$Z_c(3900)$ as a $D{\bar{D}}^{\ast }$ molecule from the pole counting rule

Abstract

A comprehensive study on the nature of the $Z_c(3900)$ resonant structure is carried out in this work. By constructing the pertinent effective Lagrangians and considering the important final-state-interaction effects, we first give a unified description to all the relevant experimental data available, including the $J/\psi \pi$ and $\pi \pi$ invariant mass distributions from the $e^{+}{e}^{-}\to J/\psi \pi \pi$ process, the $h_c\pi$ distribution from $e^{+}{e}^{-}\to h_c\pi \pi$ and also the $D{\bar{D}}^{\ast }$ spectrum in the $e^{+}{e}^{-}\to D{\bar{D}}^{\ast }\pi$ process. After fitting the unknown parameters to the previous data, we search the pole in the complex energy plane and find only one pole in the nearby energy region in different Riemann sheets. Therefore we conclude that $Z_c(3900)$ is of $D{\bar{D}}^{\ast }$ molecular nature, according to the pole counting rule method~[Nucl.~Phys.~A543, 632 (1992); Phys.~Rev.~D 35,~1633 (1987)]. We emphasize that the conclusion based upon the pole counting method is not trivial, since both the $D{\bar{D}}^{\ast }$ contact interactions and the explicit $Z_c$ exchanges are introduced in our analyses and they lead to the same conclusion.

21 pages, 9 figures. To match the published version in PRD. Additional discussion on the spectral density function is included

References in corpus (8)

• $Z_b$ and $Z_c$ Exotic States as Coupled Channel Cusps
• Could the near-threshold $XYZ$ states be simply kinematic effects?
• Nature of X(3872) from data
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Ambiversion of X(3872)
• Low-energy Scattering of $(D{\bar{D}}^{\ast }{)}^{\pm }$ System And the Resonance-like Structure $Z_c(3900)$
• The ${\Lambda }_c(2595)$ resonance as a dynamically generated state: the compositeness condition and the large $N_c$ evolution
• Bound states on the lattice with partially twisted boundary conditions

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