$Z_{cs}$, $Z_c$ and $Z_b$ states under the complex scaling method

Abstract

We investigate the $Z_b$, $Z_c$ and $Z_{cs}$ states within the chiral effective field theory framework and the $S$-wave single channel molecule picture. With the complex scaling method, we accurately solve the Schrödinger equation in momentum space. Our analysis reveals that the $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$ states are the resonances composed of the $S-$wave $(B{\bar{B}}^{\ast }+B^{\ast }\bar{B})/\sqrt{2}$, $B^{\ast }{\bar{B}}^{\ast }$, $(D{\bar{D}}^{\ast }+D^{\ast }\bar{D})/\sqrt{2}$ and $D^{\ast }{\bar{D}}^{\ast }$, respectively. Furthermore, although the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ states exhibit a significant difference in width, these two resonances may originate from the same channel, the $S-$wave $(D_s{\bar{D}}^{\ast }+D_s^{\ast }\bar{D})/\sqrt{2}$. Additionally, we find two resonances in the $S-$wave $D_s^{\ast }{\bar{D}}^{\ast }$ channel, corresponding to the $Z_{cs}(4123)$ and $Z_{cs}(4220)$ states that await experimental confirmation.

Comments: 10 pages, 5 figures, 4 tables