Relating $D^{\ast }{\bar{D}}^{\ast }$ currents with $J^{\pi }=0^{+},1^{+}$ and $2^{+}$ to $Z_c$ states

Abstract

In this work we study the $D^{\ast }{\bar{D}}^{\ast }$ current with QCD sum rules. We write the correlation function using the general current corresponding to the $D^{\ast }{\bar{D}}^{\ast }$ system and then use spin projectors to obtain the correlation function in the $0^{+},1^{+}$ and $2^{+}$ spin-parity configurations. The purpose of the present work is to investigate the possibility of explaining the recently reported $Z_c(4025)$ as a $D^{\ast }{\bar{D}}^{\ast }$ moleculelike state. As a result we find a state for each spin case with a very similar mass: $M^{S=0}=\left(3943\pm 104\right)$ MeV, $M^{S=1}=\left(3950\pm 105\right)$ MeV, $M^{S=2}=\left(3946\pm 104\right)$ MeV. We discuss that our mass results, within error bars, for $1^{+}$ or $2^{+}$ are both compatible with $Z_c(4025)$. However, our results are also compatible with a possible $D^{\ast }{\bar{D}}^{\ast }$ bound state, in agreement with predictions of some previous works. We have also calculated the current-state coupling which turns out to be larger in the $2^{+}$ case.

Comments: New discussions added, corrections related to Z_c(4020) made