A combined analysis of the $Z_c(3900)$ and the $Z_{cs}(3985)$ exotic states

Abstract

We have performed a combined analysis of the BESIII data for both the $Z_c(3900)$ and $Z_{cs}(3985)$ structures, assuming that the latter is an SU(3) flavor partner of the former one. We have improved on the previous analysis of Albaladejo $et$ $al.$ [Phys. Lett. B 755, 337 (2016)] by computing the amplitude for the $D_1\bar{D}{D}^{\ast }$ triangle diagram considering both $D$ and $S$-wave $D_1{D}^{\ast }\pi$ couplings. We have also investigated effects from SU(3) light-flavor violations, which are found to be moderate and of the order of 20%. The successful reproduction of the BESIII spectra, in both the hidden-charm and hidden-charm strange sectors, strongly supports that the $Z_{cs}(3985)$ and $Z_c(3900)$ are SU(3) flavor partners placed in the same octet multiplet. The best results are obtained when an energy-dependent term in the diagonal $D^{(\ast )}{\bar{D}}_{(s)}^{(\ast )}$ interaction is included, leading to resonances (poles above the thresholds) to describe these exotic states. We have also made predictions for the isovector $Z_c^{\ast }$ and isodoublet $Z_{cs}^{\ast }$, $D^{\ast }{\bar{D}}^{\ast }$ and $D^{\ast }{\bar{D}}_s^{\ast }$ molecules, with $J^{PC}=1^{+-}$ and $J^P=1^{+}$, respectively. These states would be heavy-quark spin symmetry partners of the $Z_c$ and $Z_{cs}$. Besides the determination of the masses and widths of the $Z_c(3900)$ and $Z_{cs}(3985)$, we also predict those of the $Z_c^{\ast }$ and $Z_{cs}^{\ast }$ resonances.

27 pages, 9 figures, and 4 tables, version published in physical review D

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