The Supersymmetric Particle Spectrum

TL;DR

This paper develops a framework to predict the supersymmetric particle spectrum in GUT-based models with radiative electroweak symmetry breaking by evolving soft-breaking parameters via renormalization group equations and minimizing the one-loop Higgs potential using tadpole diagrams. It introduces an ambidextrous RGE integration approach that uses boundary conditions at both the electroweak and GUT scales, enabling systematic exploration of the $m_t$–$\tan\beta$ plane and radiative EWSB solutions. A key finding is that radiative breaking with a low-$\tan\beta$ fixed point yields viable spectra with large $|\mu|$ and simple gaugino/Higgs mass correlations, while one-loop corrections alleviate fine-tuning relative to tree-level expectations; the LSP is typically bino-like and can constitute dark matter in much of the parameter space. The work provides analytic one-loop minimization expressions, clarifies model-independent mass correlations, and informs experimental searches and dark-matter phenomenology in SUSY GUTs.

Abstract

We examine the spectrum of supersymmetric particles predicted by grand unified theoretical (GUT) models where the electroweak symmetry breaking is accomplished radiatively. We evolve the soft supersymmetry breaking parameters according to the renormalization group equations (RGE). The minimization of the Higgs potential is conveniently described by means of tadpole diagrams. We present complete one-loop expressions for these minimization conditions, including contributions from the matter and the gauge sectors. We concentrate on the low $\tan β$ fixed point region (that provides a natural explanation of a large top quark mass) for which we find solutions to the RGE satisfying both experimental bounds and fine-tuning criteria. We also find that the constraint from the consideration of the lightest supersymmetric particle as the dark matter of the universe is accommodated in much of parameter space where the lightest neutralino is predominantly gaugino. The supersymmetric mass spectrum displays correlations that are model-independent over much of the GUT parameter space.