Fourth-order QCD renormalization group quantities in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>V</mml:mi></mml:math>scheme and the relation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>function to the Gell-Mann–Low function in QED

Kataev, A. L.; Molokoedov, V. S.

doi:10.1103/physrevd.92.054008

Cited by 34 publications

(36 citation statements)

References 90 publications

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“…Expressions in the V-scheme can be found in ref. [26]. They are: β 2 = 4224.18 − 746.01n f + 20.88n 2 f and β 3 = 43175 − 12952n f + 707.0n 2 f Some important points must be made: first the β i are independent of α s ; they are expansions in orders of , see Section 3.4.…”

Section: The Evolution Of α S In Perturbative Qcdmentioning

confidence: 99%

The QCD running coupling

Deur

Brodsky

Téramond

2016

Progress in Particle and Nuclear Physics

312

236

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We review the present theoretical and empirical knowledge for α s , the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of α s (Q 2 ) on momentum transfer Q encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on α s (Q 2 ) at high Q 2 , as predicted by perturbative QCD, and its analytic behavior at small Q 2 , based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain.In the second, more technical, part of the review, we discuss the behavior of α s (Q 2 ) in the high momentum transfer domain of QCD. We review how α s is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as "Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization-scale ambiguity. We also report recent significant measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the "Principle of Maximum Conformality", which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior α s (Q 2 ) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q 0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the GribovZwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of α s (Q 2 ) in order to bring better unity to the subject.2

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Section: The Evolution Of α S In Perturbative Qcdmentioning

confidence: 99%

The QCD running coupling

Deur

Brodsky

Téramond

2016

Progress in Particle and Nuclear Physics

312

236

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“…[70]. It is widely used in different QCDoriented studies [49,[93][94][95][96][97][98][99][100]. In this section we will use this mMOM-scheme in the SU(N c ) theory to find out the constraints imposed by its gauge-dependence on the conditions of existence of the fundamental property of the β-function factorization in the GCR.…”

Section: The Qed Generalized Crewther Relation In the Ms Mom And Os mentioning

confidence: 99%

“…(1.3) in Minkowski region and related to Euclidean Adler function, was analyzed in the mMOM-scheme at ξ = 0 in refs. [94] and [96].…”

Section: The Ns Adler Function In the Mmom-scheme In The O(a 4 S ) Apmentioning

confidence: 99%

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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.

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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.

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“…More "physical" renormalization schemes, such as "momentum subtraction" (MOM) [7,8,9] or the "Vscheme" which relies on calculating the effective potential between two heavy quarks [10,11,12] are taken to generate perturbative results that are better approximations to the exact result than these derived using MS. We note though that these renormalization schemes are more difficult to implement and also result in additional ambiguities. For example, even with the MOM schemes for renormalization, in eq.…”

Section: Introductionmentioning

confidence: 99%

Renormalization scheme dependence in a QCD cross section

2016

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The zero to four loop contribution to the cross section R e + e − for e + e − −→ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log (LL), next-to-leading-log (N LL) . . . N 3 LL perturbative contributions.It is shown how all logarithmic contributions to R e + e − can be summed and that R e + e − can be expressed in terms of the log independent contributions, and once this is done the running coupling a is evaluated at a point independent of the renormalization scale µ. All explicit dependence of R e + e − on µ cancels against its implicit dependence on µ through the running coupling a so that the ambiguity associated with the value of µ is shown to disappear. The renormalization scheme dependency of the "summed" cross section R e + e − is examined in three distinct renormalization schemes. In the first two schemes, R e + e − is expressible in terms of renormalization scheme independent parameters τ i and is explicitly and implicitly independent of the renormalization scale µ. Two of the forms are then compared graphically both with each other and with the purely perturbative results and the RG-summed N 3 LL results.

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Fourth-order QCD renormalization group quantities in theVscheme and the relation of theβfunction to the Gell-Mann–Low function in QED

Cited by 34 publications

References 90 publications

The QCD running coupling

The QCD running coupling

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

Renormalization scheme dependence in a QCD cross section

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