Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules

Abstract

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $\tau$-decay data. The determination involves the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $\overline{\mathrm{MS}}$ coupling is ${\alpha }_s(m_{\tau }^2)=0.3116\pm 0.0073$ [${\alpha }_s(M_Z^2)=0.1176\pm 0.0010$] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, ${\alpha }_s(m_{\tau }^2)=0.3194\pm 0.0167$ [${\alpha }_s(M_Z^2)=0.1186\pm 0.0021$].

arXiv commentv3: 36 pages, 11 figures. Matched published version

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• Semileptonic tau decays beyond the Standard Model
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• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Resurgence and self-completion in renormalized gauge theories
• Nonperturbative gluon exchange in $pp$ elastic scattering at TeV energies
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form
• Gluon Mass Generation from Renormalons and Resurgence
• Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate