Reanalysis of the $X(4140)$ as axialvector tetraquark state with QCD sum rules

In this article, we take the $X(4140)$ as the diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark state with $J^{PC}=1^{++}$, and study the mass and pole residue with the QCD sum rules in details by constructing two types interpolating currents. The numerical results $M_{X_{L,+}}=3.95\pm0.09\,\rm{GeV}$ and $M_{X_{H,+}}=5.00\pm0.10\,\rm{GeV}$ disfavor assigning the $X(4140)$ to be the $J^{PC}=1^{++}$ diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark state. Moreover, we obtain the masses of the $J^{PC}=1^{+-}$ diquark-antidiquark type $cs\bar{c}\bar{s}$ tetraquark states as a byproduct. The present predictions can be confronted to the experimental data in the future.