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

TL;DR

This work computes high-order QCD corrections to the massless vector-current correlator and propagates them to QED β-functions at five-loop order. It provides explicit expansions for the polarization function $Π^{NS}$ and $Π^{SI}$ and for the anomalous dimensions $γ^{NS}$ and $γ^{SI}$, enabling construction of the Adler function and $R(s)$ up to ${ m O}(α_s^4)$. It also delivers analytic MSbar and MOM β-functions for EM and QED, including full $n_f$ and charge dependence and pure QED limits, clarifying the transcendental structure of high-loop massless propagator calculations. These results advance precision tests of QED/QCD interplay and reveal intriguing patterns in the appearance of zeta constants at five loops.

Abstract

We present a concise summary of recent results for the vector correlator in massless QCD at order ${\cal O}(α_s^4)$, 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 $β$--function of order $α^2\, α_s^4$ in the MSbar- and MOM-schemes; (ii) the full five-loop result of order $α^6$ for the $β$-function of QED with a generic number of single-charged fermions, again for the MSbar- and MOM-schemes.

Figures (1)

• Figure 1: Examples of a lowest order and five-loop non-singlet (a),(b) and singlet (c),(d) diagrams contributing to the vector correlator.