2006/04/30 by Paul M. Brooks, C.J. Maxwell, C. J. Maxwell
Physics and Astronomy · #Black Holes and Theoretical Physics #Function (biology) #Gravitational singularity #Infrared #Lambda #Mathematical physics #Observable #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Renormalon #hep-ph
paper · pdf · doi:10.1103/physrevd.74.065012
published as Phys.Rev. D74 (2006) 065012 · 26 pages, 6 figures, correction of typos, additional references, amended discussion of Minkowskian freezing
arxiv created 2006/08/22 · openalex publication_date 2006/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q2>\ensuremathΛ2, where Q2=\ensuremathΛ2 is the Landau pole of the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q2<\ensuremathΛ2 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 Q2-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 Q2=\ensuremathΛ2, and then exhibits freezing behavior, vanishing at Q2=0. Finiteness at Q2=\ensuremathΛ2 implies specific relations between the residues of IR and UV renormalon singularities 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 nonperturbative and perturbative ambiguities we are led to a result for the Q2-dependence of these observables at all Q2, in which there is a single undetermined nonperturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behavior of the Minkowskian R_e+e^\ensuremath- ratio.