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

In this article, we study the $ C\gamma_5\otimes \gamma_5C$ type and $ C\otimes C$ type scalar $ cs\bar{c}\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $ M_{C\gamma_5\otimes \gamma_5C}=3.89\pm 0.05$ GeV and $ M_{C\otimes C} =5.48\pm0.10$ GeV support assigning the $ X(3915)$ as the ground state $ C\gamma_5\otimes \gamma_5C$ type tetraquark state with $ J^{PC}=0^{++}$ , but do not support assigning the $ X(4700)$ as 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)$ as 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_{1S}= 3.85^{+0.18}_{-0.17}$ GeV and 2S mass M 2S = 4.35+0.10 -0.11 GeV from the QCD sum rules, which support assigning the X(3915) as the 1S $ C\gamma_5\otimes \gamma_5C$ type tetraquark state, but do not support assigning the X(4500) as the 2S $ C\gamma_5\otimes \gamma_5C$ type tetraquark state