Environmentally selected WIMP dark matter with high-scale supersymmetry breaking

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We explore the possibility that both the weak scale and the thermal relic dark matter abundance are environmentally selected in a multiverse. An underlying supersymmetric theory containing the states of the minimal supersymmetric standard model (MSSM) and singlets, with supersymmetry and $R$ symmetry broken at unified scales, has just two realistic low-energy effective theories. One theory ($\mathrm{SM}+\stackrel{\texttildelow{}}{w}$) is the standard model augmented only by the wino, having a mass near 3 TeV, and has a Higgs boson mass in the range of (127--142) GeV. The other theory ($\mathrm{SM}+\stackrel{\texttildelow{}}{h}/\stackrel{\texttildelow{}}{s}$) has Higgsinos and a singlino added to the standard model. The Higgs boson mass depends on the single new Yukawa coupling of the theory, $y$, and is near 141 GeV for small $y$ but grows to be as large as 210 GeV as this new coupling approaches strong coupling at high energies. Much of the parameter space of this theory will be probed by direct detection searches for dark matter that push 2 orders of magnitude below the present bounds; furthermore, the dark matter mass and cross section on nucleons are correlated with the Higgs boson mass. The indirect detection signal of monochromatic photons from the Galactic center is computed, and the range of parameters that may be accessible to LHC searches for trilepton events is explored. Taking a broader view, allowing the possibility of $R$ symmetry protection to the TeV scale or axion dark matter, we find four more theories: ($\mathrm{SM}+\mathrm{\text{axion}}$), two versions of split supersymmetry, and the E-MSSM, where a little supersymmetric hierarchy is predicted. The special Higgs mass value of $(141\ifmmode\pm\else\textpm\fi{}2)\text{ }\text{ }\mathrm{GeV}$ appears in symmetry limits of three of the six theories, ($\mathrm{SM}+\mathrm{\text{axion}}$), ($\mathrm{SM}+\stackrel{\texttildelow{}}{w}$), and ($\mathrm{SM}+\stackrel{\texttildelow{}}{h}/\stackrel{\texttildelow{}}{s}$), motivating a comparison of other signals of these three theories.