Two-pion transitions in quarkonium revisited

Abstract

Two-pion transitions in charmonium and bottomonium are considered with the leading relativistic effects taken into account. The contribution of the chromo- magnetic interaction of the charmed quarks to the amplitude of the decay $\psi (2S)\to \pi \pi J/\psi$ is estimated from the available data. This contribution is enhanced by a factor of three in the decay ${\eta }_c(2S)\to \pi \pi {\eta }_c$ and should produce a noticeable modification of the rate and the spectrum in the latter decay. It is argued that the peculiar observed spectrum in the decay ${\rm Y}(3S)\to \pi \pi {\rm Y}$ arises due to a dynamical suppression of the leading nonrelativistic quarkonium amplitude and thus enhanced prominence of the relativistic terms. Also discussed are the effects of the final state interaction between the pions.

Comments: 23 pages, 2 figures