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 $\Upsilon(3S) \to \pi \pi \Upsilon$ 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.