# 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

## TL;DR

This paper investigates how the mixing of the $a^0_0(980)$ and $f_0(980)$ resonances affects decay spectra in $D^0$ meson decays, revealing significant distortions in the $
ho^+
ho^-$ mass spectrum due to isospin-breaking effects.

## Contribution

It provides a detailed analysis of the $a^0_0(980)$-$f_0(980)$ mixing manifestations in specific $D^0$ decay channels, highlighting the impact on the $
ho^+
ho^-$ spectrum and the dependence on phase differences.

## Key findings

- The $a^0_0(980)$-$f_0(980)$ mixing significantly influences the $
ho^+
ho^-$ mass spectrum.
- The $f_0(980)$ peak can be distorted due to mixing effects.
- The magnitude of distortions depends on the phase between decay amplitudes.

## Abstract

Possible manifestations of the isospin-breaking mixing of the $a^0_0(980)$ and $f_0(980)$ resonances are analyzed in the $D^0\to K^0_S \pi^+\pi^-$ and $D^0\to K^0_S\eta\pi^0$ decays. It is shown that the $a^0_0(980)-f_0(980)$ mixing has the most influence on the $\pi^+\pi^-$ mass spectrum in the decay $D^0\to K^0_S\pi^+\pi^-$. Owing to the $a^0_0(980)-f_0(980)$ mixing, the $f_0(980)$ peak in $D^0 \to K^0_Sf_0(980)\to K^0_S \pi^+\pi^-$ can experience distortions comparable with its size. The effect essentially depends on the relative phase between the amplitudes of the $D^0\to K^0_Sf_0(980)$ and $D^0\to K^0_Sa^0_0(980)$ transitions.