-charmed tetraquark $T_{cc}^{+}$ in a constituent quark model
• The $\mathbf{sQ}\bar{\mathbf{q}}\bar{\mathbf{q}}$ $(\mathbf{q}=\mathbf{u},\mathbf{d};\mathbf{Q}=\mathbf{c},\mathbf{b})$ tetraquarks in the chiral quark model
• Correlation of the hidden-charm molecular tetraquarks and the charmoniumlike structures existing in the $B\to XYZ+K$
• Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• Towards the discovery of novel $B_c$ states: radiative and hadronic transitions
• Fully-charm and -bottom pentaquarks in a Lattice-QCD inspired quark model
• Fully open-flavor tetraquark states $bc\bar{q}\bar{s}$ and $sc\bar{q}\bar{b}$ with $J^P=0^{+},1^{+}$
• Precise determination of the pole position of the exotic $Z_c(3900)$
• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• The $Z_b$ structures in a constituent quark model coupled-channels calculation
• The $\mathbf{X}(3872)$'s excitation and its connection with production at hadron colliders
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Simultaneous description of the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ processes
• Bottomonium-like tetraquarks in a chiral quark model
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• Photon-induced production of the exotic charged charmonium-like state $Z_c(3900)$ off nuclear targets and its internal structure
• $Z_c(3900)$ in a hadronic molecule and a triangle singularity approach at finite temperature
• $N^{\ast }$ states with hidden charm and a three-body nature