The hidden-charm tetraquarks with strangeness, $c\overline{c}s\overline{q}$ ($q=u$, $d$), in $J^P=0^{+}$, $1^{+}$, and $2^{+}$ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron, and multiquark phenomenology. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark, and K-type arrangements of quarks with all possible color wave functions in the four-body sector. Among the different numerical techniques to solve the Schrödinger-like four-body bound state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions, which is characterized by its simplicity and flexibility. This theoretical framework has already been used to study different kinds of multiquark systems, such as the hidden-charm pentaquarks $P_c^{+}$ and doubly charmed tetraquarks $T_{cc}^{+}$. The recently reported $Z_{cs}$ states by the BESIII and LHCb Collaborations could be associated, in our investigation, with either compact tetraquark or hadronic molecular resonance configurations. However, it is fair to recognize that our complex poles survive when either the $(c\overline{c})(s\overline{q})$ or $(c\overline{q})(s\overline{c})$ configuration is preserved, but most of them get diluted when both are considered at the same time, indicating that such states seem to be very unstable. Finally, we mention that similar types of structures are also found in the mass range between 3.8 and 4.6 GeV.

• Received 12 September 2021
• Accepted 25 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.094035

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Published by the American Physical Society