Manifestations of the $a^0_0(980)-f_0(980)$ mixing in $D^0\to K^0_S\pi^+\pi^-$ and $D^0\to K^0_S\eta\pi^0$ decays

Possible manifestations of the isospin-breaking mixing of the $a_{0}^{0} (980)$ and $f_{0} (980)$ resonances are analyzed in the $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and $D^{0} \to K_{S}^{0} η π^{0}$ decays. It is shown that the $a_{0}^{0} (980) - f_{0} (980)$ mixing has the most influence on the $π^{+} π^{-}$ mass spectrum in the decay $D^{0} \to K_{S}^{0} π^{+} π^{-}$ . Owing to the $a_{0}^{0} (980) - f_{0} (980)$ mixing, the $f_{0} (980)$ peak in $D^{0} \to K_{S}^{0} f_{0} (980) \to K_{S}^{0} π^{+} π^{-}$ can experience distortions comparable with its size. The effect essentially depends on the relative phase between the amplitudes of the $D^{0} \to K_{S}^{0} f_{0} (980)$ and $D^0\to K^0_Sa^0_0(980)$ transitions.

Manifestations of the $a_{0}^{0} (980) - f_{0} (980)$ mixing in $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and $D^{0} \to K_{S}^{0} η π^{0}$ decays

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Manifestations of the $a_{0}^{0} (980) - f_{0} (980)$ mixing in $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and $D^{0} \to K_{S}^{0} η π^{0}$ decays

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Manifestations of the a00(980)−f0(980)a00​(980)−f0​(980) mixing in D0→KS0π+π−D0→KS0​π+π− and D0→KS0ηπ0D0→KS0​ηπ0 decays

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Manifestations of the a00(980)−f0(980)a00​(980)−f0​(980) mixing in D0→KS0π+π−D0→KS0​π+π− and D0→KS0ηπ0D0→KS0​ηπ0 decays

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Manifestations of the $a_{0}^{0} (980) - f_{0} (980)$ mixing in $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and $D^{0} \to K_{S}^{0} η π^{0}$ decays

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Manifestations of the $a_{0}^{0} (980) - f_{0} (980)$ mixing in $D^{0} \to K_{S}^{0} π^{+} π^{-}$ and $D^{0} \to K_{S}^{0} η π^{0}$ decays

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