Di-pion emission in heavy quarkonia decays

Abstract

The di-pion spectrum for the ${\rm Y}(nS)\to {\rm Y}(n^{\prime }S))$ transition with $n\le 4$ has the form $\frac{dw}{dq}\sim$ (phase space) $|\eta -x{|}^2$, with $x=\frac{q^2-4m_{\pi }^2}{(\Delta M{)}^2-4m_{\pi }^2}<q^2\equiv M_{\pi \pi }^2,$ and $\Delta M=M(nS)-M(n^{\prime }S)$. 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.

Comments: 3 pages, 2 figures; Journal version