A Comprehensive Study of the Radiative Decays of $J\mathrm{/}\psi$ and $\psi (2S)$ to Pseudoscalar Meson Pairs, and Search for Glueballs

Using 53 pb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data taken at $\sqrt{s}=3.686$ GeV, a comprehensive study has been made of the radiative decays of samples of 5.1 million $J\mathrm{/}\psi$ and 24.5 million $\psi (2S)$ into pairs of pseudoscalar mesons, ${\pi }^{+}{\pi }^{-}$, ${\pi }^0{\pi }^0$, $K^{+}{K}^{-}$, $K_S^0{K}_S^0$, and $\eta \eta$. Product branching fractions for the radiative decays of $J\mathrm{/}\psi$ and $\psi (2S)$ to scalar resonances $f_0(1370,1500,1710,2100,\text{and}2200)$, and tensor resonances $f_2(1270,1525,\text{and}2230)$ have been determined, and are discussed in relation to predicted glueballs. For $\psi (2S)$ radiative decays the search for glueballs has been extended to masses between 2.5 GeV and 3.3 GeV.