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

TL;DR

This paper investigates the $J/a o b c$ reactions involving photons and mesons, analyzing the roles of the $f_0(980)$ and $a_0(980)$ resonances through vector meson dominance and invariant mass distributions.

Contribution

The study applies existing models to new reactions, providing predictions for invariant mass distributions and branching ratios related to the $f_0(980)$ and $a_0(980)$ resonances.

Findings

Branching ratios are below current experimental upper bounds.

Predictions for invariant mass distributions around $f_0(500)$, $f_0(980)$, and $a_0(980)$.

Results suggest future experimental verification is feasible.

Abstract

We study the $J/\psi \to \gamma \pi^+ \pi^-$, $\gamma \pi^0 \eta$ reactions from the perspective that they come from the $J/\psi \to \phi(\omega) \pi^+ \pi^-, \rho^0\pi^0 \eta$ 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 $J/\psi \to \omega (\phi) \pi\pi$ 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.