The $Z_c(3900)$ as a resonance from the $D\bar{D}^*$ interaction

Jun He

Published 2015-05-20Version 1

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