Interference phenomena in the decay $D^+_s\to\eta\pi^0\pi^+$ induced by the $a^0_0(980)-f_0(980)$ mixing

Using the data on the decay $D^+_s\to f_0(980)\pi^+\to K^+K^-\pi^+$, we estimate the amplitude of the process $D^+_s\to\left[f_0(980)\to (K^+K^-+K^0\bar K^0)\to a^0_0(980)\right]\pi^+\to\eta\pi^0\pi^+$, caused by the mixing of $a^0_0(980)$ and $f_0(980)$ resonances that breaks the isotopic invariance due to the $K^+$ and $K^0$ meson mass difference. Effects of the interference of this amplitude with the amplitudes of the main mechanisms responsible for the decay $D^+_s \to\eta \pi^0\pi^+$ are analyzed. As such mechanisms, we examine the transition $D^+_s\to\eta\rho^+\to\eta\pi^0\pi^+$, which is observed in experiment, and the possible transition $D^+_s\to\left(a^0_0(980) \pi^++a^+_0(980)\pi^0\right)\to\eta \pi^0\pi^+$. It is shown that the rapidly varying phase of the $a^0_0(980)-f_0(980)$ transition amplitude strongly influences on the interference curves.