Viable supersymmetric models with an inverted scalar mass hierarchy at the grand unified theory scale

Supersymmetric models with an inverted mass hierarchy (IMH: multi-TeV first and second generation matter scalars, and sub-TeV third generation and Higgs scalars) have been proposed to ameliorate phenomenological problems arising from flavor changing neutral currents and $\mathrm{CP}$ violating processes, while satisfying conditions of naturalness. Models with an IMH already in place at the grand unified theory (GUT) scale have been shown to be constrained in that, for many model parameter choices, the top squark squared mass is driven to negative values. We delineate regions of parameter space where viable models with a GUT scale IMH can be generated. We find that larger values of GUT scale first and second generation scalar masses act to suppress third generation scalars, leading to acceptable solutions if GUT scale gaugino masses are large enough. We show examples of viable models and comment on their characteristic features. For example, in these models the gluino mass is bounded from below, and effectively decouples, whilst third generation scalars remain at sub-TeV levels. While possibly fulfilling criteria of naturalness, these models present challenges for detection at future $\mathrm{pp}$ and $e^{+}{e}^{-}$ collider experiments.