Interpretation of $Z_c(4025)$ as the Hidden Charm Tetraquark States via QCD Sum Rules

Abstract

By using QCD Sum Rules, we found that the charged hidden charm tetraquark $[c u][\bar{c} \bar{d}]$ states with $ J^P = 1^-$ and $ 2^+$, which are possible quantum numbers of the newly observed charmonium-like resonance $Z_c(4025)$, have masses of $m_{1^-}^c = (4.54 \pm 0.20) \, \text{GeV}$ and $m_{2^+}^c = (4.04 \pm 0.19) \, \text{GeV}$. The contributions up to dimension eight in the Operator Product Expansion (OPE) were taken into account in the calculation. The tetraquark mass of $J^{P} = 2^{+}$ state was consistent with the experimental data of $Z_c(4025)$, suggesting the $Z_c(4025)$ state possessing the quantum number of $J^P = 2^+$. Extending to the b-quark sector, the corresponding tetraquark masses $m_{1^-}^b = (10.97 \pm 0.25) \, \text{GeV}$ and $m_{2^+}^b = (10.35 \pm 0.25) \, \text{GeV}$ were obtained, which are testable in future B-factories.