1997/06/23 by Stanley J. Brodsky, John Ellis, Einan Gardi +3 · 1 citation
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.56.6980
published as Phys.Rev.D56:6980-6992,1997 · 28 pages, LaTeX, including 6 figures requires epsfig.sty
arxiv created 1997/06/23 · openalex publication_date 1997/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show that the Pad'e approximant (PA) approach for resummation of perturbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-\ensuremathβ0 limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-setting method to higher orders in a renormalization scale- and scheme-invariant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of \ensuremathδ functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. We illustrate the method with the vacuum polarization function and the Bjorken sum rule computed in the large-\ensuremathβ0 limit.