Howe, D.M. and Maxwell, C.J. (2004) 'All-orders infrared freezing of observables in perturbative QCD.', Physical review D : particles and fields., 70 . 014002.
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.
|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.|
|Full text:||(NA) Not Applicable |
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|Publisher Web site:||http://dx.doi.org/10.1103/PhysRevD.70.014002|
|Publisher statement:||© 2004 by The American Physical Society. All rights reserved.|
|Record Created:||28 Apr 2008|
|Last Modified:||05 Aug 2011 14:12|
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