Light thresholds in Grand Unified Theories

Abstract

In a generic Grand Unified Theory with a relatively small dispersion of the spectrum around the $Z$-boson and the unification masses, a connection is established, exact at one loop level, between $M_Z$, $G_{\rm F}$, $\alpha(M_Z)$ and the strong coupling constant $\alpha_3(M_Z)$. At this level of precision, this avoids the logical and phenomenological inconsistency of predicting $\alpha_3(M_Z)$ by means of the electroweak couplings as extracted from the data in the Standard Model rather than in the complete theory. Attention is paid to the independence of the physical results from regularization and/or renormalization schemes. As a particularly relevant example, the analysis is specialized to the case of the Minimal Supersymmetric Standard Model, with emphasis on light charginos and neutralinos.