Revisiting RGEs for general gauge theories

Understand

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy.

• We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings.
• There are two sources for these discrepancies.
• Firstly, the known expressions for the scalar couplings assume a diagonal wave-function renormalisation which is not appropriate for models with mixing in the scalar sector.