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We wish to transform coordinates 

Thus the Jacobian gives d $^{3}$k = k$_{⊥}$dkdk$_{⊥}$dφ = k$_{⊥}$dωdk$_{⊥}$dφ . Hence 

Nicely, we recover the Sudakov double logarithm [251]: 

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## E.2.4 Diagrammatic Calculation, Massive Photon and Massive Quark Monojet 

The idea is to reproduce Djordjevic’s calculation of zeroth order radiation in [305]. The diagram is the same as Fig. E.1 except that the quark has a mass 

