Radiative decay into $\gamma P$ of the low lying axial-vector mesons

We evaluate the radiative decay into a pseudoscalar meson and a photon of the whole set of the axial-vector mesons dynamically generated from the vector-pseudoscalar meson ($VP$) interaction. We take into account tree level and loop diagrams coming from the axial-vector decay into a vector and a pseudoscalar meson. We find a large span for the values of the radiative widths of the different axial-vector mesons. In particular, we evaluate the radiative decay into $K \gamma$ of the two $K_1(1270)$ states, recently claimed theoretically, and discuss the experimental values quoted so far on the assumption of only one state.