  We study the spectrum and rearrangement decays of S-wave $cs\bar{c}\bar{s}$
tetraquark states in a simplified quark model. The masses and widths are
estimated by assuming that the $X(4140)$ is the lower $1^{++}$
$cs\bar{c}\bar{s}$ tetraquark. Comparing our results with experimental
measurements, we find that the recently observed $X(3960)$ by LHCb can be
assigned as the lowest $0^{++}$ $cs\bar{c}\bar{s}$ tetraquark state and the
$X_0(4140)$ could be the second lowest $0^{++}$ $cs\bar{c}\bar{s}$ tetraquark.
Predictions of ratios between partial widths for the involved tetraquarks are
given. We call for searches for more $cs\bar{c}\bar{s}$ tetraquarks with
$J^{PC}=1^{+-}$, $0^{++}$, and $2^{++}$.
