Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations

Abstract

In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $\tau$ hadronic spectral function moments, which had affected the precision of ${\alpha }_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element. In addition, the perturbative convergence of spectral function moments with a sizeable GC correction can be improved. The RF GC scheme depends on an IR factorization scale $R$ and the normalization $N_g$ of the GC renormalon. In the present work, we use three different methods to determine $N_g$, yielding a result with an uncertainty of $40\%$. Following two recent state-of-the-art strong coupling determination analyses at $\mathcal{O}({\alpha }_s^5)$, we show that using the renormalon-free GC scheme successfully reconciles the results for ${\alpha }_s(m_{\tau }^2)$ based on CIPT and FOPT. The uncertainties due to variations of $R$ and the uncertainty of $N_g$ only lead to a small or moderate increase of the final uncertainty of ${\alpha }_s(m_{\tau }^2)$, and affect mainly the CIPT expansion method. The FOPT and CIPT results obtained in the RF GC scheme may be consistently averaged. The RF GC scheme thus constitutes a powerful new ingredient for future analyses of $\tau$ hadronic spectral function moments.

arXiv comment43 pages, 5 figures; presentation in section 3.2 improved, results unchanged; version published in the Journal of High Energy Physics

References in corpus (45)

• Renormalons
• The Physics of Hadronic Tau Decays
• Measurement of the Strong Coupling Constant and the Vector and Axial-Vector Spectral Functions in Hadronic Tau Decays
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• 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
• The Determination of alpha_s from Tau Decays Revisited
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Duality violations and spectral sum rules
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Unraveling duality violations in hadronic tau decays
• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions
• What is the Top Quark Mass?
• Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory
• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Hyperasymptotics and quark-hadron duality violations in QCD
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• Bilocal expansion of the Borel amplitude and the hadronic tau decay width
• Expansion functions in perturbative QCD and the determination of ${\alpha }_s(M_{\tau }^2)$
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• Accelerated convergence of perturbative QCD by optimal conformal mapping of the Borel plane
• The strong coupling from an improved $\tau$ vector isovector spectral function
• Renormalons Beyond One-Loop
• The strong coupling from hadronic $\tau$ decays: a critical appraisal
• Normalization Constants of Large Order Behavior
• Expansions of $\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior
• Pole mass renormalon and its ramifications
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• REvolver: Automated running and matching of couplings and masses in QCD
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Resummation of the hadronic tau decay width with the modified Borel transform method
• Renormalon Subtraction from the Average Plaquette and the Gluon Condensate
• Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
• 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 ${\alpha }_s$
• Hyperasymptotic approximation to the plaquette and determination of the gluon condensate
• Evidence against naive truncations of the OPE from $e^{+}{e}^{-}\to$ hadrons below charm
• Extraction of alpha_s from the Gross--Llewellyn Smith sum rule using Borel resummation
• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Estimation of the large order behavior of the plaquette
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Higher-order behaviour of two-point current correlators

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• Mathematical Aspects of the Asymptotic Expansion in Contour Improved Perturbation Theory for Hadronic Tau Decays
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