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

Abstract

The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--β_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.

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

References in corpus (3)

• QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling
• A novel series solution to the renormalization group equation in QCD
• Renormalons: technical introduction

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