Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions

K.G. Chetyrkin

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Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions

K.G. Chetyrkin

High Energy Physics - Phenomenology · Submitted 20 May 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level.

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arXiv IDhep-ph/0405193 (version 3)

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CitationK.G. Chetyrkin. "Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions." arXiv:hep-ph/0405193 (2004). https://pith.science/paper/36LMZZ2D

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The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD. Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level. As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO. Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD.	result 0.59	0.95	0.33	asserted 1.00
s1	Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level.	result 0.58	0.77	0.68	asserted 1.00
s2	As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO.	result 0.98	0.93	0.08	asserted 1.00
s3	Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.	result 0.53	0.95	0.07	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Original abstract

The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD. Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level. As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO. Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.

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References

Forward citations

Cited by 14 Pith papers

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How the literature uses it

37 arXiv papers cite this in 45 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 31 sentences without a confident label

Builds on it 1 paper

We thereby extend the N$^3$LO results which were, for gluon and ghost propagators, presented in [ref] to N$^4$LO.

Five-loop renormalisation of QCD in covariant gauges · Scheme independent propagators · 1.00

Uses its method or tool 7 papers

The couplings are then run to high energy using the three-loop renormalization group equations with four-loop running included for $α_s$ [ref] .

Scale Invariant Instantons and the Complete Lifetime of the Standard Model · Numerical Results · 0.97
As in the quenched case, using the four-loops expression for the coupling constant in the Tayol scheme [ref]

Ghost-gluon coupling, power corrections and $\Lambda_{\bar{MS}}$ from twisted-mass lattice QCD at $N_f=2$ · Lattice computation of the coupling in the Taylor scheme · 0.87
To obtain the Coulomb piece, we converted the four-loop running of $(q)$ in momentum space [ref] to the behavior in position space using the method of [ref] , and enforced saturation of $(r)$ at long distances, as detailed in Ref. [ref] .

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With the help of the known four-loop renormalization of the QCD Lagrangian [ref] , the results for the relevant renormalization constants can be extracted.

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The quark wave function renormalization constant [equation] is required to four-loop order [ref] .

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The two-loop counterterm for $α_s$ can be found, e.g., in Ref. [ref] and the one for the gluon wave function in Ref. [ref] .

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Cites it as background 3 papers

The perturbative running of $α_T$ is known up to four loops [ref] ,

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The $$ quark mass renormalization constant has been computed up to four [ref] and five loops [ref] .

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As a result, computations of the basic renormalization group functions of QCD [ref] have recently reached the five-loop level [ref] .

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