$J/psi to gamma pipi$, $gammapi^0eta$ reactions and the $f_0(980)$ and $a_0(980)$ resonances

We study the $J/psi to gamma pi^+ pi^-$, $gamma pi^0 eta$ reactions from the perspective that they come from the $J/psi to phi(omega) pi^+ pi^-, rho^0pi^0 eta$ reactions, where the $rho^0$, $omega$, and $phi$ get converted into a photon via vector meson dominance. Using models successfully used previously to study the $J/psi to omega (phi) pipi$ reactions, we make determinations of the invariant mass distributions for $pi^+ pi^-$ in the regions of the $f_0(500)$, $f_0(980)$, and for $pi^0 eta$ in the region of the $a_0(980)$. The integrated differential widths lead to branching ratios below present upper bounds, but they are sufficiently large for future check in updated facilities.