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The Role of $\gamma_5$ in Dimensional Regularization
High Energy Physics - Phenomenology · Submitted 31 Jan 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Further we show that this \gf-scheme does not modify the BRST identities at any loop orders in contrast to BM type schemes.
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The abstract, sentence by sentence
We discuss the consistency of a new \gf -scheme with renormalization. In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. As a side effect we obtain a short proof of the Adler-Bardeen theorem. Further we show that this \gf-scheme does not modify the BRST identities at any loop orders in contrast to BM type schemes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss the consistency of a new \gf -scheme with renormalization. | contribution 0.99 | 0.85 | 0.16 | unclear 0.51 |
| s1 | In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. | method 0.67 | 0.94 | 0.14 | asserted 0.98 |
| s2 | As a side effect we obtain a short proof of the Adler-Bardeen theorem. | result 0.98 | 0.94 | 0.10 | asserted 1.00 |
| s3 | Further we show that this \gf-scheme does not modify the BRST identities at any loop orders in contrast to BM type schemes. | result 0.98 | 0.94 | 0.28 | asserted 1.00 |
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The paper
Original abstract
We discuss the consistency of a new \gf -scheme with renormalization. In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. As a side effect we obtain a short proof of the Adler-Bardeen theorem. Further we show that this \gf-scheme does not modify the BRST identities at any loop orders in contrast to BM type schemes.
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References
How the literature uses it
32 arXiv papers cite this in 87 sentences
Papers citing it · 57 sentences without a confident label
Contests it 2 papers
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[ref] for amplitudes with external axial anomaly: the ABJ anomaly equation does not hold automatically in the bare form, and the Adler-Bardeen theorem [ref] is not observed, in this treatment.[As a kind reminder, the appearance of the (gauge-non-invariant) Chern-Simons current term in the renormalization of the singlet axial-current in QCD [ref] shall not be taken as a counter-example to the general theorem on renormalization, but rather viewed as manifestation of a technical regularization issue: if the dimensional regularization scheme in use violates certain gauge symmetry or 4-dimensional $5$-involved relations (e.g. the ABJ equation), counter-terms may be added to restore those relations which are non-invariant in general (see, e.g. [ref] ).] There was also an outline of how the procedure may be performed in an algorithmic manner beyond the QCD corrections in ref.
A Procedure g5anchor to Anchor $\gamma_5$ in Feynman Diagrams for the Standard Model · Introduction · contest 0.87
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To our surprise, through the calculation of the matrix element of an external singlet axial-current operator between the vacuum and a pair of gluons, i.e. the vector–vector–axial-vector (VVA) current-correlator, in QCD with an anticommuting $γ_5$ treated according to Kreimer scheme [ref] ,[apart from a different practical treatment of the Levi-Civita tensor, which we think should not affect the conclusion and will be discussed in detail later in the text] we find that the answer to the above question is, unfortunately, negative.
An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting $\gamma_5$ · Introduction · contest 0.87
Uses its method or tool 8 papers
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We are now in position to expose the technical aspects of our calculations and discuss the results in Kreimer scheme [ref] , implemented according to the description in the previous section.
An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting $\gamma_5$ · Calculation of the VVA diagrams using Kreimer-scheme variants · 0.97
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In order to establish confidence in our results, we carried out two independent calculations, one where 't Hooft-Veltman-Breitenlohner-Maison's (HVBM's) $γ_5$ scheme [ref] was employed and one where Kreimer's $γ_5$ scheme [ref] was employed.
Mixed EW-QCD two-loop amplitudes for $q\bar{q} \to \ell^+\ell^-$ and $\gamma_5$ scheme independence of multi-loop corrections · Introduction · 0.96
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We implement the Kreimer scheme [ref] for dealing with the complications that arise from the axial anomaly and the treatment of $γ_5$ in dimensional regularization.
The $e^+ e^- \rightarrow Z H$ Process in the SMEFT Beyond Leading Order · Virtual Contributions · 1.00
Compares with it 1 paper
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On the other hand, up to 3-loop order, the difference between our treatment of $5$ from the prescriptions [ref] is not very essential, and mainly concerns the technical side and practical convenience, as well as possibly the recipe for those with intermediate IR divergences[To avoid confusion, note that even for diagrams below 4-loop orders, the bare expressions determined in our prescription are in general different from those using the prescriptions [ref] , and shall not be compared naively at the bare level.] (to be discussed in the next subsection).
A Procedure g5anchor to Anchor $\gamma_5$ in Feynman Diagrams for the Standard Model · Discussions on the multiplicative renormalizability to be checked · 0.99
Cites it as background 14 papers
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[ref] , ever since the invention of DR.
An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting $\gamma_5$ · Introduction · 0.96
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Moving beyond tree-level, it is imperative to use a consistent regularization scheme, which requires a careful treatment of chirality and $^5$ [ref] .
One-loop calculations in the chirality-flow formalism · Introduction · 0.86
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Despite the fact that Kreimer's $γ_5$ scheme was introduced a long time ago [ref] , it has not been universally accepted and embraced as a superior alternative to HVBM's $γ_5$ scheme; researchers continue to express doubts about the applicability of Kreimer's $γ_5$ scheme beyond one loop (see e.g. [ref] for a current review of the status of the $γ_5$ problem).
Mixed EW-QCD two-loop amplitudes for $q\bar{q} \to \ell^+\ell^-$ and $\gamma_5$ scheme independence of multi-loop corrections · Kreimer's prescription for $γ_5$ in dimensional regularization · 0.95
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