Rounds or Rungs

Stevenson, W. H.

doi:10.1093/nq/s9-iii.65.231c

Cited by 4 publications

(10 citation statements)

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“…The more restricted problem to find the optimal scale in a given scheme has been widely discussed in the literature and three quite distinct methods have been proposed: the principle of fastest apparent convergence (FAC) [23,24], the principle of minimal sensitivity (PMS) [27][28][29][30], and the Brodsky-Lepage-Mackenzie (BLM) [31] scale setting. The application of these methods can yield quite different predictions (see for instance the analyses in Ref.…”

Section: Scheme Dependence Of Pqcd Predictionsmentioning

confidence: 99%

Scheme dependence of NLO corrections to exclusive processes

Müller

1999

Phys. Rev. D

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We apply the so-called conformal subtraction scheme to predict perturbatively exclusive processes beyond leading order. Taking into account evolution effects, we study the scheme dependence for the photon-to-pion transition form factor and the electromagnetic pion form factor at next-to-leading order for different pion distribution amplitudes. Relying on the conformally covariant operator product expansion and using the known higher order results for polarized deep inelastic scattering, we are able to predict perturbative corrections to the hard-scattering amplitude of the photon-to-pion transition form factor beyond next-to-leading order in the conformal scheme restricted to the conformal limit of the theory.Comment: RevTeX, 25 pages, 2 figures, 5 tables, minor changes, to be published in Phys. Rev.

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Section: Scheme Dependence Of Pqcd Predictionsmentioning

confidence: 99%

Scheme dependence of NLO corrections to exclusive processes

Müller

1999

Phys. Rev. D

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“…The fixed-order estimate in the conventional procedure is also scheme dependent; i.e., different choice of renormalization scheme R will lead to different theoretical estimates. This is the well-known renormalization scheme ambiguity [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…This is not an easy task. Various scale-setting procedures have been proposed since the 1980's for deriving an optimized scale, such as Fastest Apparent Convergence (FAC) [4][5][6] 2 , the Principle of Minimum Sensitivity (PMS) [7][8][9][10], the Brodsky-Lepage-Mackenzie (BLM) [11] procedure and its extended versions such as the dressed skeleton expansion [34,35], the sequential se-BLM and x-BLM methods [36][37][38], etc., and the PMC. A short review of FAC, BLM and PMS can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Clearly, the prediction for any physical observable must be independent of the choice of renormalization scheme; this is the central property of the renormalization group (RG) invariance [18,19,[41][42][43]. As we shall discuss, the RG based equations [7][8][9][10] which incorporate the scheme parameters provide a convenient way for estimating both the scale-and scheme-dependence of the QCD predictions for a physical process [7-10, 30, 44]. In this paper, we will utilize such RG based equations for a general discussion of the RG-invariance.…”

Section: Introductionmentioning

confidence: 99%

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Self-consistency requirements of the renormalization group for setting the renormalization scale

Brodsky

2012

Phys. Rev. D

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In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariancereflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {β R i }-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance. Moreover, after PMC scale-setting, the residual initial scale-dependence at fixed order due to unknown higher-order {βi}-terms can be substantially suppressed. The PMC thus eliminates a serious systematic scale error in pQCD predictions, greatly improving the precision of tests of the Standard Model and the sensitivity to new physics at collider and other experiments.

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“…Anything else, for instance the divergence of the expansions in (1) and/or (3), depends on the chosen RS and has thus no direct physical meaning. In my view the best strategy how to proceed in such circumstances is to follow the suggestion of [12], i.e. to choose at each finite order N of perturbation theory a definite renormalization prescription and investigate the limit of finite order approximants (2), i.e.…”

Section: Discussionmentioning

confidence: 99%

On the Brodsky-Lepage-Mackenzie scale-fixing procedure, its generalizations and the “genuine” higher order corrections

Chýla¹

1995

Physics Letters B

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The question of the uniqueness of the Brodsky-Lepage-Mackenzie procedure for fixing the renormalization scale in perturbative QCD is discussed. It is shown that the resulting finite order approximants are as ambiguous as the original truncated perturbative expansions. This inherent ambiguity of the BLM procedure undermines the recent attempts to define "genuine" higher order perturbative corrections.

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Rounds or Rungs

Cited by 4 publications

References 0 publications

Scheme dependence of NLO corrections to exclusive processes

Scheme dependence of NLO corrections to exclusive processes

Self-consistency requirements of the renormalization group for setting the renormalization scale

On the Brodsky-Lepage-Mackenzie scale-fixing procedure, its generalizations and the “genuine” higher order corrections

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