Configuration mixing in strange tetraquarks $Z_{cs}$

The BESIII Collaboration has observed a candidate for a $c \bar c s \bar u$ tetraquark $Z_{cs}$ at $(3982.5^{+1.8}_{-2.6} \pm 2.1)$ MeV and width $(12.8^{+5.3}_{-4.4} \pm 3.0)$ MeV, while the LHCb Collaboration has observed a $Z_{cs}$ candidate in the $\jpsi K^-$ channel with mass of $(4003 \pm 6 ^{+4}_{-14})$ MeV and width $(131 \pm 15 \pm 26)$ MeV. In this note we examine the possibility that these two states are distinct eigenstates of a mixing process similar to that which gives rise to two axial-vector mesons labeled by the Particle Data Group $K_1(1270)$ and $K_1(1400)$. The main point is that on top of a $\bar c c$ pair, the $Z_{cs}$ states have the same light quark content as the $K_1$-s. In the compact tetraquark picture this implies several additional states, analogous to members of the $K_1$ nonet. These states have not yet been observed, nor are they required in the molecular approach. Thus experimental discovery or exclusion of these extra states will be a critical test for competing models of exotic mesons with hidden charm.