Di-pion emission in heavy quarkonia decays

Abstract

The di-pion spectrum for the $Υ(nS) \to Υ(n'S))$ transition with $n\leq 4$ has the form $\frac{dw}{dq}\sim $ (phase space) $ |η-x|^2$, with $x=\frac{q^2-4m^2_π}{(ΔM)^2 -4 m^2_π}< q^2 \equiv M^2_{ππ}, $ and $ΔM=M(nS) -M(n'S)$. The parameter $η$ 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 $η\approx 0.5; 0$, and -3, respectively.