Minima of classically scale-invariant potentials

A bstract We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in compact matrix form, used derive general expressions for stationary point equation and mass multi-field RG-improved potential. Our method improves on (but not limited to) Gildener-Weinberg approximation identifies set conditions that signal presence radiative minimum. When are satisfied at different scales, or subspaces field space, potential has more than one illustrate through simple examples study detail Standard-Model-like scenario where admits two minima. Whereas we mostly concentrate biquadratic potentials, our results carry over case by using tensor algebra.