Isospin breaking decay $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$

Abstract

There are attempts in the literature to theoretically explain the large breaking of isotopic invariance in the decay $\eta (1405)$\,$\to$\,$f_0(980){\pi }^0$\,$\to$\,$3\pi$ by the mechanism containing the logarithmic (triangle) singularity, i.e., as being due to the transition $\eta (1405)\to (K^{\ast }\bar{K}+{\bar{K}}^{\ast }K)\to (K^{+}{K}^{-}+K^0{\bar{K}}^0){\pi }^0\to f_0(980){\pi }^0\to 3\pi$. The corresponding calculations were fulfilled for a hypothetic case of the stable $K^{\ast }$ meson. Here, we show that the account of the finite width of the $K^{\ast }$ (${\Gamma }_{K^{\ast }\to K\pi }\approx 50$ MeV) smoothes the logarithmic singularities in the amplitude and results in the suppression of the calculated decay width $\eta (1405)\to f_0(980){\pi }^0\to 3\pi$ by the factor of $6-8$ as compared with the case of ${\Gamma }_{K^{\ast }\to K\pi }$\,=\,0. We also analyze the difficulties related with the assumption of the dominance of the $\eta (1405)\to (K^{\ast }\bar{K}+{\bar{K}}^{\ast }K)\to K\bar{K}\pi$ decay mechanism and discuss the possible dynamics of the decay $\eta (1405)\to \eta \pi \pi$. The decisive improvement of the experimental data on the $K\bar{K}$, $K\pi$, $\eta \pi$, and $\pi \pi$ mass spectra in the decay of the resonance structure $\eta (1405/1475)$ to $K\bar{K}\pi$ and $\eta \pi \pi$, and on the shape of the resonance peaks themselves in the $K\bar{K}\pi$ and $\eta \pi \pi$ decay channels is necessary for the further establishing the $\eta (1405)\to 3\pi$ decay mechanism.

10 pages, 8 figures. Added are the details of calculations, 2 references, and clarifying remarks

References in corpus (5)

• Possibility of measuring a0(980)-f0(980) mixing from J/psi -> phi a0
• Study a0(980)-f0(980) mixing from a0(980) -> f0(980) transition
• Lightest scalar in the SU_L(2)*SU_R(2) linear σmodel
• Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor
• Search for $f_1(1285)\to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay with VES detector

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