The Banks-Zaks expansion in perturbative QCD: an update

TL;DR

This paper updates the Banks-Zaks expansion in perturbative QCD using recent five-loop calculations, showing consistency above nf=9 but limited applicability at low nf.

Contribution

It incorporates the latest five-loop beta function and R(e+e-) calculations to refine the Banks-Zaks expansion in perturbative QCD.

Findings

Expansion is consistent above nf=9

Limited applicability of the expansion at low nf

Provides updated theoretical insights into QCD beta function

Abstract

The recent QCD calculations of the five-loop beta function and of R(e+e-) to O(alpha_s^4) provide one more term in the Banks-Zaks expansion in (16.5-nf). There is no longer any hope that the expansion could extend, even crudely, to low nf. Above nf=9, however, the results appear to be reasonably consistent from order to order.