Strong isospin symmetry breaking in light scalar meson production

Isospin symmetry breaking is discussed as a tool for studying the nature and production mechanisms of light scalar mesons. We are concerned with isospin breaking effects with an amplitude $\sim\sqrt{m_d-m_u}$ (instead of the usual $\sim m_d-m_u$), where $m_u$ and $m_d$ are the $u$ and $d$ quark masses, whose magnitude and phase vary with energy in a resonance-like way characteristic of the $K\bar K$ threshold region. We consider a variety of reactions that can experimentally reveal (or have revealed) the mixing of $a^0_0(980)$ and $f_0(980) $ resonances that breaks the isotopic invariance due to the mass difference between $K^+$ and $K^0$ mesons. Experimental results on the search for $a^0_0(980)-f_0(980)$ mixing in $f_1(1285)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$ and $\eta(14 05)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$ decays suggest a broader perspective on the isotopic symmetry breaking effects due to the $K^+$ and $K^0$ mass difference. It has become clear that not only the $a^0_0(980)-f_0(980)$ mixing but also any mechanism producing $K\bar K$ pairs with a definite isospin in an S wave gives rise to such effects, thus suggesting a new tool for studying the nature and production mechanisms of light scalars. Of particular interest is the case of a large isotopic symmetry breaking in the $\eta(1405)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$ decay due to the occurrence of anomalous Landau thresholds (logarithmic triangle singularities), i.e., due to the $\eta(1405) \to(K^*\bar K+\bar K^*K)\to(K^+K^-+K^0\bar K^0)\pi^0\to f_0(980) \pi^0\to\pi^+\pi^- \pi^0$ transition (where it is of fundamental importance that the $K^*$ meson has a finite width).