Analysis of the hadronic molecules $DK$, $D^*K$, $DK^*$ and their bottom analogs with QCD sum rules

Abstract: In this work, we construct the color-singlet-color-singlet type currents to study the masses and pole residues of charm-strange tetraquark states and their bottom analogs with $J<sup>P$ = $0^+$ and $1^+$ by using two-point QCD sum rules, where the vacuum condensates are considered up to dimension 12. The predicted masses for $DK$, $D<sup>*K$ and $DK<sup>*$ molecular states are $2.322_{ - 0.072}^{ + 0.066}$ GeV, $2.457_{ - 0.068}^{ + 0.064}$ GeV and $2.538_{ - 0.062}^{ + 0.059}$ GeV. These results are consistent well with the experimental data of $D_{s0}(2317)$, $D_{s1}(2460)$ and ${D}<em>{s1}(2536)$, respectively. The theoretical results for $BK$ and $B<sup>*K$ molecular states are $5.970</em>{ - 0.064}^{ + 0.061}$ GeV and $6.050_{ - 0.064}^{ + 0.062}$ GeV which are all higher than their own thresholds. Finally, the mass of hadronic molecule $BK<sup>*$ is predicted to be $6.158_{ - 0.063}^{ + 0.061}$ GeV. This value is lower than the threshold of $BK<sup>*$, which implies that it may be a bound hadronic molecular state.