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In this article, we study the $C\gamma_5\otimes \gamma_5C$ type and $C\otimesC$ type scalar $cs\bar{c}\bar{s}$ tetraquark states with the QCD sum rules bycalculating the contributions of the vacuum condensates up to dimension 10 in aconsistent way. The ground state masses $M_{C\gamma_5\otimes \gamma_5C}=3.89\pm0.05\,\rm{GeV}$ and $M_{C\otimes C}=5.48\pm0.10\,\rm{GeV}$ support assigningthe $X(3915)$ to be the ground state $C\gamma_5\otimes \gamma_5C$ typetetraquark state with $J^{PC}=0^{++}$, but do not support assigning the$X(4700)$ to be the ground state $C\otimes C$ type $cs\bar{c}\bar{s}$tetraquark state with $J^{PC}=0^{++}$. Then we tentatively assign the $X(3915)$and $X(4500)$ to be the 1S and 2S $C\gamma_5\otimes \gamma_5C$ type scalar$cs\bar{c}\bar{s}$ tetraquark states respectively, and obtain the 1S mass$M_{\rm 1S}=3.85^{+0.18}_{-0.17}\,\rm{GeV}$ and 2S mass $M_{\rm2S}=4.35^{+0.10}_{-0.11}\,\rm{GeV}$ from the QCD sum rules, which supportassigning the $X(3915)$ to be the 1S $C\gamma_5\otimes \gamma_5C$ typetetraquark state, but do not support assigning the $X(4500)$ to be the 2S$C\gamma_5\otimes \gamma_5C$ type tetraquark state.

Reanalysis of the $X(3915)$, $X(4500)$ and $X(4700)$ with QCD sum rules