The strong coupling from hadronic $\tau$ decays: a critical appraisal

Abstract

Several different analysis methods have been developed to determine the strong coupling via finite-energy sum-rule analyses of hadronic $\tau$ decay data. While most methods agree on the existence of the well-known ambiguity in the choice of a resummation scheme due to the slow convergence of QCD perturbation theory at the $\tau$ mass, there is an ongoing controversy over how to deal properly with non-perturbative effects. These are small, but not negligible, and include quark-hadron "duality violations" (i.e., resonance effects) which are not described by the operator product expansion (OPE). In one approach, an attempt is made to suppress duality violations enough that they might become negligible. The number of OPE parameters to be fit, however, then exceeds the number of available sum rules, necessitating an uncontrolled OPE truncation, in which a number of higher-dimension OPE contributions in general present in QCD are set to zero by hand. In the second approach, truncation of the OPE is avoided by construction, and duality violations are taken into account explicitly, using a physically motivated model. In this article, we provide a critical appraisal of a recent analysis employing the first approach and demonstrate that it fails to properly account for non-perturbative effects, making the resulting determination of the strong coupling unreliable. The second approach, in contrast, passes all self-consistency tests, and provides a competitive determination of the strong coupling from $\tau$ decays.

arXiv comment30 pages, 10 figures, layout issue in subsection header fixed

References in corpus (25)

• Renormalons
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications
• Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• Renormalization group analysis of the tau-lepton decay within QCD
• An Illustrative Example of How Quark-Hadron Duality Might Work
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Duality violations and spectral sum rules
• An updated determination of α_s from tau decays
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Constraints on Hadronic Spectral Functions From Continuous Families of Finite Energy Sum Rules
• Unraveling duality violations in hadronic tau decays
• Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions
• Heavy flavor decays, OPE and duality in two-Dimensional 't Hooft model
• Testing an approximation to large-Nc QCD with a toy model
• A new determination of α_s from hadronic τ decays
• Possible duality violations in tau decay and their impact on the determination of alpha_s
• Chiral sum rules and duality in QCD
• Contour-improved versus fixed-order perturbation theory in hadronic tau decays
• Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data
• Low-energy constants and condensates from ALEPH hadronic $\tau$ decay data
• What two models may teach us about duality violations in QCD
• The case for duality violations in the analysis of hadronic $\tau$ decays
• ${\alpha }_s$ analyses from hadronic tau decays with OPAL and ALEPH data

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• QCD Running Couplings and Effective Charges
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• Strong coupling constant and heavy quark masses in 2+1 flavor QCD
• On the Difference between FOPT and CIPT for Hadronic Tau Decays
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Renormalons in integrated spectral function moments and ${\alpha }_s$ extractions
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Evidence against naive truncations of the OPE from $e^{+}{e}^{-}\to$ hadrons below charm
• Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Determining ${\alpha }_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE
• Towards tests of quark-hadron duality with functional analysis and spectral function data
• QCD condensates and ${\alpha }_s$ from $\tau$-decay
• Hadronic tau decays and the strong coupling