that this $a_0/f_0$ large ratio was the main reason of the relatively large weight of the $W$-exchange mechanism in the fit of Ref. [@Cheng:2010vk]. Studies along the lines of Ref. [@kaminski] for $D^0 \to \bar{K}^0 \pi^0 \eta$ would help bring extra light into this issue.

Summary and conclusions
=======================

We have studied the decay of the $D^0$ decay into $K^0_s$ and a scalar resonance, $f_0(500)$, $f_0(980)$, $a_0(980)$. For this purpose we have identified the weak mechanism that allows the formation of a $\bar K^0$, that will act as a spectator, and a pair of mesons, $K\bar{K}$, $\pi \pi$, $\pi^0 \eta$, $\eta \eta$, etc., that upon interaction will give rise to the $f_0(500)$, $f_0(980)$, $a_0(980)$ resonances. The first step is the production of a $\bar{K}^0_s$ and a pair of $q \bar q$, which upon hadronization leads to these pairs of mesons. The hadronization is done in an easy way, by looking at the flavor content in meson meson of the hadronized $q \bar q$ pair. This is sufficient in the present case where we only aim at determining the shape of the invariant mass distributions and the relative weight of the different production modes, but not absolute rates. Once the weight 