# Investigation of $J/\psi \to \gamma\, \pi^0 \eta (\pi^+\pi^-, \pi^0\pi^0)$ radiative decays including final-state interactions

## TL;DR

This paper studies the role of $Kar{K}$ interactions in generating $f_0(980)$ and $a_0(980)$ resonances and their contributions to $J/ar{psi}$ radiative decays, providing theoretical branching ratios consistent with experiments.

## Contribution

It offers a coupled-channel analysis of $Kar{K}$ interactions that dynamically generates $f_0(980)$ and $a_0(980)$ resonances, including their mixing effects, and predicts their impact on $J/ar{psi}$ radiative decay branching ratios.

## Key findings

- Calculated branching fractions for $J/ar{psi}$ decays involving $f_0(980)$ and $a_0(980)$ resonances.
- Predicted decay rates are within experimental upper limits.
- Highlighted the importance of $Kar{K}$ channels in the dynamical generation of scalar mesons.

## Abstract

We revisit the coupled channel $K\bar{K}$ interactions and dynamically generate the resonances $f_0(980)$ and $a_0(980)$ within both the isospin and the physical bases. The $f_0(980)-a_0(980)$ mixing effects are generated in the scattering amplitudes of the coupled channels with the physical basis, which exploits the important role of the $K\bar{K}$ channel in the dynamical nature of these resonances. With the scattering amplitudes obtained, we investigate the $f_0(980)$ and $a_0(980)$ contributions to the $J/\psi\to \gamma\eta\pi^0$, $J/\psi\to \gamma\pi^+\pi^-$ and $J/\psi\to \gamma\pi^0\pi^0$ radiative decays through the final-state interactions. We obtain the corresponding branching fractions $Br(J/\psi\to \gamma a_0(980) \to \gamma\eta\pi^0) = (0.47\pm0.05) \times 10^{-7}$, $Br(J/\psi\to \gamma f_0(980) \to \gamma\pi^+\pi^-) = 0.37 \times 10^{-7} - 1.98 \times 10^{-6}$, $Br(J/\psi\to \gamma f_0(980) \to \gamma\pi^0\pi^0) = 0.18 \times 10^{-7} - 9.92 \times 10^{-7}$, and predict $Br(J/\psi\to \gamma a_0(980)) = 1.72 \times 10^{-8} - 3.07\times 10^{-7}$ and $Br(J/\psi\to \gamma f_0(980)) = 1.86 \times 10^{-8} - 1.89\times 10^{-5}$. These fractions are within the upper limits of the experimental measurements.