2003/03/31 by D. M. Howe, David M. Howe, C.J. Maxwell +1 · 2 citations
Physics and Astronomy · #Gravitational singularity #High-Energy Particle Collisions Research #Infrared #Massless particle #Mathematical physics #Observable #Operator product expansion #Particle physics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Perturbative QCD #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Quark #Renormalon #hep-ph
paper · pdf · doi:10.1103/physrevd.70.014002
published as Phys.Rev. D70 (2004) 014002 · 13 figures, 48 pages. Additional references. Minor textual revision
arxiv created 2004/04/02 · openalex publication_date 2004/07/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a Borel sum definition of all-orders perturbation theory for Minkowskian QCD observables such as the R_e+e^\ensuremath- 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 √(s), with the perturbative component dominating as \stackrel\ensuremath→s\ensuremath∞, and with both components contributing as \stackrel\ensuremath→s0. In the infrared \stackrel\ensuremath→s0 limit the perturbative correction to the parton model result for R_e+e^\ensuremath- has an all-orders perturbation theory component which smoothly freezes to the value R(0)=2/b, where b=(33\ensuremath-2Nf)/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 R_e+e^\ensuremath- ratio, with the perturbative freezing predictions, and find good agreement.