Partial wave analyses of $J/\overrightarrow{\psi }\gamma K^{+}{K}^{-}$ and $\gamma K_S^0{K}_S^0$

Results are presented on $J/\psi$ radiative decays to $K^{+}{K}^{-}$ and $K_S^0{K}_S^0$ based on a sample of 58M $J/\psi$ events taken with the BES II detector. A partial wave analysis is carried out using the relativistic covariant tensor amplitude method in the 1–2 GeV mass range. There is conspicuous production due to the $f_2^{\prime }\mathrm{}\left(1525\right)\mathrm{}$ and $f_0\mathrm{}\left(1710\right).$ The latter peaks at a mass of $1740\pm 4_{-25}^{+10\mathrm{}}\mathrm{MeV}$ with a width of ${166}_{-8-10}^{+5+15\mathrm{}}\mathrm{MeV}.$ Spin 0 is strongly preferred over spin 2. For the $f_2^{\prime }\mathrm{}\left(1525\right),$ the helicity amplitude ratios are determined to be $x^2=1.00\mathrm{}\pm {0.28}_{-0.36}^{+1.06\mathrm{}}$ and $y^2=0.44\mathrm{}\pm {0.08}_{-0.56}^{+0.10\mathrm{}}.$