Infrared Freezing of Euclidean QCD observables

Abstract

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q^2>Λ^2, where Q^2=Λ^2 is the Landau pole in the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q^2<Λ^2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q^2-dependence of the perturbative corrections to the Adler D function, the GLS sum rule, and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q^2=Λ^2, and then exhibits freezing behaviour, vanishing at Q^2=0. Finiteness at Q^2=Λ^2 implies specific relations between the residues of IR and UV renormalons in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained) are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of non-perturbative and perturbative ambiguities we are led to a result for the Q^2 dependence of these observables at all Q^2, in which there is a single undetermined non-perturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behaviour of the Minkowskian R_{e+e-} ratio.

26 pages, 6 figures, correction of typos, additional references, amended discussion of Minkowskian freezing

References in corpus (24)

• Renormalons
• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Calculation of Power Corrections to Hadronic Event Shapes
• Naive nonabelianization and resummation of fermion bubble chains
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Power Corrections to Event Shape Distributions
• Analytic Perturbation Theory in analyzing some QCD observables
• Testing non-perturbative strong interaction effects via the Adler function
• All-Orders Renormalon Resummations for some QCD Observables
• Disentangling running coupling and conformal effects in QCD
• IR-Renormalon Contribution to the Longitudinal Structure Function $F_L$
• A novel integral representation for the Adler function
• Power corrections and resummation of radiative corrections in the single dressed gluon approximation - the average thrust as a case study
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• Renormalons at the boundaries between perturbative and non-perturbative QCD
• All-orders infrared freezing of observables in perturbative QCD
• Low-Energy QCD and Ultraviolet Renormalons
• Borel summation and momentum-plane analyticity in perturbative QCD
• Infrared renormalons and the relations between the Gross-Llewellyn Smith and the Bjorken polarized and unpolarized sum rules
• Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
• Bjorken unpolarized and polarized sum rules: comparative analysis of large-N_F expansions
• On the infrared freezing of perturbative QCD in the Minkowskian region

Cited by in corpus (14)

• Various versions of analytic QCD and skeleton-motivated evaluation of observables
• QCD coupling below 1 GeV from quarkonium spectrum
• Hadronic vacuum polarization function within dispersive approach to QCD
• New Approach to Parton Shower MC's for Precision QCD Theory: HERWIRI1.0(31)
• HERWIRI1.0: MC Realization of IR-Improved DGLAP-CS Parton Showers
• Fixed and Unfixed Points: Infrared limits in optimized QCD perturbation theory
• Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD
• Dispersive approach to QCD: tau lepton hadronic decay in vector and axial-vector channels
• Comment on "Infrared freezing of Euclidean QCD observables"
• Exponentially Modified QCD Coupling
• Hadronic contributions to electroweak observables within DPT
• On the ambiguity of field correlators represented by asymptotic perturbation expansions
• The Banks-Zaks expansion in perturbative QCD: an update
• On the ambiguity of functions represented by divergent power series