$a^0_0(980)-f_0(980)$ Mixing and Spin Asymmetry in the $\pi^-p\to\eta\pi^0n$ Reaction

The mass difference between the $K^+$ and $K^0$ mesons induces mixing of the $a^0_0(980)$ and $f_0(980)$ resonances. The mixing amplitude is large, on the order of $m_{K}(m^2_{K^0}-m^2_{K^+})^{1/2}\approx\sqrt\alpha\,m^2_K$ near the $K\bar K$ thresholds, and its phase changes sharply by 90$^\circ$. A high-energy experiment on the $\pi^-p\to\eta\pi^0n$ reaction in a polarized target is proposed. In this experiment, the presence of $a^0_0(980)-f_0(980)$ mixing can be unambiguously and simply identified by the presence of a large jump in the azimuthal asymmetry of the cross section for production of the $\eta\pi^0$ system in the $S$ wave near the $K\bar K$ thresholds. Our estimates of the magnitude of the polarization effect, which is expected to be observed in the experiment, are almost model-independent.