Effective couplings and Perturbative Unification

Abstract

In this paper we study the influence of the threshold effects due to massive degrees of freedom in the evolution with scale of gauge coupling constants. We first describe in detail the (standard) mass dependent renormalization prescription we use. This guides us to introduce and work with effective couplings, which are finite, process independent, and include complete threshold effects. We compute the evolution of the effective couplings in both, the Standard Model and its Minimal Supersymmetric extension, from \mz\ to the high energy region. We find that the effects from thresholds due to the standard massive gauge bosons are non--negligible, contrary to what is generally assumed when using other, less--accurate, descriptions of the thresholds, as for example in the step--function approximation. Moreover, we find that thresholds are relevant when studying perturbative SUSY unification, changing the conclusions reached when using the step--function approach. We find that threshold effects bring conflict between the known experimental data at $m_Z$, the naturalness upper bound on the masses of SUSY partners and the $perturbative$ unification of couplings.