Molecular states from $D^{(*)}\bar{D}^{(*)}/B^{(*)}\bar{B}^{(*)}$ and $D^{(*)}D^{(*)}/\bar{B}^{(*)}\bar{B}^{(*)}$ interactions (2011.04980v4)

Abstract: In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $D^{()}\bar{D}^{()}/B^{()}\bar{B}^{()}$ and $D^{()}D^{()}/\bar{B}^{()}\bar{B}^{()}$ interactions in the quasipotential Bethe-Salpeter equation (qBSE) approach. With the help of Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the $\pi$, $\eta$, $\rho$, $\omega$ and $\sigma$ exchanges, as well as $J/\psi$ or $\Upsilon$ exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$, and $Z_b(10650)$, can be related to the $D\bar{D}^{*}$, $D^\bar{D}^{}$, $B\bar{B}^{*}$, and $B^\bar{B}^{}$ interactions with quantum numbers $I^G(J^P)=1^+(1^{+})$, respectively. The $D\bar{D}^{*}$ interaction is also attractive enough to produce a pole with $0^+(0^+)$ which is related to the $X(3872)$. Within the same theoretical frame, the existence of $D\bar{D}$ and $B\bar{B}$ molecular states with $0(0^+)$ are predicted. The possible $D^\bar{D}^$ molecular states with $0(0^+, 1^+, 2^+)$ and $1(0^+)$ and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $DD/\bar{B}\bar{B}$ interaction while a bound state is found with $0(1^+)$ from $DD^/\bar{B}\bar{B}^$ interaction. The $D^D^/\bar{B}^\bar{B}^$ interaction produces three molecular states with $0(1^+)$, $0(2^+)$ and $1(2^+)$.