'The low lying scalar resonances in the $D^0$ decays into $K^0_s$ and $f_0(500)$, $f_0(980)$, $a_0(980)$'
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Introduction
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The rates for $D^0$ decay into $K^0_s$ and a scalar resonance, $f_0(980)$, $a_0(980)$ are measured by the CLEO collaboration in Ref. [@Muramatsu:2002jp] and Ref. [@Rubin:2004cq] respectively and the rates are relatively large. The $f_0(980)$ is seen through its decay into $\pi^+ \pi^-$ and the $a_0(980)$ through the $\pi^0 \eta$ channel. Related references on the issue can be seen in the PDG [@pdg]. Theoretical work on these decays is scarce and is mostly devoted to issues related to CP violation or $D^0-D^{*0}$ mixing. In Ref. [@kaminski] a thorough study is done of the $D^0 \to K^0_s \pi^+ \pi^-$ reaction and the amplitude is parametrized in terms of form factors, resonance parameters and different couplings, amounting to a set of 33 free parameters, which are fitted to the Belle [@Poluektov:2010wz] and BaBar [@delAmoSanchez:2010xz] data. The purpose is to have a good amplitude that can be used to determine the $D^0-D^{*0}$ mixing parameters and the Cabibbo-Kobayashi-Maskawa (CKM) angle $\gamma$.

The aim of the present work is different, we only evaluate the part of the $D^0 \to K^0_s \pi^+ \pi^-$ amplitude corresponding to a $K^0_s$ and 