Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop

Abstract

We present a concise summary of recent results for the vector correlator in massless QCD at order $\mathcal{O}({\alpha }_s^4)$, 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.

Comments: 14 pages, 1 figure; Few misprints corrected. Results are untouched