Two-pion transitions in quarkonium revisited

Two-pion transitions in charmonium and bottomonium are considered with the leading relativistic effects taken into account. It is estimated that the contribution of the chromo-magnetic interaction of the charmed quarks to the amplitude of the decay ψ(2S)→ππJ/ψ is at the level of (15-20)%. This contribution is enhanced by a factor of 3 in the decay ηc(2S)→ππηc, producing a significant modification of the rate and the spectrum in the latter decay. It is also suggested that the peculiar observed spectrum in the decay Υ(3S)→ππΥ can be explained by a relative prominence of the relativistic terms, if the leading nonrelativistic quarkonium amplitude is dynamically suppressed. Also discussed are the effects of the final state interaction between the pions.