Generalization of the BLM procedure and its scales in any order of pQCD

Details Generalization of the BLM procedure and its scales in any order of pQCD Generalization of the BLM procedure and its scales in any order of pQCD

2004-11-30

arxiv.org/abs/hep-ph/0411397v4

JHEP 0706:009,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, JHEP3, 4 figures are enclosed as eps-file, final version to be published in JHEP

Scientific paper

10.1088/1126-6708/2007/06/009

The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--\beta_0 approximation''. As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to R_{e^+e^-} in QCD at N$^3$LO. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.

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