General scalar renormalisation group equations at three-loop order

Abstract

For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and derive $\beta$ functions for scalar masses and cubic interactions from it. As an example, the results are applied to compute all renormalisation group equations in $U(n)\times U(n)$ scalar theories.

match published version, corrected eq.(4.5)

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Cited by in corpus (12)

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• Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Peccei-Quinn Symmetry Breaking via Asymptotically Safe Dynamical Scalegenesis: A Walking Axicolor and Axion
• RG-stable parameter relations of a scalar field theory in absence of a symmetry
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• ARGES -- Advanced Renormalisation Group Equation Simplifier
• Conformal Windows beyond Asymptotic Freedom
• Gradient Flow and Holography from a Local Wilsonian Cutoff
• General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order