K}^2 \, p_{\bar K}~~
   \\ &\times ~~
 \frac{8 \pi m_{\rm inv}^2 \Gamma_{K^*}(m_{\rm inv})}{|m_{\rm inv}^2 - m_{K^*}^2 + i m_{K^*} \Gamma_{K^*}(m_{\rm inv})|^2}\, ,\end{aligned}$$ where $$\label{Eq:12}
  \Gamma_{K^*}(m_{\rm inv}) = \frac{m_{K^*}^2}{m_{\rm inv}^2} \, \frac{{\widetilde{p}_\pi}^{\,3}}{\widetilde{p}_\pi^{\,3}|_{\rm on}}\,\Gamma_{K^*}|_{\rm on}\, ,$$ where $\Gamma_{K^*}|_{\rm on}=49.1$ MeV is the nominal width for the $K^*$, and $\widetilde{p}_\pi$, $\widetilde{p}_\pi|_{\rm on}$ the pion momenta in the $K^*$ rest frame with $K^*$ mass $m_{\rm inv}$ or $m_{K^*}$ respectively, $$\label{Eq:13}
\widetilde{p}_\pi = \frac{\lambda^{1/2}(m_{\rm inv}^2,m_K^2,m_\pi^2)}{2m_{\rm inv}}.$$ In Eq. (\[Eq:12\]) we have taken into account that the $K^* \to K \pi$ proceeds in $P$-wave.

In Fig. \[Fig:4\] we plot the results for Eq. (\[Eq:5\]) with $\Gamma_{R,23}$ replaced by Eqs. (\[Eq:9\]) and (\[Eq:11\]), and also when $\Gamma_{R,23}$ is replaced by $\Gamma_{f_1}$.

![Production of $K \pi \bar K$ coming from $K^* \bar K$ decay of the $f_1(1285)$ considering the decay of $K^*$ into $K \pi$. The dashed line accounts for $K \pi \bar K$ production and the solid line accounts for the decay of the $f_1(1285)$ into other channels.[]{data-label="Fig:4"}](fig4.eps "fig:"){width="50.00000%"}\

Fig. \[Fig:4\] is very intuitive, we see a double peak structure. The first peak accounts for the standard $f_1(1285)$ decay into $K \pi \bar K$ observed with the shape of the $f_1(1285)$. The ratio of strengths at the 