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Reviews of topical problems

Strong isospin symmetry breaking in light scalar meson production

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S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation

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 amplitude $\sim\sqrt{m_{\rm d}-m_{\rm u}}$ (instead of the usual $\sim (m_{\rm d}-m_{\rm u})$), where $m_{\rm u}$ and $m{\rm _d}$ are the u and d quark masses, respectively, whose magnitude and phase vary with energy in a resonance-like way characteristic of the ${\rm K}\bar {\rm K}$ threshold region. The review considers a variety of reactions that can reveal (or have revealed) experimentally the mixing of ${\rm a}^0_0(980)$- and ${\rm f}_0(980)$ resonances that breaks the isotopic invariance due to the mass difference of the ${\rm K}^+$ and ${\rm K}^0$ mesons. The experimental results on the search for the ${\rm a}^0_0(980)-{\rm f}_0(980)$ mixing in the ${\rm f}_1(1285)\to {\rm f}_0(980)\pi^0\to\pi^+\pi^-\pi^0$ è $\eta(1405)\to {\rm f}_0(980)\pi^0\to\pi^+\pi^-\pi^0$ decays have suggested a broader perspective on the isotopic symmetry breaking effects due to the ${\rm K}^+{\rm K}^0$ mass difference. It has become clear that not only the ${\rm }a^0_0(980)-{\rm f}_0(980)$ mixing but also any mechanism producing ${\rm K}\bar {\rm K}$ pairs with a definite isospin in the 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 violation in the $\eta(1405)$\,$\to$\,${\rm f}_0(980)\pi^0$\,$\to$\,$\pi^+\pi^-\pi^0$ decay due to the occurrence of anomalous Landau thresholds (logarithmic triangle singularities), i.e., due to the $\eta(1405)\to({\rm K}^*\bar {\rm K}+\bar {\rm K}^*{\rm K})\to({\rm K}^+{\rm K}^-+{\rm K}^0\bar {\rm K}^0)\pi^0\to {\rm f}_0(980)\pi^0\to\pi^+\pi^-\pi^0$ transition (where the ${\rm K}^*$ meson should be crucially considered to be of finite width).