the PDG [@PDG].

We have taken advantage to make a more refined evaluation. Indeed, in Eq. we have $\Gamma_R\equiv\Gamma_{f_1(1285)}$ in the denominator. Since we are evaluating the partial decay width into $K\pi\bar K$ and $\pi a_0(980)$ we write $$\begin{aligned}
\nonumber&\Gamma_R=\Gamma_{f_1(1285)}-\Gamma_{f_1(1285)\to K\pi\bar K}|_{\rm on}-\Gamma_{f_1(1285)\to \pi a_0(980)}|_{\rm on}
\\&+\Gamma_{f_1(1285)\to K\pi\bar K}(M_{\rm inv})+\Gamma_{f_1(1285)\to \pi a_0(980)}(M_{\rm inv})\, ,\end{aligned}$$ which guarantees that on shell, $M_{\rm inv}=1285$ MeV, $\Gamma_{R}=24.1$ MeV. The values that we obtain are $\Gamma_{f_1(1285)\to K\pi\bar K}|_{\rm on}/\Gamma_{f1(1285)}=0.095$, $\Gamma_{f_1(1285)\to \pi a_0(980)}|_{\rm on}/\Gamma_{f1(1285)}=0.275$.

![The differential cross section for the decay $f_1(1285)\to\pi a_0(980)$ with the full wave function of Eq. (\[Eq:24\]).[]{data-label="Fig:8"}](fig8.eps "fig:"){width="50.00000%"}\

![The differential cross section for the decay $f_1(1285)\to K\pi\bar K$ with the full wave function of Eq. (\[Eq:24\]).[]{data-label="Fig:9"}](fig9.eps "fig:"){width="50.00000%"}\

![Same as Fig. \[Fig:4bis\] with the complete wave function of Eq. .[]{data-label="Fig:9bis"}](fig9bis.eps "fig:"){width="50.00000%"}\

We also make a more detailed comparison with the results of Ref. [@Barberis:1998by]. In Fig. \[Fig:10\] we show our results folded with a resolution of 20 MeV to facilitate comparison with the experimental numbers. We normalize the results approximately to the peak of the experimental distribution. We can see that the agreement with experiment is fair.

![Comparison of the results of Fig. \[Fig:8\], convoluted with a resolution of 20 MeV, with the 