Predicting the ${\bar{D}}_s^{(\ast )}{D}_s^{(\ast )}$ bound states as the partners of $X(3872)$

Abstract

In this work, we investigate the SU(3) flavor symmetry, heavy quark spin symmetry and their breaking effects in the di-meson systems. We prove the existence of the $[{\bar{D}}_s^{\ast }{D}_s^{\ast }{]}^{0^{++}}$, $[{\bar{D}}_s^{\ast }{D}_s/{\bar{D}}_s^{}{D}_s^{\ast }{]}^{1^{+-}}$, and $[{\bar{D}}_s^{\ast }{D}_s^{\ast }{]}^{1^{+-}}$ bound states as the consequence of two prerequisites in the SU(3) flavor symmetry and heavy quark spin symmetry. The first prerequisite, the $X(3872)$ as the weakly ${\bar{D}}^{\ast }D/\bar{D}{D}^{\ast }$ bound state is supported by its mass and decay branching ratios. The second prerequisite, the existence of the $[{\bar{D}}_s{D}_s{]}^{0^{++}}$ bound state is supported by the lattice QCD calculation [arXiv:2011.02542(hep-lat)] and the observation of $\ddot{I}{‡}_{c0}(3930)$ by the LHCb Collaboration[Phys.Rev.Lett.125,242001, Phys.Rev.D102,112003]. We hope the future experimental analyses can search for these bound states in the $B\to D_{(s)}^{(\ast )}{\bar{D}}_{(s)}^{(\ast )}h$ processes ($h$ denotes the light hadrons). The $[{\bar{D}}_s^{\ast }{D}_s^{\ast }{]}^{0^{++}}$ bound state is also expected to be reconstructed in the $J/\ddot{I}ˆ\ddot{I}•$ final state in the $B\to J/\ddot{I}ˆ\ddot{I}•K$ decay.

9 pages, 5 figures; add the coupled-channel discussions in EFT; to be published in Science Bulletin