  We study the mass spectra of hidden-charm tetraquark systems with quantum
numbers $(I^G)J^P=(1^+)1^+$ using QCD sum rules. The analysis incorporates the
complete next-to-leading order (NLO) contribution to the perturbative QCD part
of the operator product expansions, with particular attention to operator
mixing effects due to renormalization group evolution. For the
$\bar{d}c\bar{c}u$ system, the masses of two mixed operators,
$J_{1,5}^{\text{Mixed}}$ and $J_{2,6}^{\text{Mixed}}$, are determined to be
$3.89^{+0.18}_{-0.12}$ GeV and $4.03^{+0.06}_{-0.07}$ GeV, respectively,
closely matching those of $Z_c$(3900) and $Z_c(4020)$. Similarly, for the
$\bar{s}c\bar{c}u$ states, the masses of $J_{1,5}^{\text{Mixed}}$ and
$J_{2,6}^{\text{Mixed}}$ are found to be $4.02^{+0.17}_{-0.09}$ GeV and
$4.21^{+0.08}_{-0.07}$ GeV, respectively, in close proximity to
$Z_{cs}$(3983)/$Z_{cs}$(4000) and $Z_{cs}$(4220), consistent with the
expectation that they are the partners of $Z_c$(3900) and $Z_c$(4020). Our
results highlight the crucial role of operator mixing, an inevitable effect in
a complete NLO calculation, in achieving a robust phenomenological description
for the tetraquark system.
