Molecular picture for $X_{0}(2900)$ and $X_1(2900)$

Abstract

Inspired by the newly observed $X_{0}(2900)$ and $X_1(2900)$ at LHCb, the $K^*\bar{D}^*$ and $K\bar{D}_1$ interactions are studied in the quasipotential Bethe-Salpeter equation approach combined with the one-boson-exchange model. The bound and virtual states from the interactions are searched for as the poles in the complex energy plane of scattering amplitude. A bound state with $I(J^P)=0(0^+)$ and a virtual state with $0(1^-)$ are produced from the $K^*\bar{D}^*$ interaction and $K\bar{D}_1$ interaction, and can be related to the $X_{0}(2900)$ and $X_1(2900)$ observed at LHCb, respectively. A bound state with $I(J^P)=0(1^+)$ and a virtual state with $I(J^P)=0(2^+)$ are also predicted from the $K^*\bar{D}^*$ interaction with a small $\alpha$ value, which can be searched in future experiments.