Quadratic Divergences in Kaluza-Klein Theories

Abstract

We investigate the so-called ``Kaluza-Klein regularisation'' procedure in supersymmetric extensions of the standard model with additional compact dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This procedure uses a specific mathematical manipulation to obtain a finite result for the scalar potential. By performing the full calculation, we show that the finiteness of this result is not only a consequence of the underlying supersymmetry, but also the result of an implicit fine-tuning of the coefficients of the terms that control the ultraviolet behaviour. The finiteness of the Higgs mass at one-loop level seems therefore to be an artefact of the regularisation scheme, and quadratic divergences are expected to reappear in higher orders of perturbation theory.