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We investigate the masses of $cs \bar c \bar s$ tetraquark states in adiquark-antidiquark picture employing the relativized quark model proposed byGodfrey and Isgur. Only the antitriplet diquark states in color space arecalculated. The diquark masses are obtained with the relativized potentialfirstly, and then the diquark and antidiquark are treated as the usualantiquark and quark, respectively, and the masses of the tetraquark states areobtained by solving the Schr\"{o}dinger equation with the relativized potentialbetween the diquark and antidiquark. The theoretical uncertainties induced byscreening effects are also taken into account. It is found that the resonanceof $X(4140)$ can be regarded as the $cs \bar c \bar s$ tetraquark groundstates, and the $X(4700)$ can be assigned as the $2S$ excited tetraquark state.When the internal excited diquarks are taken into account, the resonance of$X(4500)$ can be explained as the tetraquark composed of one $2S$ scalardiquark and one scalar antidiquark. In our approach, the $X(4274)$ cannot beexplained as a tetraquark state, however, it can be a good candidate of theconventional $\chi_{c1}(3^3P_1)$ state. In addition, other charmonium-likestates $\chi_{c0}(3915)$, $X(4350)$, $X(4630)$ and $X(4660)$, as the $cs \bar c\bar s$ tetraquark states, are also discussed.

The $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$ in the relativized quark model