Theoretical description of the J/ψ→η(η′)h1(1380)\boldsymbol{J/\psi \to \eta (\eta') h_1(1380)}, J/ψ→η(η′)h1(1170)\boldsymbol{J/\psi \to \eta (\eta') h_1(1170)} and J/ψ→π0b1(1235)0\boldsymbol{J/\psi \to \pi^0 b_1(1235)^0} reactions

We have made a study of the $J/\psi \to \eta' h_1, \eta h_1$ (with $h_1$ being $h_1(1170)$ and $h_1(1380)$) and $J/\psi \to \pi^0 b_1(1235)^0$ assuming the axial vector mesons to be dynamically generated from the pseudoscalar-vector meson interaction. We have taken the needed input from previous studies of the $J/\psi \to \phi \pi \pi, \omega \pi \pi$ reactions. We obtain fair agreement with experimental data and provide an explanation on why the recent experiment on $J/\psi \to \eta' h_1(1380), h_1(1380) \to K^{*+} K^- +c.c.$ observed in the $K^+ K^- \pi^0$ mode observes the peak of the $h_1(1380)$ at a higher energy than its nominal mass.Comment: 21 pages, 6 figure