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

TL;DR

This paper predicts new $ar{D}_s^{(*)} D_s^{(*)}$ bound states based on SU(3) flavor and heavy quark spin symmetries, supported by existing theoretical and experimental evidence, and suggests future experimental searches.

Contribution

It demonstrates the existence of specific $ar{D}_s^{(*)} D_s^{(*)}$ bound states as symmetry partners of $X(3872)$, incorporating symmetry breaking effects and existing lattice QCD and experimental data.

Findings

Predicted new bound states $[ar{D}_s^{*}D_s^{*}]^{0^{++}}$, $[ar{D}_s^{*}D_s/ar{D}_s D_s^{*}]^{1^{+-}}$, and $[ar{D}_s^{*}D_s^{*}]^{1^{+-}}$.

Supported the existence of $[ar{D}_s D_s]^{0^{++}}$ bound state from lattice QCD and $ ext{chi}_{c0}(3930)$ observation.

Suggested experimental processes for detecting these states in $B$ decays.

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 $[\bar{D}_{s}^{*}D_{s}^{*}]^{0^{++}}$, $[\bar{D}_{s}^{*}D_{s}/\bar{D}_{s}^{}D_{s}^*]^{1^{+-}}$, and $[\bar{D}_{s}^{*}D_{s}^{*}]^{1^{+-}}$ 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 $\bar{D}^{*}D/\bar{D} D^{*}$ 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 $\chi_{c0}(3930)$ 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 $B\to D_{(s)}^{(*)}\bar{D}^{(*)}_{(s)}h$ processes ($h$ denotes the light hadrons). The $[\bar{D}_{s}^{*}D_{s}^{*}]^{0^{++}}$ bound state is also expected to be reconstructed in the $J/\psi \phi$ final state in the $B\to J/\psi \phi K$ decay.