Di-pion emission in heavy quarkonia decays

The di-pion spectrum for the $\Upsilon(nS)\to\Upsilon (n'S)$ transition with $n\le4$ has the form ${dw}/{dq}\sim$ (phase space) $|\eta-x|^2$, with $x=\frac{q^2-4m^2_\pi}{(\Delta M)^2-4m^2_\pi}<q^2\equiv M^2_{\pi\pi}$, and $\Delta M=M(nS)-M(n'S)$. The parameter $\eta$ is calculated and the spectrum is shown to reproduce the experimental data for all 3 types of decays: $3\to 1,2\to1$ and $3\to2$ with $\eta\approx0.5;0$, and $-3$, respectively.