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Naturalness, Dark Matter, and Unification with a 125 GeV Higgs


The naturalness of a Higgs boson with a mass near 125 GeV is explored in a variety of weak-scale supersymmetric models. If supersymmetry is realized in nature, then a Higgs mass of this size strongly points towards a non-minimal implementation. The Minimal Supersymmetric Standard Model now requires large A-terms to avoid multi-TeV stops. The fine-tuning is at least 1% for low messenger scales, and an order of magnitude worse for high messenger scales. Naturalness is significantly improved in theories with a singlet superfield S coupled to the Higgs superfields via λ S Hu Hd$. If λ is perturbative up to unified scales, a fine-tuning of about 10% is possible with a low mediation scale. Larger values of λ, implying new strong interactions below unified scales, allow for a highly natural 125 GeV Higgs boson over a wide range of parameters. Even for λ as large as 2, where a heavier Higgs might be expected, a light Higgs boson naturally results from singlet-doublet scalar mixing. Although the Higgs is light, naturalness allows for stops as heavy as 1.5 TeV and a gluino as heavy as 3 TeV.

Using a simplified model framework, we assess observational limits and discovery prospects for neutralino dark matter, taken here to be a general admixture of bino, wino, and Higgsino. Experimental constraints can be weakened or even nullified in regions of parameter space near 1) purity limits, where the dark matter is mostly bino, wino, or Higgsino, or 2) blind spots, where the relevant couplings of dark matter to the Z or Higgs bosons vanish identically. We analytically identify all blind spots relevant to spin-independent and spin-dependent scattering and show that they arise for diverse choices of relative signs among M1, M2, and μ. At present, XENON100 and IceCube still permit large swaths of viable parameter space, including the well-tempered neutralino. On the other hand, upcoming experiments should have sufficient reach to discover dark matter in much of the remaining parameter space. Our results are broadly applicable, and account for a variety of thermal and non-thermal cosmological histories, including scenarios in which neutralinos are just a component of the observed dark matter today. Because this analysis is indifferent to the fine-tuning of electroweak symmetry breaking, our findings also hold for many models of neutralino dark matter in the MSSM, NMSSM, and Split Supersymmetry. We have identified parameter regions at low tan β which sit in a double blind spot for both spin-independent and spin-dependent scattering. Interestingly, these low tan β regions are independently favored in the NMSSM and models of Split Supersymmetry which accommodate a Higgs mass near 125 GeV.

Finally, we consider precision b-τ Yukawa unification as an alternate motivation for supersymmetry near the weak scale. We show that for an LSP that is a bino-Higgsino admixture, this requirement leads to an upper-bound on the stop and sbottom masses in the several TeV regime because the threshold correction to the bottom mass at the superpartner scale is required to have a particular size. For tan β ∼ 50, which is needed for t-b-τ unification, the stops must be lighter than 2.8 TeV when At has the opposite sign of the gluino mass, as is favored by renormalization group scaling. For lower values of tan β, the top and bottom squarks must be even lighter. Yukawa unification plus dark matter implies that superpartners are likely in reach of the LHC, after the upgrade to 14 (or 13) TeV, independent of any considerations of naturalness. We present a model-independent, bottom-up analysis of the SUSY parameter space that is simultaneously consistent with Yukawa unification and the Higgs mass. We study the flavor and dark matter phenomenology that accompanies this Yukawa unification. A large portion of the parameter space predicts that the branching fraction for Bs → μ+ μ- will be observed to be significantly lower than the SM value.

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