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arXiv · 2408.05267

General Quartic $β$-Function at Three Loops

Tom Steudtner·Anders Eller Thomsen
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Abstract

We determine the three-loop $\overline{\text{MS}}$ quartic $ β$-function for the most general renormalisable four-dimensional theories. A general parametrization of the $ β$-function is compared to known $ β$-functions for specific theories to fix all coefficients. Three-loop $ β$-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.

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Tom Steudtner, Anders Eller Thomsen. 2024-08-09. General Quartic $β$-Function at Three Loops. https://arxiv.org/abs/2408.05267

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