Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory

Abstract

We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for beta-functions by direct calculation in several simplified models. We apply our results to the Standard Model and its extension with an arbitrary number of Higgs doublets and provide expressions for all four-loop gauge couplings beta-functions with matrix Yukawa interactions.

arXiv comment6 pages, 1 table; typos corrected, matches version published in PRL

References in corpus (32)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• SARAH 4: A tool for (not only SUSY) model builders
• Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision
• Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• Facts of life with gamma(5)
• Gauge Coupling Beta Functions in the Standard Model to Three Loops
• Limit Cycles and Conformal Invariance
• Yukawa coupling beta-functions in the Standard Model at three loops
• Higgs self-coupling beta-function in the Standard Model at three loops
• β-function for the Higgs self-interaction in the Standard Model at three-loop level
• Constraints on RG Flow for Four Dimensional Quantum Field Theories
• A Feynman Diagram Analyser DIANA
• Standard Model Vacuum Stability and Weyl Consistency Conditions
• Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops
• Revisiting RGEs for general gauge theories
• Three-loop SM beta-functions for matrix Yukawa couplings
• Four-loop strong coupling beta-function in the Standard Model
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Top-Yukawa effects on the $\beta$-function of the strong coupling in the SM at four-loop level
• Three loop gauge beta-function for the most general single gauge-coupling theory
• Leading QCD-induced four-loop contributions to the $\beta$-function of the Higgs self-coupling in the SM and vacuum stability
• Six-loop beta functions in general scalar theory
• Weyl Consistency Conditions and ${\gamma }_5$
• Gauge and Yukawa coupling beta functions of two-Higgs-doublet models to three-loop order
• On three-loop RGE for the Higgs sector of 2HDM
• Gauge coupling beta functions to four-loop order in the Standard Model
• General scalar renormalisation group equations at three-loop order
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme

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• Asymptotic safety in the Litim-Sannino model at four loops
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