$Z_{cs}$, $Z_c$ 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 Schr\"odinger 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 $(B\bar{B}^{*}+B^{*}\bar{B})/\sqrt{2}$, $B^{*}\bar{B}^*$, $(D\bar{D}^{*}+D^{*}\bar{D})/\sqrt{2}$ and $D^{*}\bar{D}^*$, 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 $(D_{s}\bar{D}^{*}+D_{s}^{*}\bar{D})/\sqrt{2}$. Additionally, we find two resonances in the $S-$wave $D_s^*\bar{D}^*$ channel, corresponding to the $Z_{cs}(4123)$ and $Z_{cs}(4220)$ states that await experimental confirmation.