Generalization of the BLM procedure and its scales in any order of pQCD
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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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Forward citations
Cited by 2 Pith papers
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Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results
Explores numerical optimization of perturbative QCD series for the Bjorken sum rule coefficient and Adler function via renormalization group methods drawn from prior literature.
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