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Weyl Consistency Conditions and $\gamma_{5}$

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arxiv 1901.02749 v2 pith:CH3RG22H submitted 2019-01-09 hep-th hep-ph

C. Poole , A. E. Thomsen This is my paper · ORCID
classification hep-thhep-ph
keywords gammatermambiguitiesbetacoefficientconditionsconsistencyfunctions
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model. Using Weyl Consistency Conditions, we present a scheme-independent relation between the coefficient of this term and a corresponding term in the three-loop Yukawa $\beta$-functions, where a semi-na\"ive treatment of $\gamma_{5}$ is sufficient, thereby fixing this ambiguity. We briefly outline an argument by which the same method fixes similar ambiguities at higher orders.

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Cited by 4 Pith papers

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  3. Four-Loop Renormalisation of Chiral Gauge Theories with Non-Anticommuting $\gamma_5$ in the BMHV Scheme

    hep-ph 2025-06 conditional novelty 7.0 of 10

    First 4-loop BMHV renormalization of an Abelian chiral gauge theory, with explicit finite symmetry-restoring counterterms and an application to the SM fermionic sector.

  4. Gauge coupling beta functions and gauge field anomalous dimensions at four loops in the Standard Model

    hep-ph 2026-07 conditional novelty 6.0 of 10

    Four-loop Standard Model gauge beta functions are confirmed by a direct Feynman-diagram calculation, and four-loop gauge-field anomalous dimensions are computed for the first time.

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