  In this article, we distinguish the charge conjugations of the interpolating
currents, calculate the contributions of the vacuum condensates up to
dimension-10 in the operator product expansion, and study the masses and pole
residues of the $J^{PC}=1^{-\pm}$ hidden charmed tetraquark states with the QCD
sum rules. We suggest a formula $\mu=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$
with the effective mass ${\mathbb{M}}_c=1.8\,\rm{GeV}$ to estimate the energy
scales of the QCD spectral densities of the hidden charmed tetraquark states,
which works very well. The numerical results disfavor assigning the
$Z_c(4020)$, $Z_c(4025)$, $Y(4360)$ as the diquark-antidiquark (with the Dirac
spinor structure $C-C\gamma_\mu$) type vector tetraquark states, and favor
assigning the $Z_c(4020)$, $Z_c(4025)$ as the diquark-antidiquark type $1^{+-}$
tetraquark states. While the masses of the tetraquark states with symbolic
quark structures $c\bar{c}s\bar{s}$ and $c\bar{c}(u\bar{u}+d\bar{d})/\sqrt{2}$
favor assigning the $Y(4660)$ as the $1^{--}$ diquark-antidiquark type
tetraquark state, more experimental data are still needed to distinguish its
quark constituents. There are no candidates for the positive charge conjugation
vector tetraquark states, the predictions can be confronted with the
experimental data in the future at the BESIII, LHCb and Belle-II.
