A quark-level hadronization plus meson rescattering model reproduces why D_s -> pi+ pi+ pi- contains only the f0(980) resonance while D+ -> pi+ pi+ pi- contains both f0(500) and f0(980).
Qualitative explanation of the data on the decays $D^0\to a_0(980)^\pm\pi^\mp$ and $D^+\to a_0(980)^{+(0)}\pi^{0(+)}$ in the four-quark model of the $a_0(980)$ resonance
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abstract
It is shown that the values of the ratios $\mathcal{B}(D^0\to a_0(980)^+\pi^-)/\mathcal{B} (D^0\to a_0(980)^-\pi^+ )$ and $\mathcal{B}(D^+\to a_0(980)^+\pi^0)/\mathcal{B} (D^+\to a_0(980)^0 \pi^+)$, recently measured by the BESIII Collaboration, are naturally explained in the four-quark model of the $a_0(980) $ resonance.
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Roles of $f_{0}(500)$ and $f_{0}(980)$ in the $D_{(s)}^{+}\rightarrow\pi^{+}\pi^{+}\pi^{-}$ decays
A quark-level hadronization plus meson rescattering model reproduces why D_s -> pi+ pi+ pi- contains only the f0(980) resonance while D+ -> pi+ pi+ pi- contains both f0(500) and f0(980).