Revising the $f_1(1420)$ resonance

We have studied the production and decay of the $f_1(1285)$ into $\pi a_0(980)$and$K^* \bar K$ as a function of the mass of the resonance and find a shoulder around 1400 MeV, tied to a triangle singularity, for the $\pi a_0(980)$mode,andapeakaround1420MeVwithabout60MeVwidthforthe$K^* \bar K$ mode. Both these features agree with the experimental information on which the $f_1(1420)$ resonance is based. In addition, we find that if the $f_1(1420)$ is a genuine resonance, coupling mostly to $K^{\ast }\bar{K}$ as seen experimentally, one finds unavoidably about a 20% fraction for $\pi a_0(980)$ decay of this resonance, in drastic contradiction with all experiments. Altogether, we conclude that the $f_1(1420)$ is not a genuine resonance, but the manifestation of the $\pi a_0(980)$ and $K^{\ast }\bar{K}$ decay modes of the $f_1(1285)$ at higher energies than the nominal one.