Towards QCD running in 5 loops: quark mass anomalous dimension

Baikov, P.A.; Federation, Russian; Chetyrkin, K.G.; Kühn, Johann H.

doi:10.22323/1.197.0056

Cited by 5 publications

(7 citation statements)

References 34 publications

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“…(3.15)- (3.19). This completes the five-loop renormalization program for general groups, providing a generalization -and independent confirmation -of the previously known SU(3) coefficients [6,9,42,45], relevant for physical QCD.…”

Section: Discussionsupporting

confidence: 72%

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Complete renormalization of QCD at five loops

Luthe

Maier

Marquard

et al. 2017

J. High Energ. Phys.

102

118

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Section: Discussionsupporting

confidence: 72%

“…As a second check, specializing to SU(3) allows us to compare with the Feynman-gauge 5-loop result given in eq. (3.2) of [42]. Again, we find full agreement.…”

Section: Ghost Field Anomalous Dimensionsupporting

confidence: 74%

Complete renormalization of QCD at five loops

Luthe

Maier

Marquard

et al. 2017

J. High Energ. Phys.

102

118

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show abstract

“…Calculations are ongoing for β 4 [20]. All the β i coefficients are gauge independent in the M S scheme [21].…”

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

298

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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“…The quark mass anomalous dimension has important implications: the Higgs boson decay rate into charm and bottom quarks, respectively, is proportional to the square of the respective quark mass at the scale of m H , which, for given on-shell mass, depends on the fore-mentioned anomalous dimension (see, e.g., recent discussions in [1,[7][8][9][10][11]). The generalization of the result from SU (3) to an arbitrary compact semi simple Lie group, as presented in this paper, gives additional insight into the structure of the result.…”

Section: Introductionmentioning

confidence: 99%

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

Baikov

Chetyrkin

Kühn

2017

J. High Energ. Phys.

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Abstract:We extend the O(α 5 s ) result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of fourloop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

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Towards QCD running in 5 loops: quark mass anomalous dimension

Abstract: We report first results of an ongoing project devoted to the analytical calculation of the QCD β -function and the quark mass anomalous dimension at the five loop level.11th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)

Cited by 5 publications

References 34 publications

Complete renormalization of QCD at five loops

Complete renormalization of QCD at five loops

The QCD running coupling

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

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