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 $K^{\ast }{\bar{D}}^{\ast }$ 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 $K^{\ast }{\bar{D}}^{\ast }$ 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 $K^{\ast }{\bar{D}}^{\ast }$ interaction with a small $\alpha$ value, which can be searched in future experiments.

Comments: 5 pages, 2 figures; more discussions added; typos corrected