Analysis of the hidden-charm-hidden-strange tetraquark mass spectrum via the QCD sum rules

In the present work, we construct the diquark-antidiquark type four-quark currents to investigate the mass spectrum of the ground state hidden-charm-hidden-strange tetraquark states with the quantum numbers $J^{PC}=0^{++}$, $1^{+-}$, $1^{++}$ and $2^{++}$ via the traditional QCD sum rules in a comprehensive way. We update old calculations, perform new calculations and analysis in a rigorous way, and take account of the net light-flavor $SU\left(3\right)$ breaking effects in a consistent way. And we make more reasonable identifications for the $X\left(3960\right)$, $X\left(4140\right)$, $X\left(4274\right)$, $X\left(4500\right)$, $X\left(4685\right)$ and $X\left(4700\right)$ and supersede some old identifications. Furthermore, we consider our previous theoretical predictions, and make reasonable/suitable identifications of the new LHCb states $h_c\left(4000\right)$ and ${\chi }_{c1}\left(4010\right)$.