Analysis of the $X(3960)$ and related tetraquark molecular states via the QCD sum rules

Abstract: In this work, we study the $D\bar{D}$, $DD$, $D\bar{D}s$, $DD_s$, $D_s\bar{D}_s$ and $D_sD_s$ tetraquark molecular states with the $J^{PC}=0^{++}$ via the QCD sum rules. The prediction $M{D_s\bar {D}s} = 3.98\pm0.10\, \rm{GeV}$ is in very good agreement with the experimental value $M{X(3960)} = 3956 \pm 5\pm 10 \,\rm{MeV}$ from the LHCb collaboration and supports assigning the $X(3960)$ as the $D_s^+D_s^-$ molecular state with the $J^{PC}=0^{++}$. We take account of our previous works on the four-quark states consisting of two color-neutral clusters, and acquire the mass spectrum of the ground state hidden-charm and doubly-charm tetraquark molecular states.