Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED   beta-function at five loop
  We present a concise summary of recent results for the vector correlator in massless QCD at order ${\cal O}(\alpha_s^4)$, with all colour factors being given for a generic colour group. As a direct consequence we arrive at: (i) the full QCD contribution to the QED $\beta$--function of order $\alpha^2\, \alpha_s^4$ in the MSbar- and MOM-schemes; (ii) the full five-loop result of order $\alpha^6$ for the $\beta$-function of QED with a generic number of single-charged fermions, again for the MSbar- and MOM-schemes. 
P. A. Baikov, K. G. Chetyrkin, J. H. K\"uhn and J. Rittinger
hep-ph hep-th