Abstract

Very recently the LHCb Collaboration reported the discovery of two open charm tetraquark states, $X_{0}(2866)$ and $X_{1}(2904)$. In the present work, we study the $D^{(\ast)}$ and $\bar{K}^{(\ast)}$ interaction in the one-boson exchange model and show that the $X_{0}(2866)$ can be understood as a $D^{\ast}\bar{K}^{\ast}$ molecule with $I(J^{P})=0(0^{+})$, or at least it has a large molecular component. On the other hand, the $X_{1}(2904)$ can not be interpreted as a molecular state. Inspired by the discovery of the $X_0(2866)$ and the fact that the $D^*\bar{K}^*$ interaction is strong enough to generate a bound state, we also discuss likely existence of other open charm molecules. In the meson-meson sector, two molecules near the mass thresholds of $DD^{\ast}$ and $D^{\ast}D^{\ast}$ with $I(J^{P})=0(1^{+})$ are obtained, and using the heavy quark flavor symmetry their $\bar{B}\bar{B}^{\ast}$ and $\bar{B}^{\ast}\bar{B}^{\ast}$ counterparts are also predicted. In the meson-baryon sector, 7 open charm molecules with $I=1/2$ near the mass thresholds of $D^{(\ast)}\Sigma_{c}^{(\ast)}$ naturally appear, as dictated by the heavy quark spin symmetry.

Highlights

  • Since the Belle Collaboration discovered Xð3872Þ [1], a lot of exotic states that can not fit into the conventional quark model have been reported by collaborations all over the world, which offers the chance to study the strong interaction, and challenges existing theories and models

  • We study the DðÃÞ and KðÃÞ interaction in the one-boson exchange model and show that X0ð2866Þ can be understood as a DÃK à molecule with IðJPÞ 1⁄4 0ð0þÞ, or at least it has a large molecular component

  • The results indicate that a bound state near the mass threshold of DK Ã is likely to exist, but with a cutoff much larger than the preferred value of about 1 GeV

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Summary

INTRODUCTION

Since the Belle Collaboration discovered Xð3872Þ [1], a lot of exotic states that can not fit into the conventional quark model have been reported by collaborations all over the world, which offers the chance to study the strong interaction, and challenges existing theories and models. In 2003, the BABAR Collaboration reported a narrow structure in the Dþs π0 invariant mass distribution with a mass of 2.32 GeV and quantum number JP 1⁄4 0þ [17], whose mass is much lower than the quark model prediction [18]. Very recently the LHCb Collaboration reported the discovery of two new states, X0ð2866Þ and X1ð2904Þ, in the DþK− invariant mass spectrum of the BÆ → DþD−KÆ decay [27,28] Their corresponding quantum number, mass, and width (in units of MeV) are JP 1⁄4 0þ ∶ m 1⁄4 2866 Æ 7; Γ 1⁄4 57 Æ 13; ð1Þ.

FORMALISM
NUMERICAL RESULTS AND DISCUSSIONS
SUMMARY AND CONCLUSION
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