Mass hierarchies and scalar field self-couplings

Abstract

One (internal gauge boson) loop corrections to the scalar field self-couplings of a spontaneously broken Abelian gauge theory are shown to be independent of one loop shifts in mass (and vacuum expectation value) from tree approximation values, suggesting that stability of arbitrarily large mass ratios under perturbation theory may be possible under an appropriately chosen set of renormalization conditions. However, imposition of a large mass ratio is shown to lead to overly large first order corrections to scalar field self-couplings, independent of the choice of renormalization conditions.