Effect of coupled channels of the multi-channel pion-pion scattering in two-pion transitions of the $\mathrm{{\rm Y}}$ mesons

The effect of isoscalar S-wave processes $\pi \pi \to \pi \pi ,K\bar{K},\eta \eta$ is considered in the analysis of data (from the ARGUS, CLEO, CUSB, Crystal Ball, Belle, BABAR collaborations) on the bottomonia decays — $\mathrm{{\rm Y}}(mS)\to \mathrm{{\rm Y}}(nS)\pi \pi$ ($m>n, m=2,3,4,5, n=1,2,3$). It is shown that the dipion mass spectra of these decays are explained by the unified mechanism related to the contribution of the multichannel $\pi \pi$ scattering in the final states of these reactions. Since in the analysis the multichannel $\pi \pi$-scattering amplitudes did not change in comparison with the ones in our combined analysis of data on the multichannel $\pi \pi$ scattering and on the charmonia decays — $J\mathrm{/}\psi \to \varphi (\pi \pi ,K\bar{K})$ and $\psi (2S)\to J\mathrm{/}\psi (\pi \pi )$ (from the Crystal Ball, DM2, Mark II, Mark III, and BES II) — the results confirm all our earlier conclusions on the scalar mesons.