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 $\varphi$) 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.

5 pages

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• Understanding spin parity of $P_c(4450)$ and $Y(4274)$ in a hadronic molecular state picture
• Molecular picture for $X_0(2900)$ and $X_1(2900)$
• $\bar{K}\Lambda$ molecular explanation to the newly observed $\Xi (1620{)}^0$
• Analysis of recent CLAS data on $f_1(1285)$ photoproduction
• Interpretation of $Y(4390)$ as an isoscalar partner of $Z(4430)$ from $D^{\ast }(2010){\bar{D}}_1(2420)$ interaction
• Hidden-strange molecular states and the $N\varphi$ bound state via a QCD van der Waals force
• Investigation of pion-induced $f_1(1285)$ production off a nucleon target within an interpolating Reggeized approach
• New type of hydrogenlike charm-pion or charm-kaon matter
• Correlation function for the $n{\bar{D}}_{s0}^{\ast }(2317)$ interaction and the issue of elastic unitarity
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays