As an aftermath of the debate between Voloshin and Kuang and Yan since 1986, we now have a fairly clear picture of the type of experiments in the $c\overline{c}$ and $b\overline{b}$ heavy-quarkonium systems (most of them accessible in the near future) which will give definitive guidance to theory. They include measurements of the rate $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to \Upsilon \left(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)\pi \pi$ and $\Gamma \left(\psi \right(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{})\to p\overline{p})B\left(\psi \right(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{})\to \frac{J}{\psi \pi \pi })B(\frac{J}{\psi }\to e^{+}{e}^{-})$, $\Gamma \left(\Upsilon \mathrm{}\right(1D)\mathrm{}\to \Upsilon \mathrm{}(1S\left)\mathrm{}\pi \pi \right)$, $\Gamma \left(\psi \mathrm{}\right(1D)\mathrm{}\to \frac{J}{\psi \pi \pi })$, and at some future date a measurement of $\Gamma \left(\psi \right(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{})\to \gamma {\eta }_c$. If the Lipkin-Tuan model does have significance for heavy-quarkonium dipion mass spectra, measurement of the spectra in $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to \Upsilon \mathrm{}(1S,2S)\mathrm{}\pi \pi$, $\psi \mathrm{}(1D,2S)\mathrm{}\to \frac{J}{\psi \pi \pi }$ [and ultimately $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to \Upsilon \left(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)\pi \pi$ mass spectrum] as well as the rate for $\psi \mathrm{}\left(1D\right)\mathrm{}\to \frac{J}{\psi \pi \pi }$ shall be quite revealing.

• Received 24 April 1990

DOI:https://doi.org/10.1103/PhysRevD.42.3207