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We present a unified analysis of the decays of bottomonia Upsilon(mS) ->Upsilon(nS) pi pi (m>n, m=2,3,4,5, n=1,2,3), charmonia J/psi -> phi (pi pi, KantiK), psi(2S) -> J/psi pi pi and the isoscalar S-wave processes pi pi -> pipi, K antiK, eta eta. In this analysis we extend our recent study of low-lying(m=2,3) radial excitations of bottomonia to modes involving higher (m=4,5)excited states. Similarly as for the data on lower radial excitations, weconfirm that the data for higher radially excited states from the BaBar andBelle collaborations can be described under conditions that the finalbottomonium is a spectator and the multichannel pi pi scattering is consideredin a model-independent approach based on analyticity, unitarity and theuniformization procedure. Indeed we show that the dipion mass distributions inthe two-pion transitions of both charmonia and bottomonia states are explainedby a unified mechanism based on the contribution of the pi pi and K antiKcoupled channels including their interference (final-state interactions).Therefore, our main result is that the lower and higher radially excited statesof charmonia and bottomonia have no specific features in mutual comparison andcan be understood in a unified picture, e.g. proposed by our approach.

Unified description of BaBar and Belle data on the bottomonia decays Upsilon(mS) -> Upsilon(nS) pi+ pi-