Hadronic molecular states from the $K\bar{K}^{\ast}$ interaction

Abstract.

In this work, the $K\bar{K}^{\ast}$ interaction is studied in a quasipotential Bethe-Salpeter equation approach combined with the one-boson-exchange model. With the help of the hidden-gauge Lagrangian, the exchanges of pseudoscalar mesons ($\pi$ and $\eta$) and vector mesons ($\rho$, $\omega$ and $\phi$) are considered to describe the $K\bar{K}^{\ast}$ interaction. Besides the direct vector-meson exchange which can be related to the Weinberg-Tomozawa term, pseudoscalar-meson exchanges also play important roles in the mechanism of the $K\bar{K}^{\ast}$ interaction. The poles of scattering amplitude are searched to find the molecular states produced from the $K\bar{K}^{\ast}$ interaction. In the case of quantum number $I^{G}(J^{PC}) = 0^{+}(1^{++})$, a pole is found with a reasonable cutoff, which can be related to the $f_{1}(1285)$ in experiment. Another bound state with $0^{-}(1^{+-})$ is also produced from the $K\bar{K}^{\ast}$ interaction, which can be related to the $h_{1}(1380)$. In the isovector sector, the interaction is much weaker and a bound state with $1^{+}(1^{+})$ relevant to the $b_{1}(1235)$ is produced but at a larger cutoff. Our results suggest that in the hadronic molecular state picture the $f_{1}(1285)$ and $b_{1}(1235)$ are the strange partners of the X(3872) and $Z_{c}(3900)$, respectively.