The low lying scalar resonances in the D⁰ decays into K⁰ₛ and f₀(500), f₀(980), a₀(980)

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The D⁰ decay into K⁰ₛ and a scalar resonance, f₀(500), f₀(980), a₀(980), is studied obtaining the scalar resonances from final state interaction of a pair of mesons produced in a first step in the D⁰ decay into K⁰ₛ 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 B⁰ decays into J/ψ and a scalar meson that have at least one Cabibbo suppressed vertex. Concretely the a₀(980) production is Cabibbo allowed here, while it cannot be seen in the B⁰ₛ decay into J/ψa₀(980) and is doubly Cabibbo suppressed in the B⁰ decay into J/ψa₀(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.