Molecular nature of the $a_1$(1260) axial-vector meson

We investigate $\pi \rho$ scattering based on the coupled-channel formalism with the $\pi \rho$ and $K{\bar{K}}^{\ast }$ ($\bar{K}{K}^{\ast }$) channels included. We construct the kernel amplitudes by using the meson-exchange model and compute the coupled integral equation for $\pi \rho$ scattering. By performing the partial-wave expansion, we show explicitly that the $a_1(1260)$ meson is dynamically generated by the coupled-channel formalism. The $a_1$ meson only appears by including the $K{\bar{K}}^{\ast }$ ($\bar{K}{K}^{\ast }$) channel. We obtain the pole position of the $a_1$ meson as $\sqrt{s_R}=(1170.7-i173.0)$ MeV. We conclude that the $a_1$ meson can be interpreted as a kaon and vector kaon molecular state.