Determination of $\alpha_s(m_Z)$ by the non-perturbative decoupling method

TL;DR

This paper introduces a new non-perturbative decoupling method to determine the strong coupling constant _s(m_Z), achieving results consistent with previous measurements and providing a novel approach with different systematic uncertainties.

Contribution

The paper develops and applies a decoupling strategy for three heavy quarks to relate pure gauge theory results to three-flavor QCD, enabling a new precise determination of _s(m_Z).

Findings

_s(m_Z) = 0.11823(84)

Consistent with FLAG and previous ALPHA results

Demonstrates a new decoupling approach with different systematic errors

Abstract

We present the details and first results of a new strategy for the determination of $\alpha_s(m_Z)$. By simultaneously decoupling 3 fictitious heavy quarks we establish a relation between the $\Lambda$-parameters of three-flavor QCD and pure gauge theory. Very precise recent results in the pure gauge theory can thus be leveraged to obtain the three-flavour $\Lambda$-parameter in units of a common decoupling scale. Connecting this scale to hadronic physics in 3-flavour QCD leads to our result in physical units, $\Lambda^{(3)}_{\bar{\rm MS}} = 336(12)\, {\rm MeV}$, which translates to $\alpha_s(m_Z) = 0.11823(84)$. This is compatible with both the FLAG average and the previous ALPHA result, with a comparable, yet still statistics dominated, error. This constitutes a highly non-trivial check, as the decoupling strategy is conceptually very different from the 3-flavour QCD step-scaling method, and so are their systematic errors. These include the uncertainties of the combined decoupling and continuum limits, which we discuss in some detail. We also quantify the correlation between both results, due to some common elements, such as the scale determination in physical units and the definition of the energy scale where we apply decoupling.