Weyl Consistency Conditions and ${\gamma }_5$

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-naïve 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.

arXiv comment9 pages, 3 figures. Version 2 notation updated to match Ref. [16], text expanded, calculation details clarified, conclusions unaffected

References in corpus (10)

• Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model
• Facts of life with gamma(5)
• Higgs self-coupling beta-function in the Standard Model at three loops
• Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order
• Three-loop SM beta-functions for matrix Yukawa couplings
• Four-loop strong coupling beta-function in the Standard Model
• Top-Yukawa effects on the $\beta$-function of the strong coupling in the SM at four-loop level
• Renormalization group equations and matching in a general quantum field theory with kinetic mixing
• Renormalization Group Equations in Gauge Theories with Multiple U(1) Groups
• The a-function for gauge theories

Cited by in corpus (24)

• Precise Values of Running Quark and Lepton Masses in the Standard Model
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• Gauge coupling beta functions to four-loop order in the Standard Model
• Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• General scalar renormalisation group equations at three-loop order
• General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• Fermion Traces Without Evanescence
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• The Standard Model at 200 GeV
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Three-loop QCD corrections to the electroweak boson masses
• Perturbative running of the topological angles
• Asymptotic safety in the Litim-Sannino model at four loops
• ARGES -- Advanced Renormalisation Group Equation Simplifier
• $\text{RGE++}:$ A $\text{C++}$ library to solve renormalisation group equations in quantum field theory
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$
• Gradient Flow and Holography from a Local Wilsonian Cutoff
• General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order