Effect of the $K\bar{K}$ and $\eta \eta$ channels and interference phenomena in the two-pion and $K\bar{K}$ transitions of charmonia and bottomonia

It is shown that the basic shape of dipion and $K\bar{K}$ mass spectra in decays $J\mathrm{/}\psi \to \varphi (\pi \pi ,K\bar{K})$, $\psi (2S)\to J\mathrm{/}\psi \pi \pi$, $Y(4260)\to J\mathrm{/}\varphi \pi \pi$ and in the two-pion transitions of bottomonia states are explained by an unified mechanism based on the contribution of the $\pi \pi$, $K\bar{K}$ and $\eta \eta$ coupled channels including their interference. The role of the individual $f_0$ resonances in making up the shape of the dipion mass distributions in the charmonia and bottomonia decays is considered.