General Gauge-Yukawa-Quartic $β$-Functions at 4-3-2--Loop Order

We determine the full set of coefficients for the completely general 4-loop gauge and 3-loop Yukawa $β$-functions for the most general renormalizable four-dimensional theories. Using a complete parametrization of the $β$-functions, we compare the general form to the specific $β$-functions of known theories to constrain the unknown coefficients. The Weyl consistency conditions provide additional constraints, completing the determination.

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