Unified description ofBABARand Belle data on the bottomonia decaysϒ(mS)→ϒ(nS)π+π−

We present a unified analysis of the decays of bottomonia $\\mathrm{\\ensuremath{\\Upsilon}}(mS)\\ensuremath{\\rightarrow}\\mathrm{\\ensuremath{\\Upsilon}}(nS)\\ensuremath{\\pi}\\ensuremath{\\pi}$ ($mgn$, $m=2,3,4,5$, $n=1,2,3$), charmonia $J/\\ensuremath{\\psi}\\ensuremath{\\rightarrow}\\ensuremath{\\phi}(\\ensuremath{\\pi}\\ensuremath{\\pi},K\\overline{K})$, $\\ensuremath{\\psi}(2S)\\ensuremath{\\rightarrow}J/\\ensuremath{\\psi}\\ensuremath{\\pi}\\ensuremath{\\pi}$, and the isoscalar $S$-wave processes $\\ensuremath{\\pi}\\ensuremath{\\pi}\\ensuremath{\\rightarrow}\\ensuremath{\\pi}\\ensuremath{\\pi},K\\overline{K},\\ensuremath{\\eta}\\ensuremath{\\eta}$. 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 $\\ensuremath{\\pi}\\ensuremath{\\pi}$ 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 $\\ensuremath{\\pi}\\ensuremath{\\pi}$ and $K\\overline{K}$ 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.