Di-pion emission in heavy quarkonia decays

Abstract

The di-pion spectrum for the $\Upsilon(nS) \to \Upsilon (n'S))$ transition with $n\leq 4$ has the form $\frac{dw}{dq}\sim $ (phase space) $ |\eta-x|^2$, with $x=\frac{q^2-4m^2_\pi}{(\Delta M)^2 -4 m^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: $3\to 1, 2\to 1$ and $3\to 2$ with $\eta \approx 0.5; 0$, and -3, respectively.