Results for $\alpha_s$ from the decoupling strategy

TL;DR

This paper presents a new analysis method using decoupling to determine the strong coupling constant _s(m_Z), achieving results consistent with previous measurements but with different systematic error considerations.

Contribution

It introduces a decoupling strategy for _s determination, providing an independent cross-check with different systematic uncertainties compared to existing methods.

Findings

Results compatible with FLAG and previous ALPHA measurements.

Decoupling strategy offers a different systematic error profile.

Estimated small  and 1/M contaminations in the coupling.

Abstract

We present analysis details and new results for the strong coupling $\alpha_s(m_Z)$, determined by the decoupling strategy. We measure a massive gradient flow (GF) coupling defined in finite volume with Schr\"odinger functional (SF) boundary conditions in a theory with $N_\text{f}=3$ degenerate heavy quarks of mass $M$. The massive couplings are matched to effective couplings in pure gauge. Using the running in the pure gauge theory and the perturbative relation of the Lambda parameters, the Lambda parameter of the three flavor theory is obtained by an extrapolation to infinite M. Our final result is compatible both with the FLAG average and with the previous ALPHA result, albeit with a slightly smaller, yet still statistics dominated, error. This constitutes a non-trivial check, as the decoupling strategy is conceptually very different from the 3-flavor QCD step-scaling method, and so are most of its systematic errors. These include the uncertainties of the decoupling and continuum limits, which we discuss in some detail. Furthermore, by relying on decoupling once again, we could estimate the small $O(a)$ and $O(1/M)$ contaminations to the massive GF coupling stemming from the SF boundaries by means of pure gauge simulations.