Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting

TL;DR

This paper introduces a novel, scheme-independent method using the principle of maximum conformality and infinite-order scale setting to precisely determine the QCD coupling constant across all energy scales from jet observables at a single experiment.

Contribution

It develops an innovative approach based on intrinsic conformality and maximum likelihood to accurately extract the strong coupling constant from event-shape data at the Z boson peak.

Findings

Achieved a precise measurement of s(M_Z)=0.1182b10.0007

Method eliminates bin-interval selection errors in data analysis

Results are consistent with the world average s value.

Abstract

We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust ($T$) and $C$-parameter ($C$) distributions in $e^+e^-$ annihilation at a single annihilation energy $\sqrt{s}=M_Z$ (i.e.\ at the $Z^0$ peak). This new method is based on the \emph{intrinsic conformality} (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e.\ the PMC$_\infty$), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the $N_C \to 0$ limit. This new method is based on the scale-invariance of the iCF, which allows determination of $\alpha_s(\mu_0)$ at any scale $\mu_0$, and on the Maximum Likelihood statistical approach. We propose a novel approach to determining the best-fitting range by considering all possible intervals over the entire range of bins available in the perturbative region and selecting that which returns the most-likely-lowest $\chi^2_{\rm min}$. This new method is designed to eliminate the errors that arise due to selection of the bin-interval and that have been neglected in previous analyses. In particular, using data for thrust and $C$-parameter at the $Z^0$ peak from ALEPH, OPAL, DELPHI and L3 experiments, we obtain the average value: $\alpha_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $\alpha_s(M_Z)$ is consistent with the world average...