explains the features of the experiment of Ref. [@Barberis:1998by]. The conclusion of all these observations is that the $f_1(1420)$ is not a genuine resonance, but the manifestation of the $K^* \bar K$ and $\pi a_0(980)$ decay modes of the $f_1(1285)$ resonance. This would go in line with the conclusions of Refs. [@Ketzer:2015tqa; @Aceti:2016yeb] that the “$a_1(1420)$” is not a genuine resonance, but the manifestation of the $\pi f_0(980)$ decay mode of the $a_1(1260)$ resonance.

Formalism
=========

The resonance $f_1(1420)$ is observed in very high energy collisions, which we depict in Fig. \[Fig:1\], and the resonance is observed in the invariant mass of particles 2 and 3.

![Diagrammatic representation of the process producing the resonance, observed in the decay channel $2+3$.[]{data-label="Fig:1"}](fig1.eps "fig:"){width="40.00000%"}\

In the Mandl and Shaw normalization of fermion fields [@MandlShaw:2010] we have for this process with three particles in the final state $$\label{Eq:1}
  \frac{\mathrm{d}^2\sigma}{\mathrm{\rm d} t \,\mathrm{d} M_{23} } = \frac{1}{32\, p_a^2 \, s}\, \prod(2m_F) \frac{1}{(2\pi)^3}\, \widetilde{p}_2 \overline{\sum}\sum|T|^2,$$ where $m_F$ refers to the masses of the fermions, and the sum and average of $|T|^2$ is done over the polarizations of all particles involved. In Eq. (\[Eq:1\]) $\widetilde{p}_2$ is the momentum of particle 2 in the rest frame of the 