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

Abstract: We investigate $\pi\rho$ scattering based on the coupled-channel formalism with the $\pi\rho$ and $K\bar{K}^*$ ($\bar{K}K^*$) 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 $K\bar{K}^*$ ($\bar{K}K^*$) channel. We obtain the pole position of the $a_1$ meson as $\sqrt{s_R} = (1170.7 - i 173.0)$ MeV. We conclude that the $a_1$ meson can be interpreted as a kaon and vector kaon molecular state.