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

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 $DK^\ast$ might also exist as virtual states, and the $0(1^+)$ $DK^\ast$ 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.