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

Abstract

We investigate the dynamically generated $h_1$ state with spin-parity $J^P=1^{+}$ and a mass around 1790~MeV, arising from the $K^{\ast }{\bar{K}}^{\ast }$ interaction within the chiral unitary approach. The partial decay widths into the $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ channels are calculated via a triangular loop mechanism. In this mechanism, the $h_1$ state couples to $K^{\ast }{\bar{K}}^{\ast }$, and final-state interactions between $K^{\ast }$ and ${\bar{K}}^{\ast }$ proceed through pseudoscalar-meson exchange, leading to the final states $\bar{K}$ (or $\pi$) and $K_1(1270)$ [or $b_1(1235)$]. We also present the invariant mass distributions of a vector meson and a pseudoscalar meson originating from the decays of $K_1(1270)$ or $b_1(1235)$, along with the corresponding decay widths. Our results show that these decay widths are all of the order of a few MeV. We hope that future experiments can test the predictions presented here, thereby helping to identify this $h_1$ state.