Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments I: Renormalon-Free Gluon Condensate Scheme

Abstract

We propose a simple and easy-to-implement scheme for a renormalon-free gluon condensate (GC) matrix element, which is analogous to implementations of short-distance heavy-quark mass renormalization schemes existing in the literature already for a long time. Because the scheme is based on a perturbative subtraction at the level of the matrix element, with a freely adaptable infrared factorization scale, it can be implemented with little effort for any observable where the GC is relevant. The scheme depends on the renormalon norm of the GC which has to be supplemented independently. We apply the scheme to the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions of $\tau$ hadronic spectral function moments. These expansions exhibit a long-standing discrepancy for moments used in high-precision determinations of the strong coupling in the commonly used GC scheme that is not renormalon-free. We show that the scheme is capable of resolving the FOPT-CIPT discrepancy problem. At the same time, the perturbative behaviour of the moments that previously showed bad convergence properties and for which the non-perturbative corrections from the GC are sizeable, is substantially improved. The new GC scheme may provide a powerful theoretical tool for future phenomenological applications.

arXiv comment49 pages, 5 figures; Sec. 5.3 added; version published in the Journal of High Energy Physics

References in corpus (41)

• Renormalons
• Hadronic Z- and tau-Decays in Order alpha_s^4
• 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
• QCD phenomenology of static sources and gluonic excitations at short distances
• Infrared Renormalization Group Flow for Heavy Quark Masses
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• An updated determination of α_s from tau decays
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Strange Quark Mass Determination from Cabibbo-Suppressed Tau Decays
• On Higgs decays to hadrons and the R-ratio at N^4LO
• ${\alpha }_s$ 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?
• Model-independent determination of the gluon condensate in four-dimensional SU(3) gauge theory
• Scheme variations of the QCD coupling and hadronic $\tau$ decays
• Determination of the QCD $\Lambda$-parameter and the accuracy of perturbation theory at high energies
• R-evolution: Improving perturbative QCD
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• Expansion functions in perturbative QCD and the determination of ${\alpha }_s(M_{\tau }^2)$
• The strong coupling from an improved $\tau$ vector isovector spectral function
• The MSR Mass and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ Renormalon Sum Rule
• Surviving the renormalon in heavy quark potential
• Modified Contour-Improved Perturbation Theory
• Expansions of $\tau$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• On the Difference between FOPT and CIPT for Hadronic Tau Decays
• 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
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
• Renormalon Subtraction from the Average Plaquette and the Gluon Condensate
• Hyperasymptotic approximation to the plaquette and determination of the gluon condensate
• Correlator of heavy-quark currents at small q^2 in the large-beta_0 limit
• Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation
• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Higher-order behaviour of two-point current correlators
• New method for renormalon subtraction using Fourier transform

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