is also what corresponds to the $K^0_s [\pi^+ \pi^-]_s$, $M_2$ amplitude of Ref. [@kaminski], the one that considers the $s$-wave interaction of the pions and the $f_0(500)$ and $f_0(980)$ resonances, or the $a_0(980)$ when we consider in addition the $K^0_s [\pi^0 \eta]_s$ amplitude.

Results
=======

In Fig. \[Fig:dgamr600\], we show the results of our calculation. We have taken the cut off $q_{\rm qmax} = 600$ MeV as in Ref. [@weihong]. We superpose the two mass distributions $d\Gamma /dM_{\rm inv}$ for $\pi^+ \pi^-$ (solid line) and $\pi^0
\eta$ (dashed line). The scale is arbitrary, since it corresponds to taking $V_p = 1000$ in Eqs. (\[eq:fzero\]) and (\[eq:azero\]), but it is the same for the two distributions, which allows us to compare $f_0(980)$ with $a_0(980)$ production. As we discussed before, it is a benefit of the weak interactions that we can see simultaneously both the $I=0$ $f_0(980)$ and $I=1$ $a_0(980)$ productions in the same $D^0 \to \bar{K}^0 R$ decay.

![The $\pi^+ \pi^-$ (solid line) and $\pi^0 \eta$ (dashed line) invariant mass distributions for the $D^0 \to \bar{K}^0 \pi^+
\pi^-$ decay and $D^0 \to \bar{K}^0 \pi^0 \eta$ decay, respectively. A smooth background is plotted below the $a_0(980)$ and $f_0(980)$ peaks.[]{data-label="Fig:dgamr600"}](dgamr600.eps)

When it comes 