Amplitude analysis of $\ddot{I}ˆ(3686)\to {\hat{I}}^3{K}_S^0{K}_S^0$

Abstract

Using $(2712\pm 14)\times 10^6$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, we perform the first amplitude analysis of the radiative decay $\ddot{I}ˆ(3686)\to {\hat{I}}^3{K}_S^0{K}_S^0$ 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 $K_S^0{K}_S^0$ 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 $J/\ddot{I}ˆ$ decays. The production behaviors of $f_0$ and $f_2$ poles in $\ddot{I}ˆ(3686)\to {\hat{I}}^3{K}_S^0{K}_S^0$ are qualified with their residues and the converted branching fractions. By comparing with $J/\ddot{I}ˆ\to {\hat{I}}^3{K}_S^0{K}_S^0$ decay, the ratios $\frac{\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3{f}_{0,2})}{\mathcal{B}(J/\ddot{I}ˆ\to {\hat{I}}^3{f}_{0,2})}$ are determined, which provides crucial experimental inputs on the internal structure of the $f_{0,2}$ states, especially their potential mixing with glueball components.

20 pages, 4 figures, submitted to JHEP