The gell-mann-low function of QCD in the three-loop approximation

Tarasov, O.V.; Vladimirov, A. A.; Zharkov, A. Yu.

doi:10.1016/0370-2693(80)90358-5

Cited by 873 publications

(738 citation statements)

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“…For completeness we want to list the results for the coefficients which are given by [44,45,46,14] [14] is the treatment of the four-loop vacuum diagrams. The task is simplified due to the fact that only the divergent parts in ε are needed.…”

Section: Massive Vacuum Integrals and The β Functionmentioning

confidence: 99%

Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α 4 s and α 3 s , respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e + e − annihilation. The knowledge of the complete mass dependence at order α 2 s has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α 2 QED corrections to the µ decay. Its relevance for the determination of the Fermi constant G F is discussed. Finally the calculation of the three-loop relation between the MS and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.

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Section: Massive Vacuum Integrals and The β Functionmentioning

confidence: 99%

Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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“…Thus, one needs only to know Π S to order a 2 s and the anomalous dimension γ SS q (a s ) to order a 3 s to find all Q-dependent terms in Π S at O(a 3 s ), since the beta function and the quark mass anomalous dimension γ m are reliably known to order a 3 s from Refs. [17][18][19][20]. As we shall see later both problems are eventually reduceable to calculation of a specific class of diagrams representing some massless Feynman integrals (FI) depending on only one external momentum (to be named p-integrals below) and with the number of loops not exceeding three.…”

Section: Preliminariesmentioning

confidence: 99%

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs3) in pQCD

1997

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“…For instance, in QCD the four loop β-function and mass anomalous dimensions have recently been determined in MS in [8,9]. These built on the earlier loop calculations of [10,11,12,13]. However, the situation in the NATM is unfortunately not as advanced.…”

Section: Introductionmentioning

confidence: 99%

Three-loop renormalization of the SU(N) non-abelian Thirring model

Bennett

Gracey

1999

Nuclear Physics B

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Abstract. We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a non-abelian colour group SU (N c ) but also depend on the number of flavours, N f . The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MS renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the non-abelian Thirring model with other models with a four-fermi interaction. One feature to emerge from the computation is the establishment of the fact that the SU (N f ) Gross Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.

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The gell-mann-low function of QCD in the three-loop approximation

Cited by 873 publications

References 10 publications

Results and techniques of multi-loop calculations

Results and techniques of multi-loop calculations

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs3) in pQCD

Three-loop renormalization of the SU(N) non-abelian Thirring model

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