Strong isospin symmetry breaking in light scalar meson production

Abstract

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 $\eta (1405)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ 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 $\eta (1405)\to (K^{\ast }\bar{K}+{\bar{K}}^{\ast }K)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ transition (where it is of fundamental importance that the $K^{\ast }$ meson has a finite width).

33 pages, 29 figures. v2: New reference [118] added in the arXiv version

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• Semileptonic decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ as the probe of constituent quark-antiquark pairs in the light scalar mesons
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