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arXiv · 2007.06591

General scalar renormalisation group equations at three-loop order

Tom Steudtner
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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.

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Tom Steudtner. 2020-07-13. General scalar renormalisation group equations at three-loop order. https://doi.org/10.1007/jhep12(2020)012

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