Abstract

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 (K) over bar), psi(2S) -> J/psi pi pi, and the isoscalar S-wave processes pi pi -> pi pi, K (K) over bar, 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 (K) over bar 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.