Probing QCD perturbation theory at high energies with continuum extrapolated lattice data

TL;DR

This paper demonstrates how continuum extrapolated lattice data can effectively test QCD perturbation theory at high energies, overcoming experimental limitations and providing precise non-perturbative insights into the strong coupling constant.

Contribution

It introduces a method using lattice data and finite size techniques to compare perturbative and non-perturbative QCD at high energies, aiding in precise determination of the b4-parameter.

Findings

Non-perturbative data up to b4s b7 0.1 is needed for 3% b4-parameter accuracy.

Perturbation theory can be misleading at b4s b7 0.2 due to overestimated precision.

Finite size techniques enable stepping up energy scales by factors of 2.

Abstract

Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the accessible energy scales. We here show how continuum extrapolated lattice data may overcome such problems and provide excellent probes of renormalized perturbation theory. This work corresponds to an essential step in the ALPHA collaboration's project to determine the $\Lambda$-parameter in 3-flavour QCD. I explain the basic techniques used in the high energy regime, namely the use of mass-independent renormalization schemes for the QCD coupling constant in a finite Euclidean space time volume. When combined with finite size techniques this allows one to iteratively step up the energy scale by factors of 2, thereby quickly covering two orders of magnitude in scale. We may then compare perturbation theory (with $\beta$-functions available up to 3-loop order) to our non-perturbative data for a 1-parameter family of running couplings. We conclude that a target precision of 3 percent for the $\Lambda$-parameter requires non-perturbative data up to scales where $\alpha_s\approx 0.1$, whereas the apparent precision obtained from applying perturbation theory around $\alpha_s \approx 0.2$ can be misleading. This should be taken as a general warning to practitioners of QCD perturbation theory.