Amplitude analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mi>S</mml:mi></mml:msub><mml:msub><mml:mi>K</mml:mi><mml:mi>S</mml:mi></mml:msub></mml:math> system produced in radiative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> decays

An amplitude analysis of the ${K}_{S}{K}_{S}$ system produced in radiative $J/\ensuremath{\psi}$ decays is performed using the $(1310.6\ifmmode\pm\else\textpm\fi{}7.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }J/\ensuremath{\psi}$ decays collected by the BESIII detector. Two approaches are presented. A mass-dependent analysis is performed by parametrizing the ${K}_{S}{K}_{S}$ invariant mass spectrum as a sum of Breit-Wigner line shapes. Additionally, a mass-independent analysis is performed to extract a piecewise function that describes the dynamics of the ${K}_{S}{K}_{S}$ system while making minimal assumptions about the properties and number of poles in the amplitude. The dominant amplitudes in the mass-dependent analysis include the ${f}_{0}(1710)$, ${f}_{0}(2200)$, and ${f}_{2}^{\ensuremath{'}}(1525)$. The mass-independent results, which are made available as input for further studies, are consistent with those of the mass-dependent analysis and are useful for a systematic study of hadronic interactions. The branching fraction of radiative $J/\ensuremath{\psi}$ decays to ${K}_{S}{K}_{S}$ is measured to be $(8.1\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, where the uncertainty is systematic and the statistical uncertainty is negligible.