Towards general scalar-Yukawa renormalisation group equations at three-loop order

Abstract

For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature results, general expressions are obtained for field anomalous dimensions, Yukawa interactions, as well as fermion masses. The renormalisation group evolution of scalar quartic, cubic and mass terms is determined up to a few unknown coefficients. The combined results are applied to compute the renormalisation group evolution of the gaugeless Litim-Sannino model.

arXiv commentv2: correct error in quartic RGEs, add example, match version to be published; v3: fix typos and computational errors

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• Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Emergent Supersymmetry at Large $N$
• B-Anomalies from flavorful U(1)' extensions, safely
• Conformal Windows beyond Asymptotic Freedom
• General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order