  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, K
antiK), psi(2S) -> J/psi pi pi and the isoscalar S-wave processes pi pi -> pi
pi, 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, we
confirm that the data for higher radially excited states from the BaBar and
Belle collaborations can be described under conditions that the final
bottomonium is a spectator and the multichannel pi pi scattering is considered
in a model-independent approach based on analyticity, unitarity and the
uniformization procedure. Indeed we show that the dipion mass distributions in
the two-pion transitions of both charmonia and bottomonia states are explained
by a unified mechanism based on the contribution of the pi pi and K antiK
coupled channels including their interference (final-state interactions).
Therefore, our main result is that the lower and higher radially excited states
of charmonia and bottomonia have no specific features in mutual comparison and
can be understood in a unified picture, e.g. proposed by our approach.
