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All-orders infrared freezing of observables in perturbative QCD

Howe, D.M.; Maxwell, C.J.

Authors

D.M. Howe

C.J. Maxwell



Abstract

We consider a Borel sum definition of all-orders perturbation theory for Minkowskian QCD observables such as the Re1e2 ratio, and show that both this perturbative component and the additional nonperturbative all-orders operator product expansion ~OPE! component can remain separately well-defined for all values of energy As, with the perturbative component dominating as s!`, and with both components contributing as s!0. In the infrared s!0 limit the perturbative correction to the parton model result for Re1e2 has an all-orders perturbation theory component which smoothly freezes to the value R(0)52/b, where b5(33 22Nf )/6 is the first QCD beta-function coefficient, with Nf flavors of massless quark. For freezing one requires Nf,9. The freezing behavior 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(Q2), the perturbative component remains defined into the infrared if all the renormalon singularities are taken into account, but no analogue of the APT reorganization of perturbation theory is possible. We perform phenomenological comparisons of suitably smeared low-energy data for the Re1e2 ratio, with the perturbative freezing predictions, and find good agreement.

Citation

Howe, D., & Maxwell, C. (2004). All-orders infrared freezing of observables in perturbative QCD. Physical Review D, Particles and fields, 70, https://doi.org/10.1103/physrevd.70.014002

Journal Article Type Article
Publication Date 2004-07
Deposit Date Apr 28, 2008
Publicly Available Date Apr 28, 2008
Journal Physical Review D, Particles and fields
Print ISSN 0556-2821
Electronic ISSN 1089-4918
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 70
DOI https://doi.org/10.1103/physrevd.70.014002
Keywords Operator product expansion, Total cross-section, Tau-Lepton decay, Renormalization-group analysis, Interval 1350-2400 Mev, To-leading order, Of-mass energies, E&E annihilation, Form-factor, Renormalon resummations.

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