All-orders infrared freezing of observables in perturbative QCD

Abstract

We consider a Borel sum definition of all-orders perturbation theory for Minkowskian QCD observables such as the R(e+e-) ratio, and show that both this perturbative component and the additional non-perturbative Operator Product Expansion (OPE) component can remain separately well-defined for all values of energy sqrt(s), with the perturbative component dominating as s-->infinity, and with both components contributing as s-->0. In the infrared s-->0 limit the perturbative correction to the parton model result for R(e+e-) has an all-orders perturbation theory component which smoothly freezes to the value R(0)=2/b, where b=(33-2Nf)/6 is the first QCD beta-function coefficient with Nf flavours of massless quarks. For freezing one requires Nf<9. The freezing behaviour is manifested by the ``contour-improved'' or ``Analytic Perturbation Theory'' (APT), in which an infinite subset of analytical continuation terms are resummed to all-orders. We show that for the Euclidean Adler-D function, D(Q^2), the perturbative component remains defined into the infrared provided that ALL the renormalon singularities care taken into account, but no analogue of the APT reorganisation of perturbation theory is possible. We perform phenomenological comparisons of suitably smeared low-energy data for the R(e+e-) ratio, with the perturbative freezing perdictions, and find good agreement.

13 figures, 48 pages. Additional references. Minor textual revision

References in corpus (34)

• Renormalons
• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Naive nonabelianization and resummation of fermion bubble chains
• Measurements of the Cross Section for e+e- -> hadrons at Center-of-Mass Energies from 2 to 5 GeV
• Resummation of $({\beta }_0{\alpha }_s{)}^n$ Corrections in QCD: Techniques and Applications to the $\tau$ Hadronic Width and the Heavy Quark Pole Mass
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Renormalization group analysis of the tau-lepton decay within QCD
• Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Can the QCD running coupling have a causal analyticity structure?
• Analytic Perturbation Theory in analyzing some QCD observables
• Testing non-perturbative strong interaction effects via the Adler function
• a_1(1260) dominance in the process e+e- \to 4πat energies 1.05--1.38 GeV
• Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ in the energy region $\sqrt[]{s}$ from 0.98 to 1.38 GeV.}
• All-Orders Renormalon Resummations for some QCD Observables
• Disentangling running coupling and conformal effects in QCD
• Relations between Observables and the Infrared Fixed-Point in QCD
• A Measurement of the Total Cross Section for $e^{+}{e}^{-}\to hadrons$ at $\sqrt{s}$=10.52 GeV
• The Bjorken Sum Rule in the Analytic Approach to Perturbative QCD
• Renormalization Scheme and Higher Loop Stability in Hadronic $\tau$ Decay within Analytic Perturbation Theory
• Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• Large-order Behaviour due to Ultraviolet Renormalons in QCD
• The Gross--Llewellyn Smith Sum Rule in the Analytic Approach to Perturbative QCD
• Analytic Approach to Perturbative QCD
• Low-Energy QCD and Ultraviolet Renormalons
• RS-invariant all-orders renormalon resummations for some QCD observables
• Renormalon-inspired resummations for vector and scalar correlators- estimating the uncertainty in {alpha}_{s}({m}_τ^{2}) and and α({M}_{Z}^{2})
• All-orders infra-red freezing of R(e+e-) in perturbative QCD
• QCD coupling up to third order in standard and analytic perturbation theories
• Improving alpha_QED(M_Z^2) and the charm mass by analytic continuation
• The uncertainty in ${\alpha }_s(M_Z^2)$ determined from hadronic tau decay measurements
• Direct Extraction of QCD Lambda MS-bar from e+e- Jet Observables
• Remark on the perturbative component of inclusive $\tau$-decay

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