Predicting charmed-strange molecular tetraquarks with $K^{(*)}$ and $T$-doublet (anti-)charmed meson

Abstract

In this work, we systematically investigate the charmed-strange molecular tetraquarks composed of a $K^{(*)}$ meson and a $T$-doublet (anti-)charmed meson. Our analysis is performed within the one-boson-exchange model, with a careful treatment of $S$-$D$ wave mixing and coupled-channel effects. We identify the $X_1(2900)$ resonance, observed by LHCb, as a molecular state in the coupled $K \bar{D}_1 / K^* \bar{D}_1 / K^* \bar{D}_2^*$ system with quantum numbers $I(J^P)=0(1^-)$. This state is dominated by the $K \bar{D}_1$ component but exhibits a significant admixture from the $K^* \bar{D}_1$ channel. Furthermore, we predict several partner states of the $X_1(2900)$ in the $K^*\bar{D}_1$ and $K^{(*)}\bar{D}_2^*$ systems. We also extend our framework to the $K^{(*)} {D}_1/K^{(*)} {D}_2^*$ systems, where our results suggest a series of $T_{c \bar s}$-type charmed-strange molecular tetraquark candidates. These findings provide a comprehensive picture of the molecular spectrum in the charmed-strange sector and can be tested in future experimental studies.

Figures (6)

• Figure 1: The invariant mass spectra of $X_0(2900)$ and $X_1(2900)$ in the $D^-K^+$ from $B^+\to D^+D^-K^+$. The data are obtained from the LHCb LHCb:2020blsLHCb:2020pxc. The vertical dashed lines are thresholds of the $K^*\bar{D}^*$, $K^*\bar{D}_1$, $K\bar{D}_2^*$, $K^*\bar{D}_1$, and $K^*\bar{D}_2^*$ channels.
• Figure 2: Effective interaction for the $K\bar{D}_1$ system with $I(J^P)=0(1^-)$ in the OBE model with $\Lambda=1.0~{\rm GeV}$.
• Figure 3: The bound state properties including the mass, the RMS radius, and the probabilities of various components as functions of the cutoff $\Lambda$ for the coupled $K \bar{D}_1 / K^* \bar{D}_1 / K^* \bar{D}_2^*$ system with $I(J^P)=0(1^-)$. In the plot of the obtained mass versus the cutoff parameter $\Lambda$, the horizontal line-dot symbol marks the central value of the experimentally observed mass of the $X_1(2900)$, while the shaded background indicates the associated uncertainty LHCb:2020blsLHCb:2020pxc.
• Figure 4: The binding energy, the RMS radius, and the probabilities of various components as functions of the cutoff $\Lambda$ for the coupled $K \bar{D}_2^* / K^* \bar{D}_1 / K^* \bar{D}_2^*$ system with $I(J^P)=0(2^-)$.
• Figure 5: Loosely bound states obtained for the $K^* D_1$ system with the cutoff parameter $\Lambda$ ranging from 0.8 to 2.0 GeV, taking into account $S$-$D$-wave mixing effects. The star in the upper-left region denotes the loosely bound state that appears at the smallest cutoff value where binding begins, with the corresponding $\Lambda$ value explicitly given. The points from upper-left to lower-right indicates that in each step of the calculation, the cutoff $\Lambda$ increases by 0.02 GeV. The box in the lower-right region indicates the loosely bound solution with a binding energy of about 20 MeV and a root-mean-square radius near 1 fm, also accompanied by its corresponding $\Lambda$ value.