Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$

Abstract

We relate the interactions of the ${\bar{D}}^{(\ast )}{K}^{\ast }$ and $D^{(\ast )}{K}^{\ast }$ systems to those of $D^{(\ast )}{D}^{(\ast )}$ and $D^{(\ast )}{\bar{D}}^{(\ast )}$ respectively, considering the residual strong interactions at the near-threshold energy is too weak to excite the strange quarks inside the hadrons. We propose an effective model to describe the low-energy S-wave interactions that are undertaken by the light $u$, $d$ quarks between two separated heavy hadrons. We find that the existence of molecules in the heavy-(anti)heavy sectors will naturally lead to the emergence of molecular states in ${\bar{D}}^{(\ast )}{K}^{\ast }$ and $D^{(\ast )}{K}^{\ast }$ systems. The recently observed $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$ can be well identified as the $0(0^{+})$ and $1(0^{+})$ partners of $T_{cc}(3875)$ and $Z_c(3900)$ in the charmed strange sector, respectively. We also predict their members under the {\it heavy} ($c$ and $s$) quark symmetry and SU(2) flavor symmetry. Most of them are very good molecule candidates, for example, (i) the $0(1^{+})$ states in $D^{\ast }{D}^{\ast }$, $\bar{D}{K}^{\ast }$, ${\bar{D}}^{\ast }{K}^{\ast }$; (ii) the $0^{(+)}(2^{+(+)})$ states in $D^{\ast }{\bar{D}}^{\ast }$, ${\bar{D}}^{\ast }{K}^{\ast }$, $D^{\ast }{K}^{\ast }$; (iii) the $1^{-}(0^{++})$ state in $D^{\ast }{\bar{D}}^{\ast }$ and $1(1^{+})$ state in $D^{\ast }{K}^{\ast }$. The $0^{+}(0^{++})$ state in $D\bar{D}$ and the $0(1^{+})$ state in $D{K}^{\ast }$ might also exist as virtual states, and the $0(1^{+})$ $D{K}^{\ast }$ can serve as a key to infer the existence of $0^{+}(0^{++})$ $D\bar{D}$. The $D_s\pi$ invariant mass spectrum of $T_{c\bar{s}0}^a(2900)$ is also studied within the coupled-channel approach, and the molecular interpretation of $T_{c\bar{s}0}^a(2900)$ is consistent with the experimental data. Searching for the predicted states in experiments is crucial to discriminate the different pictures for interpreting these near-threshold exotica.

Comments: 13 pages, 6 figs, and 4 tables