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 $M_{X}=3.87^{+0.09}_{-0.09}\,\rm{GeV}$ and $M_{Z}=3.91^{+0.11}_{-0.09}\,\rm{GeV}$ support assigning the $X(3872)$ and $Z_c(3900)$ (or $Z_c(3885)$) as the $1^{++}$ and $1^{+-}$ diquark-antidiquark type tetraquark states, respectively.