Isotopic Symmetry Breaking in the $\eta (1405)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$. Decay through a $K\bar{K}$ Loop Diagram and the Role of Anomalous Landau Thresholds

Abstract

Anomalous isotopic symmetry breaking in the $\eta (1405)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay through a mechanism featuring anomalous Landau thresholds in the form of logarithmic triangle singularities, i.e., through 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, has been analyzed. It has been shown that this effect can be correctly quantified only by taking into account the nonzero $K^{\ast }$ width. Different scales of isotopic symmetry breaking associated with the $K^{+}-K^0$ mass difference are compared.

Comments: 5 pages, 8 figures