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.

5 pages, 8 figures

References in corpus (3)

• $f_1(1285)$ decays into $a_0(980){\pi }^0$, $f_0(980){\pi }^0$ and isospin breaking
• Isospin breaking decay $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$
• Mechanisms of the isospin-breaking decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$

Cited by in corpus (8)

• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• Considerations on the Schmid theorem for triangle singularities
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass
• Strong isospin symmetry breaking in light scalar meson production
• Decay $X(3872)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and $S$-wave $D^0{\bar{D}}^0\to {\pi }^{+}{\pi }^{-}$ scattering length
• Simultaneous description of the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ processes
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Observation of $\psi (3686)\to \gamma \eta (1405)$ via $\eta (1405)\to f_0(980){\pi }^0$