to compare with the experiment we can see that the $f_0(980)$ signal is quite narrow and it is easy to extract its contribution to the branching ratios by assuming a smooth background (shown in Fig. \[Fig:dgamr600\] by the dotted line) below the $f_0(980)$ peak as a continuation of the $f_0(500)$ broad structure at lower energies. For the case of the $\pi^0 \eta$ distribution we get a clear peak that we associate to the $a_0(980)$ resonance, remarkably similar in shape to the one found in the experiment [@Rubin:2004cq]. Yet it is obvious that not all the strength seen in Fig. \[Fig:dgamr600\] can be attributed to the $a_0(980)$ resonance. One should recall that the chiral unitary approach provides amplitudes, in this case the $\pi^0 \eta$ amplitude, but the amplitudes provide poles that one associates to resonances but also background contributions, and this is the case of the $\pi^0 \eta$ distribution. In order to get a “$a_0(980)$” contribution we subtract a smooth background that we depict by a open dotted line in the figure. By doing that we have a remaining “resonant” shape with an apparent width of $80$ MeV, which is in the middle of the $50 - 100$ MeV of the 