Analysis of the X(3872), Z_c(3900) and Z_c(3885) as axial-vector tetraquark states with QCD sum rules

In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion, study the masses and pole residues of the $J^{PC}=1^{+\pm }$ hidden charmed tetraquark states with the QCD sum rules, and explore the energy scale dependence in details for the first time. The predictions $M_X=3.87_{-0.09}^{+0.09}\mathrm{G}\mathrm{e}\mathrm{V}$ and $M_Z=3.91_{-0.09}^{+0.11}\mathrm{G}\mathrm{e}\mathrm{V}$ support assigning the $X(3872)$ and $Z_c(3900)$ (or $Z_c(3885)$) as the $1^{++}$ and $1^{+-}$ diquark-antidiquark type tetraquark states, respectively.