The low lying scalar resonances in the D⁰ decays into K⁰_s and f₀(500), f₀(980), a₀(980)

The $D^0$ decay into $K^0_s$ and a scalar resonance, $f_0(500)$, $f_0(980)$, $a_0(980)$, is studied obtaining the scalar resonances from final state interaction of a pair of mesons produced in a first step in the $D^0$ decay into $K^0_s$ and the pair of pseudoscalar mesons. This weak decay is very appropriate for this kind of study because it allows to produce the three resonances in the same decay in a process that is Cabibbo allowed, hence the rates obtained are large compared to those of $\bar{B}^0$ decays into $J/\psi$ and a scalar meson that have at least one Cabibbo suppressed vertex. Concretely the $a_0(980)$ production is Cabibbo allowed here, while it cannot be seen in the $\bar{B}^0_s$ decay into $J/\psi a_0(980)$ and is doubly Cabibbo suppressed in the $\bar{B}^0$ decay into $J/\psi a_0(980)$ and has not been identified there. The fact that the three resonances can be seen in the same reaction, because there is no isospin conservation in the weak decays, offers a unique opportunity to test the ideas of the chiral unitary approach where these resonances are produced from the interaction of pairs of pseudoscalar mesons.