Structure Analysis of the $f_J\left(1710\right)$ in the Radiative Decay $\mathit{J}\mathit{/}\mathit{\psi }\to \mathit{\gamma }{K}^{+}{K}^{-}$

The data on $J/\psi \to \gamma K^{+}{K}^{-}$ from the BES experiment at the Beijing electron-positron collider have been analyzed. We find two resonances in the 1.7 GeV region which were identified as $f_J\left(1710\right)$: a scalar with mass $1781\pm 8_{-31\mathrm{}}^{+10\mathrm{}}\left(\mathrm{MeV}\right)$ and width $85\pm {24}_{-19\mathrm{}}^{+22\mathrm{}}\left(\mathrm{MeV}\right)$, and a tensor with mass $1696\pm 5_{-34\mathrm{}}^{+9\mathrm{}}\left(\mathrm{MeV}\right)$ and width $103\pm {18}_{-11\mathrm{}}^{+30\mathrm{}}\left(\mathrm{MeV}\right)$. The resulting branching ratios $B(J/\psi \to \gamma f_J)B(f_J\to K^{+}{K}^{-})$ are ( $0.8\pm {0.1}_{-0.1\mathrm{}}^{+0.3\mathrm{}}){10}^{-4\mathrm{}}$ for $J=0\mathrm{}$ and ( $2.5\pm {0.4}_{-0.4\mathrm{}}^{+0.9\mathrm{}}){10}^{-4\mathrm{}}$ for $J=2\mathrm{}$, respectively.