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
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2024
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| _version_ | 1866915492915052544 |
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| author | Di Giustino, Leonardo Brodsky, Stanley J. Ratcliffe, Philip G. Wang, Sheng-Quan Wu, Xing-Gang |
| author_facet | Di Giustino, Leonardo Brodsky, Stanley J. Ratcliffe, Philip G. Wang, Sheng-Quan Wu, Xing-Gang |
| contents | We present a new approach to determining the strong coupling $α_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $Λ_{\mathrm{QCD}}$ 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 $α_s(μ_0)$ at any scale $μ_0$, 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 $χ^2_{\rm min}$. 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: $α_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $α_s(M_Z)$ is consistent with the world average... |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_08570 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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 Di Giustino, Leonardo Brodsky, Stanley J. Ratcliffe, Philip G. Wang, Sheng-Quan Wu, Xing-Gang High Energy Physics - Phenomenology High Energy Physics - Theory We present a new approach to determining the strong coupling $α_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $Λ_{\mathrm{QCD}}$ 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 $α_s(μ_0)$ at any scale $μ_0$, 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 $χ^2_{\rm min}$. 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: $α_s(M_Z)= 0.1182^{+0.0007}_{-0.0007}$, for the strong coupling. This determination of $α_s(M_Z)$ is consistent with the world average... |
| title | 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 |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.08570 |