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

TL;DR

This paper uses QCD sum rules to predict the masses of charm-strange and bottom hadronic molecules, aligning some with experimental data and suggesting potential bound states.

Contribution

First application of two-point QCD sum rules considering up to dimension 12 condensates for these molecular states.

Findings

Predicted masses for $DK$, $D^*K$, and $DK^*$ match experimental data.

Masses for $BK$ and $B^*K$ are above their thresholds.

Predicted $BK^*$ mass suggests a possible bound state.

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 $J^P$ = $0^+$ and $1^+$ by using two-point QCD sum rules, where the vacuum condensates are considered up to dimension 12. The predicted masses for $DK$, $D^*K$ and $DK^*$ 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 ${D}_{s1}(2536)$, respectively. The theoretical results for $BK$ and $B^*K$ molecular states are $5.970_{ - 0.064}^{ + 0.061}$ GeV and $6.050_{ - 0.064}^{ + 0.062}$ GeV which are all higher than their own thresholds. Finally, the mass of hadronic molecule $BK^*$ is predicted to be $6.158_{ - 0.063}^{ + 0.061}$ GeV. This value is lower than the threshold of $BK^*$, which implies that it may be a bound hadronic molecular state.