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

Abstract

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

Comments: 27 pages, 519 tensor structures and coefficients