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

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 $Br(J/\psi \to \gamma a_0(980)\to \gamma \eta {\pi }^0)=(0.47\pm 0.05)\times 10^{-7}$, $Br(J/\psi \to \gamma f_0(980)\to \gamma {\pi }^{+}{\pi }^{-})=0.37\times 10^{-7}-1.98\times 10^{-6}$, $Br(J/\psi \to \gamma f_0(980)\to \gamma {\pi }^0{\pi }^0)=0.18\times 10^{-7}-9.92\times 10^{-7}$, 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.