Generalization of BLM procedure and its scales in any order of pQCD: A Practical approach

The Brodsky--Lepage--Mackenzie procedure is sequentially extended to any fixed order of perturbative QCD. The rearranged perturbation series looks like a continued fraction representation. A generalization of this procedure is developed, which represents a specific version of the Fastest Apparent Convergence prescription. This generalized BLM procedure is applied to the Adler function D at N

^3

LO and N

^4

LO. The net effect of this generalized BLM improvement on the D and

R_{e^+e^-}

functions in QCD is discussed.

quantum chromodynamics
perturbation theory: higher-order
renormalization
renormalization group
radiative correction
Feynman graph: higher-order
electron positron: annihilation
hadron: electroproduction
cross section: ratio

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