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General scalar renormalisation group equations at three-loop order
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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.
Forward citations
Cited by 2 Pith papers
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Constraints on the $O(n)$ model from a negative number of flavors
The paper extends O(n) spectrum constraints to negative n via the O(n)-Sp(n) duality and derives closed-form two-loop anomalous dimensions for all phi^k operators from two known cases.
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Gauge coupling beta functions and gauge field anomalous dimensions at four loops in the Standard Model
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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