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

Abstract

Supergravity grand unified models (SUGRA GUTs) are highly motivated and allow for a high degree of electroweak naturalness when the superpotential parameter $\ensuremath{\mu}\ensuremath{\sim}100--300\text{ }\text{ }\mathrm{GeV}$ (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 ten-dimensional irreducible representations (irreps), 2. models based on $SO(10)$ where the Higgs multiplets live in a single ten-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 ${m}_{{\stackrel{\texttildelow{}}{W}}_{1},{\stackrel{\texttildelow{}}{Z}}_{1,2}}\ensuremath{\lesssim}300\text{ }\text{ }\mathrm{GeV}$ and gluinos with ${m}_{\stackrel{\texttildelow{}}{g}}\ensuremath{\lesssim}2--4\text{ }\text{ }\mathrm{TeV}$. 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 ${e}^{+}{e}^{\ensuremath{-}}$ collider with $\sqrt{s}\ensuremath{\sim}$ multi-TeV scale but measurements at a 50--100 TeV hadron collider are also possible.