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We perform a theoretical study of the $J/\psi \to \omega (\phi) K^* \bar{K} +c.c. \to \omega (\phi) K^0 \pi^+ K^-$ reactions with the assumption that the$f_1(1285)$ is dynamically generated from a single channel $K^* \bar{K} + c.c$interaction in the chiral unitary approach. Two peaks in the $K^0 \pi^+ K^-$invariant mass distribution are observed, one clear peak locates at the$f_1(1285)$ nominal mass, the other peak locates at around $1420\; \rm MeV$with about $70 \;\rm MeV$ width. We conclude that the former peak is associatedwith the $f_1(1285)$ and the latter peak is not a genuine resonance but amanifestation of the kinematic effect in the higher energy region caused by the$K^* \bar{K} + c.c.$ decay mode of the $f_1(1285)$.

$J/\psi$ decays into $\omega (\phi) f_1(1285)$ and $\omega (\phi) \,''f_1(1420)''$