Dark Matter and Supersymmetry in the LHC Era
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We report investigations of physical possibilities beyond the Standard Model, performed in the years between Runs I and II of the Large Hadron Collider (LHC). First, we explore the feasibility of using a hadron collider to unmask hidden sectors by means of a novel signal, the ``monocline". Dilepton production provides the cleanest channel to anticipate a monocline. A compelling sector to seek is dark matter with scalar messengers coupling it to standard fermions. We present current bounds from dilepton spectrum measurements at the LHC and make predictions for sensitivities at Run II of the LHC as well as at a future 100 TeV collider. Second, we corner the space of parameters of supersymmetric frameworks with an appreciable Yukawa coupling between the Higgs fields and a gauge singlet, the so-called Fat Higgs and $\lambda$-SUSY models, in the context of the discovery of the 125 GeV Higgs particle. These models are motivated by their alleviation of the electroweak fine-tuning that supersymmetry breaking entails, via raising the tree-level quartic coupling Higgs boson. Heavy Higgs scalars that couple strongly to the standard Higgs boson induce large radiative corrections to the Higgs quartic coupling, which is crucial to phenomenology; in particular, a very large ratio of the Higgs VEVs ($\tan \beta$), that was previously presumed unfavorable in these models, becomes viable and can be probed by future experiments. In such regions, the most stringent limits come from dark matter constraints on the lightest neutralino. Finally, we place limits on colored scalar production at the LHC in supersymmetric models where gauginos acquire both Dirac and Majorana masses, that we call ``mixed gauginos". While it was known that purely Dirac gluinos were less constrained by LHC searches than their purely Majorana counterparts, we find that the constraints further weaken or strengthen depending on which of the ``mixed" colored fermions acquires a Majorana mass. Also explored are the effects on squark production of turning on Majorana masses for electroweak gauginos. This dissertation consists of previously published and unpublished co-authored material.