Role of the $f_1(1285)$ state in the $J/\psi \to \phi \bar{K} K^*$ and $J/\psi \to \phi f_1(1285)$ decays

We study the role of the $f_1(1285)$ resonance in the decays of $J/\psi \to \phi \bar{K} K^*$ and $J/\psi \to \phi f_1(1285)$. The theoretical approach is based on the results of chiral unitary theory where the $f_1(1285)$ resonance is dynamically generated from the $K^* \bar{K} - c.c.$ interaction. In order to further test the dynamical nature of the $f_1(1285)$ state, we investigate the $J/\psi \to \phi \bar{K} K^*$ decay close to the $\bar{K} K^*$ threshold and make predictions for the ratio of the invariant mass distributions of the $J/\psi \to \phi \bar{K} K^*$ decay and the $J/\psi \to \phi f_1(1285)$ partial decay width with all the parameters of the mechanism fixed in previous studies. The results can be tested in future experiments and therefore offer new clues on the nature of the $f_1(1285)$ state.