Two-pole structure of the $h_1(1415)$ axial-vector meson: resolving mass discrepancy

We investigate isoscalar axial-vector mesons using a coupled-channel formalism. The kernel amplitudes are constructed from meson-exchange diagrams in the $t$- and $u$-channels, which are derived from effective Lagrangians based on hidden local symmetry. We incorporate six channels: $\pi\rho$, $\eta\omega$, $K\bar{K}^*$, $\eta\phi$, $\eta'\omega$, and $\eta'\phi$, and solve the off-shell coupled integral equations. We first discuss the dynamical generation of the $h_1(1170)$. The pole diagram for $h_1(1595)$ has a certain effect on the generation of $h_1(1170)$. We observe two poles at $(1387-i6)$ MeV and $(1452-i51)$ MeV, which exhibit a two-pole structure of the $h_1(1415)$ meson. This two-pole structure may resolve the discrepancy in the experimental data on the mass of $h_1(1415)$. The results show that the lower pole couples strongly to the $K\bar{K}^*$ channel, while the higher pole couples predominantly to the $\eta\phi$ channel. This provides insights into the nature of $h_1$ mesons and explains ossible discrepancies in the mass of $h_1(1415)$.