Estimating the Mass of Hidden Charm 1+(1+) Tetraquark State via QCD Sum Rules

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 $$m_{1^+}^c = (3912^{+306}_{-153}) \, \text {MeV}$$ , which is consistent, within the errors, with the experimental observation of $$Z_c^+(3900)$$ . Extending to the b-quark sector, $$m_{1^+}^b = (10561^{+395{}^{}}_{-163}) \,\text {MeV}$$ is obtained. The calculational result strongly supports the tetraquark picture for the "exotic" states of $$Z_c^+(3900)$$ and $$Z_b^+(10610)$$ .