The fact that we have now weak interactions that allow for isospin violation permit that both the $f_0(980)$ and $a_0(980)$ resonances are produced in the same reaction. This is a novelty with respect to strong interactions that are isospin conserving. The present weak decay presents then a new challenge since one can determine the relative weight of production of each one of these resonances in the same reaction, a new situation with respect to what one has in strong interaction reactions.

Formalism
=========

The process for $D^0 \to K^0_s R$ proceeds at the elementary quark level as depicted in Fig. \[Fig:feyn\] (A). The process is Cabibbo allowed, the $s\bar{d}$ pair produces the $\bar{K}^0$, which will convert to the observed $K^0_s$ through time evolution with the weak interaction. The remaining $u\bar{u}$ pair gets hadronized adding an extra $\bar{q}q$ with the quantum mumbers of the vacuum, $\bar{u}u +
\bar{d}d + \bar{s}s$. This topology is the same as for the $\bar{B}_s \to J/\psi s\bar{s}$ (substituting the $s\bar{d}$ by $c\bar{c}$) [@Stone:2013eaa], that upon hadronization of the $s\bar{s}$ pair leads to the production of the $f_0(980)$ [@weihong], which couples mostly to the hadronized $K
\bar{K}$ components.

![(A): Dominant diagrams for $D^0 \to \bar{K}^0 u \bar{u})$ 