Determination of closed-flavour πJ/ψ and πϒ cross sections at low energies from dipion decays

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The scale of low energy and cross sections on light hadrons is of great importance to searches for the quark–gluon plasma using the heavy-quarkonium suppression signature. Unfortunately, little is known about these near-threshold cross sections at present, and recent theoretical estimates span many orders of magnitude. Here we use experimental data on the four observed closed-flavour heavy quarkonium hadronic decays ψ′ → ππJ/ψ, ϒ′ → ππϒ, ϒ″ → ππϒ and ϒ″ → ππϒ′, combined with simple models of the transition amplitudes, to estimate the pion scattering cross sections of and mesons near threshold. Specifically we consider the closed-flavour reactions πJ/ψ → πψ′, πϒ → πϒ′, πϒ → πϒ″ and πϒ′ → πϒ″ and their time-reversed analogues. Our results may be useful in constraining theoretical models of the strong interactions of heavy quarkonia, and can be systematically improved through future detailed studies of dipion decays, notably ψ′ → ππJ/ψ and ϒ″ → ππϒ.