Generalized focus point and mass spectra comparison of highly natural SUGRA GUT models

Supergravity grand unified models (SUGRA GUTs) are highly motivated and allow for a high degree of electroweak naturalness when the superpotential parameter mu~ 100-300 GeV (preferring values closer to 100 GeV). We first illustrate that models with radiatively-driven naturalness enjoy a generalized focus-point behavior wherein all soft terms are correlated instead of just scalar masses. Next, we generate spectra from four SUGRA GUT archetypes: 1. SO(10) models where the Higgs doublets live in different 10-dimensional irreducible representations (irreps), 2. models based on SO(10) where the Higgs multiplets live in a single 10-dimensional irrep but with D-term scalar mass splitting, 3. models based on SU(5) and 4. a more general SUGRA model with 12 independent parameters. Electroweak naturalness implies for all models a spectrum of light higgsinos with m(higgsinos)< 300 GeV and gluinos with m(gluino)< 2-4 TeV. However, masses and mixing in the third generation sfermion sector differ distinctly between the models. These latter differences would be most easily tested at a linear e^+e^- collider with \sqrt{s}~ multi-TeV-scale but measurements at a 50-100 TeV hadron collider are also possible.