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

TL;DR

This paper computes high-order corrections in massless QCD and QED, providing precise five-loop beta-functions and vector correlator results that enhance understanding of quantum field theory renormalization.

Contribution

It presents the first complete five-loop QED beta-function and high-order QCD vector correlator calculations for a generic gauge group, extending previous lower-order results.

Findings

Full QCD contribution to QED beta-function at order alpha^2 alpha_s^4

Five-loop QED beta-function for generic fermion content

Results applicable in MSbar and MOM renormalization schemes

Abstract

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.