Strong isospin symmetry breaking in light scalar meson production
N.N. Achasov,
G.N. Shestakov
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 resonancelike 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 ${\rm f}_1(1285)\to {\rm f}_0(980)\pi^0\to\pi^+\pi^\pi^0$ и $\eta(1405)\to {\rm f}_0(980)\pi^0\to\pi^+\pi^\pi^0$ 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).
