$J/\psi \to \gamma \pi \pi$, $\gamma {\pi }^0\eta$ reactions and the $f_0(980)$ and $a_0(980)$ resonances

Abstract

We study the $J/\psi \to \gamma {\pi }^{+}{\pi }^{-}$, $\gamma {\pi }^0\eta$ reactions from the perspective that they come from the $J/\psi \to \varphi (\omega ){\pi }^{+}{\pi }^{-},{\rho }^0{\pi }^0\eta$ reactions, where the ${\rho }^0$, $\omega$, and $\varphi$ get converted into a photon via vector meson dominance. Using models successfully used previously to study the $J/\psi \to \omega (\varphi )\pi \pi$ 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.

14 pages, 9 figures