Amplitude analysis of $\psi(3686)\to \gamma K_S^0 K_S^0 $

Abstract

Using $(2712\pm14)\times10^6$ $\psi(3686)$ events collected with the BESIII detector, we perform the first amplitude analysis of the radiative decay $\psi(3686)\to \gamma K_S^0 K_S^0$ within the mass region $M_{K_S^0 K_S^0 }<2.8$ GeV/$c^2$. Employing a one-channel K-matrix approach for the description of the dynamics of the $K^0_S K^0_S$ system, the data sample is well described with four poles for the $f_0$-wave and three poles for the $f_2$-wave. The determined pole positions are consistent with those of well-established resonance states. The observed $f_0$ and $f_{2}$ states are found to be in agreement with those produced in radiative $J/\psi$ decays. The production behaviors of $f_0$ and $f_2$ poles in $\psi(3686)\to\gamma K_S^0 K_S^0$ are qualified with their residues and the converted branching fractions. By comparing with $J/\psi\to\gamma K_S^0 K_S^0$ decay, the ratios $\frac{\mathcal{B}(\psi(3686)\to\gamma f_{0,2})}{\mathcal{B}(J/\psi\to\gamma f_{0,2})}$ are determined, which provides crucial experimental inputs on the internal structure of the $f_{0,2}$ states, especially their potential mixing with glueball components.