TTP08-03 Massless propagators: applications in QCD and QED

We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $\alpha_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $\beta$ function of quenched QED.