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

Abstract

Abstract We investigate the $$Z_b$$ Z b , $$Z_c$$ Z c and $$Z_{cs}$$ 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 ( 10610 ) , $$Z_b(10650)$$ Z b ( 10650 ) , $$Z_c(3900)$$ Z c ( 3900 ) and $$Z_c(4020)$$ Z c ( 4020 ) states are the resonances composed of the S-wave $$(B\bar{B}^{*}+B^{*}\bar{B})/\sqrt{2}$$ ( B B ¯ ∗ + B ∗ B ¯ ) / 2 , $$B^{*}\bar{B}^*$$ B ∗ B ¯ ∗ , $$(D\bar{D}^{*}+D^{*}\bar{D})/\sqrt{2}$$ ( D D ¯ ∗ + D ∗ D ¯ ) / 2 and $$D^{*}\bar{D}^*$$ D ∗ D ¯ ∗ , respectively. Furthermore, although the $$Z_{cs}(3985)$$ Z cs ( 3985 ) and $$Z_{cs}(4000)$$ Z cs ( 4000 ) states exhibit a significant difference in width, these two resonances may originate from the same channel, the S-wave $$(D_{s}\bar{D}^{*}+D_{s}^{*}\bar{D})/\sqrt{2}$$ ( D s D ¯ ∗ + D s ∗ D ¯ ) / 2 . Additionally, we find two resonances in the S-wave $$D_s^*\bar{D}^*$$ D s ∗ D ¯ ∗ channel, corresponding to the $$Z_{cs}(4123)$$ Z cs ( 4123 ) and $$Z_{cs}(4220)$$ Z cs ( 4220 ) states that await experimental confirmation.