Strange molecular partners of the $Z_c(3900)$ and $Z_c(4020)$

Abstract

Quantum Chromodynamics presents a series of exact and approximate symmetries which can be exploited to predict new hadrons from previously known ones. The $Z_c(3900)$ and $Z_c(4020)$ resonances, which have been theorized to be isovector $D^{\ast }\bar{D}$ and $D^{\ast }{\bar{D}}^{\ast }$ molecules [$I^G(J^{PC})=1^{-}(1^{+-})$], are no exception. Here we argue that from SU(3)-flavor symmetry, we should expect the existence of strange partners of the $Z_c$'s with hadronic molecular configurations $D^{\ast }{\bar{D}}_s$-$D{\bar{D}}_s^{\ast }$ and $D^{\ast }{\bar{D}}_s^{\ast }$ (or, equivalently, quark content $c\bar{c}s\bar{q}$, with $q=u,d$). The quantum numbers of these $Z_{cs}$ and $Z_{cs}^{\ast }$ resonances would be $I(J^P)$ = $\frac{1}{2}(1^{+})$. The predicted masses of these partners depend on the details of the theoretical scheme used, but they should be around the $D^{\ast }{\bar{D}}_s$-$D{\bar{D}}_s^{\ast }$ and $D^{\ast }{\bar{D}}_s^{\ast }$ thresholds, respectively. Moreover, any of these states could be either a virtual pole or a resonance. We show that, together with a possible triangle singularity contribution, such a picture nicely agrees with the very recent BESIII data of the $e^{+}{e}^{-}\to K^{+}(D_s^{-}{D}^{\ast 0}+D_s^{\ast -}{D}^0)$.

Comments: 8 pages, 5 figures; note added commenting on the Zcs structures reported recently by LHCb