The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD

TL;DR

This work presents the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha(4)(s)n(2)(f) to the absorptive parts of vector and scalar correlators to form an important gauge-invariant subset of the full omicron(alpha( 4)(s)) correction.

Abstract

We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha_s^4) correction to $e^+ e^- annihilation into hadrons and the Higgs decay rate into hadrons respectively. They discriminate between different widely used estimates of the full result.

Figures (1)

• Figure 1: (a) Diagram whose calculation took $\approx$ 300 hours. (b) Diagram contributing to the QED $\beta$-function in ${\cal O}(\alpha_{\rm em}^6 n_f^3)$.