Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1997-06-23
Phys.Rev.D56:6980-6992,1997
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages, LaTeX, including 6 figures requires epsfig.sty
Scientific paper
10.1103/PhysRevD.56.6980
We show that the Pade 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-$\beta_0$ 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 delta-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-$\beta_0$ limit.
Brodsky Stanley J.
Ellis John
Gardi Einan
Karliner Marek
Samuel Mark A.
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