Infrared structure of $e^+e^- \to 3$ jets at NNLO: QED-type   contributions
  The NNLO QCD corrections to the $e^+e^- \to 3$ jets can be decomposed according to their colour factors. Out of the seven colour factors, three are of QED-type: $1/N^2$, $N_F/N$ and $N_F^2$. We use the antenna subtraction method to compute these contributions, providing complete expressions for the subtraction terms in $N_F/N$ and $N_F^2$. 
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, G. Heinrich