Looking through the QCD conformal window with perturbation theory

Lorenzo Di Pietro,Marco Serone

doi:10.1007/jhep07(2020)049

Abstract

We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of the overline{mathrm{MS}} β-function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large-nf results are also used. We argue that the perturbative series for the overline{mathrm{MS}} β-function is most likely asymptotic and non -Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find substantial evidence that QCD with nf = 12 flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also nf = 11 might sit within the conformal window. We also compute the anomalous dimensions γ and γg of respectively the fermion mass bilinear and the gauge kinetic term operator at the fixed point, and compare them with the available lattice results. The conformal window might extend for lower values of nf , but our methods break down for nf< 11, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit.

Highlights

Lattice methods are the only ones so far based on first principles.2 Studying a nonabelian gauge theory in its conformal phase on the lattice is a hard task and there is no consensus yet on the value of n∗f for QCD
We argue that the perturbative series for the MS β-function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory
We report our numerical results for the conformal window both for QCD with nc = 3 and for the Veneziano limit

Summary

Introduction

We will make use of results in the large-nf limit of non-abelian gauge theories. The nature of the ordinary perturbative expansion of β and γ in non-abelian gauge theories is only known in the large-nf limit at fixed nc. In this case both β and γ admit, at each known order in the 1/nf expansion, a convergent series expansion in MS, in contrast to what happens in other more physical renormalization schemes, such as momentum subtraction or onshell [27].

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Conclusion