Implications of the Z_(cs)(3985) and Z_(cs)(4000) as two different states

Recently, the hidden charm tetraquark states $Z_{cs}(3985)$ and $Z_{cs}(4000)$ with strangeness were observed by the BESIII and LHCb collaborations, respectively, which are great breakthroughs for exploring exotic QCD structures. The first and foremost question is whether they are the same state. In this work, we explore the implications of the narrower state $Z_{cs}(3985)$ in BESIII and the wider one $Z_{cs}(4000)$ in LHCb as two different states. Within a solvable nonrelativistic effective field theory, we include the possible violations of heavy quark spin symmetry and SU(3) flavor symmetry in a comprehensive approach. If $Z_{cs}(3985)$ and $Z_{cs}(4000)$ are two different states, our results show that $Z_{cs}(4000)/Z_{cs}(3985)$ is the pure $(|\bar{D}_s^*D\rangle+/- |\bar{D}_sD^*\rangle)/\sqrt{2}$ state, and the SU(3) flavor partner of $Z_{c}(3900)$ is $Z_{cs}(4000)$ rather than the $Z_{cs}(3985)$. Another two important consequences are the existence of a tensor $\bar{D}_s^*D^*$ resonance with mass about 4126 MeV and width 13 MeV, and the suppression of the decay mode $Z_{cs}(3985) \to J/\psi K$. The two consequences can be tested in experiments and distinguish the two-state interpretation from the one-state scheme.