Four-loop Dyson-Schwinger-Johnson anatomy

D. J. Broadhurst

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Four-loop Dyson-Schwinger-Johnson anatomy

D. J. Broadhurst

High Energy Physics - Phenomenology · Submitted 13 Sep 1999

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

The authors' main claim Dyson-Schwinger equations are used to evaluate the 4-loop anomalous dimensions of quenched QED in terms of finite, scheme-independent, 3-loop integrals.

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What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.93 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Dyson-Schwinger equations are used to evaluate the 4-loop anomalous dimensions of quenched QED in terms of finite, scheme-independent, 3-loop integrals. Three of the results serve as strong checks of terms from scheme-dependent 4-loop QCD calculations. The fourth, for the anomalous dimension of $\bar\psi\sigma_{\mu\nu}\psi$, was previously known only to 2-loop order. The 4-loop beta function has 24 unambiguous terms. Two of the simplest give $\beta_4=\frac13(22-160)=-46$. The rational, $\zeta_3$ and $\zeta_5$ parts of the other 22 miraculously sum to zero. Vertex anomalous dimensions have 40 terms, with no dramatic cancellations. Our methods come from work by the late Kenneth Johnson, done more than 30 years ago. They are entirely free of the subtractions and infrared rearrangements of later methods.

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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	Dyson-Schwinger equations are used to evaluate the 4-loop anomalous dimensions of quenched QED in terms of finite, scheme-independent, 3-loop integrals.	contribution 0.57	0.86	0.60	asserted 1.00
s1	Three of the results serve as strong checks of terms from scheme-dependent 4-loop QCD calculations.	interpretation 0.74	0.72	0.12	asserted 0.99
s2	The fourth, for the anomalous dimension of $\bar\psi\sigma_{\mu\nu}\psi$, was previously known only to 2-loop order.	gap 0.96	0.43	0.13	asserted 1.00
s3	The 4-loop beta function has 24 unambiguous terms.	result 0.98	0.76	0.21	asserted 1.00
s4	Two of the simplest give $\beta_4=\frac13(22-160)=-46$.	result 1.00	0.75	0.13	asserted 1.00
s5	The rational, $\zeta_3$ and $\zeta_5$ parts of the other 22 miraculously sum to zero.	result 0.98	0.78	0.13	asserted 1.00
s6	Vertex anomalous dimensions have 40 terms, with no dramatic cancellations.	result 1.00	0.83	0.07	asserted 1.00
s7	Our methods come from work by the late Kenneth Johnson, done more than 30 years ago.	method 0.56	0.05	0.03	asserted 1.00
s8	They are entirely free of the subtractions and infrared rearrangements of later methods.	method 0.98	0.27	0.04	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.90.

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The paper

Original abstract

Dyson-Schwinger equations are used to evaluate the 4-loop anomalous dimensions of quenched QED in terms of finite, scheme-independent, 3-loop integrals. Three of the results serve as strong checks of terms from scheme-dependent 4-loop QCD calculations. The fourth, for the anomalous dimension of $\bar\psi\sigma_{\mu\nu}\psi$, was previously known only to 2-loop order. The 4-loop beta function has 24 unambiguous terms. Two of the simplest give $\beta_4=\frac13(22-160)=-46$. The rational, $\zeta_3$ and $\zeta_5$ parts of the other 22 miraculously sum to zero. Vertex anomalous dimensions have 40 terms, with no dramatic cancellations. Our methods come from work by the late Kenneth Johnson, done more than 30 years ago. They are entirely free of the subtractions and infrared rearrangements of later methods.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

An Asymptotic Expansion for the Number of 2-Connected Chord Diagrams
math.CO 2020-09 conditional novelty 8.0 of 10

The number of 2-connected chord diagrams on n chords is asymptotically e^{-2}(2n-1)!!(1 - 6/(2n-1) - 4/((2n-3)(2n-1)) - ...), derived from a new generating-function recurrence.
Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
hep-ph 1999-10 accept novelty 6.0 of 10

The three-loop MS-bar to RI conversion factors for quark mass and field are computed, showing the NNNLO term is comparable to the NNLO one at 2 GeV and that lattice matching should move to about 3 GeV.

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5 arXiv papers cite this in 9 sentences

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Builds on it 1 paper

The 5-loop extension of the work of Ref. [ref] , based on the calculations of definite 5-loop anomalous dimensions in QED from the 4-loop finite scheme-independent integrals, should demonstrate the cancellation of $ζ_5$ and $ζ_7$ terms and clarify whether $ζ_3$- contribution is appearing or not.

Is it possible to check urgently the 5-loop analytical results for the $e^+e^-$-annihilation Adler function ? · Proposed procedures of cross-checks · 0.97

Compares with it 1 paper

[equation] Note that the quenched limit $n_f = 0$ coincides with the results of Baker, Johnson, and Willey [ref] at two loops and Broadhurst at three loops [ref] .

Hopf-algebraic Renormalization of QED in the linear covariant Gauge · Higher order gauge parameters · 0.95

Cites it as support 1 paper

The performed by different methods calculations of the order $O(A^4)$-approximation to Eq.([ref]) [ref] , [ref] are supporting this feature.

Conformal invariance and the expressions for $C_F^4\alpha_s^4$ contributions to the Bjorken polarized and the Gross-Llewellyn Smith sum rules · Introduction · 0.97

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