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

TL;DR

This paper investigates whether the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ are distinct states, using an effective field theory approach, and predicts experimental signatures to differentiate these interpretations.

Contribution

It provides a theoretical framework to distinguish the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ as separate states, including predictions for related resonances and decay modes.

Findings

$Z_{cs}(4000)$ is a SU(3) partner of $Z_c(3900)$

Predicted a tensor $ar{D}_s^*D^*$ resonance at 4126 MeV with 13 MeV width

Suppressed decay mode $Z_{cs}(3985) o J/ ext{ extit{psi}} K$

Abstract

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.