Using a four dimensional approach, we show that the singularities for smallgluon momenta, which arise in the usual three dimensional treatment of theannihilation decay, disappear if all poles in the relative energy are takeninto account correctly in the integration. We obtain an explicit formula forthe decay width which involves a non locality originating from the kineticenergy. We calculate not only the familiar logarithmic dependence on thebinding energy, but also the constant to be added to the logarithm. Forpositronium this differs from an earlier result in the literature and leads toa modified life time. In QCD there is a non abelian loop graph whichcontributes to the decay amplitude to the same order as the tree graph.Contrary to the original version, which contained some errors, the constantturns out to be large and negative. For reasonable parameters, this negative constant practically cancels thepositive logarithm, so that the whole approach of expanding with respect to thebinding energy breaks down.
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