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

Михайлов, С. В.

doi:10.1088/1126-6708/2007/06/009

Cited by 61 publications

(169 citation statements)

References 38 publications

Supporting

Mentioning

160

Contrasting

Order By: Relevance

“…The analytical results for the {β}-expanded expressions of d 2 and d 3 coefficients in this model were first obtained in ref. [73] and confirmed later on in ref. [78].…”

Section: Jhep02(2018)161supporting

confidence: 72%

“…Let us now to move aside slightly and consider the {β}-expansion approach [73] for representing PT coefficients of the RG invariant quantity, namely for d k -coefficients of the PT D NS (a s )-series, proposed and used in ref. [73], which is the high-order PT QCD generalization of the suggested MS-version of the BLM scale-fixing approach in ref.…”

Section: Jhep02(2018)161mentioning

confidence: 99%

“…[73], which is the high-order PT QCD generalization of the suggested MS-version of the BLM scale-fixing approach in ref. [74].…”

Section: Jhep02(2018)161mentioning

confidence: 99%

“…[69,73,76] all β k -dependent contributions in eqs. (2.5a)-(2.5b) should be absorbed into the set of scales of the initially defined in the MSscheme QCD coupling constant.…”

Section: Jhep02(2018)161mentioning

confidence: 99%

See 3 more Smart Citations

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Garkusha

Kataev

Molokoedov

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O(a 4 s ) level of perturbation theory. It is known that in the gauge-invariant renormalization MS-scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the MS-scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O(a 3 s ) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = −3, −1 and ξ = 0. In the O(a 4 s ) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = −3 at the O(a 3 s ) approximation. It is demonstrated that if factorization property for the MS-like 1 Affiliation from 2011 till 2015.Open Access, c The Authors. Article funded by SCOAP 3 .https://doi.org/10.1007/JHEP02(2018)161 JHEP02(2018)161schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

show abstract

“…The analytical results for the {β}-expanded expressions of d 2 and d 3 coefficients in this model were first obtained in ref. [73] and confirmed later on in ref. [78].…”

Section: Jhep02(2018)161supporting

confidence: 72%

Section: Jhep02(2018)161mentioning

confidence: 99%

“…[73], which is the high-order PT QCD generalization of the suggested MS-version of the BLM scale-fixing approach in ref. [74].…”

Section: Jhep02(2018)161mentioning

confidence: 99%

“…[69,73,76] all β k -dependent contributions in eqs. (2.5a)-(2.5b) should be absorbed into the set of scales of the initially defined in the MSscheme QCD coupling constant.…”

Section: Jhep02(2018)161mentioning

confidence: 99%

See 2 more Smart Citations

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Garkusha

Kataev

Molokoedov

2018

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…A proposed extension of BLM is a method called "sequential extended BLM" (seBLM) [5]. The purpose of seBLM is to optimize the pQCD convergence.…”

Section: Introductionmentioning

confidence: 99%

Setting the renormalization scale in perturbative QCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

Hong¹,

Wu²,

Ma³

et al. 2015

Phys. Rev. D

View full text Add to dashboard Cite

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all-orders. In this paper we discuss two distinct methods. One is based on the "Principle of Maximum Conformality" (PMC), which provides a systematic all-orders method to eliminate the scale-and scheme-ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the "sequential extended BLM" (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low-orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher-orders. We then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R e + e − at four-loop order in pQCD.

show abstract

Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules

Kataev

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken , the Ellis-Jaffe sum rules of polarized lepton-nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axialvector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the U(1) and SU(N c ) models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical O(α 4 ) and O(α 2 s ) conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed.

show abstract

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

Cited by 61 publications

References 38 publications

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

Setting the renormalization scale in perturbative QCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules

Contact Info

Product

Resources

About