Zc(3900)as a resonance from theDD¯*interaction

Abstract

In this paper it is proposed that the charged charmonium-like state ${Z}_{c}(3900)$ is a resonance above the threshold from the $D{\overline{D}}^{*}$ interaction. The $D{\overline{D}}^{*}$ interaction is described by the one-boson exchange model with light meson exchanges plus a short-range $J/\ensuremath{\psi}$ exchange. The scattering amplitude is calculated within a Bethe-Salpeter equation approach, and the poles near the $D{\overline{D}}^{*}$ threshold are searched. In the isoscalar sector, two poles found under the $D{\overline{D}}^{*}$ threshold---i.e., bound states---have the quantum numbers ${I}^{G}({J}^{\mathrm{PC}})={0}^{\ensuremath{-}}({1}^{+\ensuremath{-}})$ and ${0}^{+}({1}^{++})$. The latter can be related to the $X(3872)$. In the isovector sector, a bound state with ${I}^{G}({J}^{P})={1}^{+}({1}^{+})$ is found with a large cutoff at about 3 GeV. If a cutoff at about 2 GeV is adopted with which a pole carrying the quantum number of the $X(3872)$ is produced at an energy of about 3871 MeV, the pole for the bound state with ${1}^{+}({1}^{+})$ runs across the threshold to a second Riemann sheet and becomes a resonance above the $D{\overline{D}}^{*}$ threshold, which can be identified with the ${Z}_{c}(3900)$. With such a cutoff, the $D{\overline{D}}^{*}$ invariant mass spectrum is also investigated and the experimental results found by BESIII can be reproduced.