Estimating the mass of the hidden charm $1^{+}(1^{+})$ tetraquark state via QCD sum rules

Abstract

By using QCD sum rules, the mass of the hidden charm tetraquark $[cu][\bar{c}\bar{d}]$ state with $I^G(J^P)=1^{+}(1^{+})$ (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance $Z_c^{+}(3900)$. In the calculation, contributions up to dimension eight in the operator product expansion(OPE) are taken into account. We find $m_{1^{+}}^c=(3912_{-153}^{+306})\text{MeV}$, which is consistent, within the errors, with the experimental observation of $Z_c^{+}(3900)$. Extending to the b-quark sector, $m_{1^{+}}^b=(10561_{-163}^{+395})\text{MeV}$ is obtained. The calculational result strongly supports the tetraquark picture for the "exotic" states of $Z_c^{+}(3900)$ and $Z_b^{+}(10610)$.

Comments: 13 pages,3 figures, 1 table, version to appear in EPJC