Dipion transitions in heavy quarkonium high excitations and heavy quarkonium hybrids

We report on preliminary results for dipion transitions involving heavy quarkonium and heavy hybrid states of size much larger than the typical hadronic scale. For these states the usual QCD multipole expansion does not hold. As an alternative, we propose an interaction Lagrangian for pions and the QCD string. It allows us to calculate the light quark mass dependence of the string tension, elastic pion scattering off the string, and the decay of string excitations by pion emission. We then introduce an interaction Lagrangian of pions with heavy quarkonium and heavy hybrid states such that it reproduces the previous results in the static limit. For illustration purposes, we calculate a couple of selected transitions with this Lagrangian. We also discuss the missing ingredients in order to achieve a full leading order calculation.