A coherent study of $\chi_{c0,2}\to VV$, $PP$ and $SS$

We investigate the decays of $\chi_{c0,2}$ into vector meson pairs ($VV$), pseudoscalar pairs ($PP$), and scalar pairs ($SS$) in a general factorization scheme. The purpose is to clarify the role played by the OZI-rule violations and SU(3) flavour breakings in the decay transitions, and their correlations with the final state meson wavefunctions. For $\chi_{c0,2}\to VV$ and $PP$, we obtain an overall self-contained description of the experimental data. Applying this factorization to $\chi_{c0}\to f_0^i f_0^j$, where $i, j=1, 2, 3$ denotes $f_0(1710)$, $f_0(1500)$ and $f_0(1370)$, respectively, we find that specific patterns will arise from the model predictions for the decay branching ratio magnitudes, and useful information about the structure of those three scalars can be abstracted.