Based on the hadronic resonance picture, we explore a unified framework to describe the observed $Z_{cs}$ and $Z_c$ states that are close to the thresholds of the $D^{(*)}{\overline{D}}_s^{(*)}$ and $D^{(*)}{\overline{D}}^{(*)}$ systems, respectively. We assume that the $Z_{cs}(4000)$ and $Z_{cs}(3985)$ are two different states. Specifically, we assign the $Z_{cs}(4000)$ as the SU(3) partner of the $Z_c(3900)$ ($J^{PC}=1^{+-}$) due to its observation in the $J/\mathrm{\Psi }K$ channel, the difficulty of this assignment is the large width difference between the $Z_{cs}(4000)$ and the $Z_c(3900)$ state. Then the $Z_{cs}(3985)$ should corresponds to the $Z_c$ state that is close to the threshold of $D{\overline{D}}^{*}$ system with $J^{PC}=1^{++}$, the difficulty of this assignment is the absence of such a $Z_c$ state in experiment. We construct the effective potentials of the $Z_{cs}$ and $Z_c$ states by analogy with the effective potentials of the leading-order and next-to-leading-order $N-\overline{N}$ interactions. Then we introduce an SU(3) breaking factor $g_x$ to identify the differences between the effective potentials in the $Z_{cs}$ and $Z_c$ states. We perform two calculations to discuss the differences and similarities of the $Z_{cs}$ and $Z_c$ states. In the first calculation, we show that the above two difficulties can be explained simultaneously by the inclusion of the SU(3) breaking effect. In the second calculation, we show that this framework is promising to simultaneously describe the interactions of the observed $Z_{cs}$ and $Z_c$ states that are close to the thresholds of the $D^{(*)}{\overline{D}}_s^{(*)}$ and $D^{(*)}{\overline{D}}^{(*)}$ systems, respectively.

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• Bound states
• Effective field theory
• Particle interactions
• Phenomenology