Radiative Gluon/Photon: Tree Level vs. Higher Corrections

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Can there be cases where the cross section for the production of a radiative soft photon or gluon be larger than its tree level diagram ? Or in general, are there cases where higher corrections be larger than tree level in any interaction ?
 
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Well, there are processes that are completely forbidden at tree level but occur at loop level. Like photon/photon scattering.
 
Yes. As an example e+e- -> e+e- gamma has an infrared collinear divergence: i.e. the cross-section blows up as the photon gets arbitrarily soft.
 
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