Molecular nature of the a1(1260) axial-vector meson

Abstract

We investigate $\ensuremath{\pi}\ensuremath{\rho}$ scattering based on the coupled-channel formalism with the $\ensuremath{\pi}\ensuremath{\rho}$ and $K{\overline{K}}^{*}$ ($\overline{K}{K}^{*}$) channels included. We construct the kernel amplitudes by using the meson-exchange model and compute the coupled integral equation for $\ensuremath{\pi}\ensuremath{\rho}$ 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 $K{\overline{K}}^{*}$ ($\overline{K}{K}^{*}$) channel. We obtain the pole position of the ${a}_{1}$ meson as $\sqrt{{s}_{R}}=(1170.7\ensuremath{-}i173.0)\text{ }\text{ }\mathrm{MeV}$. We conclude that the ${a}_{1}$ meson can be interpreted as a kaon and vector kaon molecular state.