Beyond the CMSSM without an Accelerator: Proton Decay and Direct Dark
  Matter Detection
  We consider two potential non-accelerator signatures of generalizations of
the well-studied constrained minimal supersymmetric standard model (CMSSM). In
one generalization, the universality constraints on soft supersymmetry-breaking
parameters are applied at some input scale $M_{in}$ below the grand unification
(GUT) scale $M_{GUT}$, a scenario referred to as `sub-GUT'. The other
generalization we consider is to retain GUT-scale universality for the squark
and slepton masses, but to relax universality for the soft
supersymmetry-breaking contributions to the masses of the Higgs doublets. As
with other CMSSM-like models, the measured Higgs mass requires supersymmetric
particle masses near or beyond the TeV scale. Because of these rather heavy
sparticle masses, the embedding of these CMSSM-like models in a minimal SU(5)
model of grand unification can yield a proton lifetime consistent with current
experimental limits, and may be accessible in existing and future proton decay
experiments. Another possible signature of these CMSSM-like models is direct
detection of supersymmetric dark matter. The direct dark matter scattering rate
is typically below the reach of the LUX-ZEPLIN (LZ) experiment if $M_{in}$ is
close to $M_{GUT}$, but may lie within its reach if $M_{in} \lesssim 10^{11}$
GeV. Likewise, generalizing the CMSSM to allow non-universal
supersymmetry-breaking contributions to the Higgs offers extensive
possibilities for models within reach of the LZ experiment that have long
proton lifetimes.
