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 \( \overline{\mathrm{MS}} \) 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 from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.
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Steudtner, T. General scalar renormalisation group equations at three-loop order. J. High Energ. Phys. 2020, 12 (2020). https://doi.org/10.1007/JHEP12(2020)012
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DOI: https://doi.org/10.1007/JHEP12(2020)012