Inconsistency of the data on the $K_1(1270) \to \pi K^*_0(1430)$ decay width
We show, using the same Lagrangian for the $K_1(1270) \to \pi K^*_0(1430)$ and $K^*_0(1430) \to K_1(1270) \pi$ decays, that the present PDG data on the partial decay width of $K_1(1270) \to \pi K^*_0(1430)$ implies a width for $K^*_0(1430) \to K_1(1270) \pi$ decay which is about ten times larger than the total $K^*_0(1430)$ width. A discussion on this inconsistency is done, stressing its relationship to the existence of two $K_1(1270)$ states obtained with the chiral unitary theory, which are not considered in the experimental analyses of $K\pi\pi$ data.