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Register a new userThe Standard Model hierarchy, fine-tuning, and negativity of the Higgs mass squared
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Marko B. Popovic
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I discuss standard motivation for the new physics at the 1 TeV scale. Although the arguments for new exotic phenomena seem to be very supportive I argue that the Standard Model still might offer a good description far beyond this energy scale. I analyze three Standard Model cases with specific boundary conditions at the lowest energies. These conditions essentially eliminate the hierarchy and fine-tuning problems. In the first model where quartic scalar interactions are required to decouple, the Higgs is predicted to weigh around 39 GeV. In the second model with composite Higgs, the top Yukawa coupling is required to be one (by hand, i.e. reflecting the assumed ground state) and the Higgs mass of about 138 GeV is favored. The third model has condensation mechanism embedded in two dimensions. The top Yukawa coupling being one comes about as prediction rather then requirement, i.e. $g_t={3g_2 over 2}sqrt{1+{1over3}(g_1over g_2)^2} (1-textit{few}%)approx 1.025 (1-textit{few}%)$ where $g_2$, $g_1$ are electroweak $SU(2)times U(1)$ gauge couplings, and the SM Higgs is expected to weigh in between 114.8 and 118.6 GeV.
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The recent discovery of a 125 GeV Higgs, as well as the lack of any positive findings in searches for supersymmetry, has renewed interest in both the supersymmetric Higgs sector and fine-tuning. Here, we continue our study of the phenomenological MSSM (pMSSM), discussing the light Higgs and fine-tuning within the context of two sets of previously generated pMSSM models. We find an abundance of models with experimentally-favored Higgs masses and couplings. We investigate the decay modes of the light Higgs in these models, finding strong correlations between many final states. We then examine the degree of fine-tuning, considering contributions from each of the pMSSM parameters at up to next-to-leading-log order. In particular, we examine the fine-tuning implications for our model sets that arise from the discovery of a 125 GeV Higgs. Finally, we investigate a small subset of models with low fine-tuning and a light Higgs near 125 GeV, describing the common features of such models. We generically find a light stop and bottom with complex decay patterns into a set of light electroweak gauginos, which will make their discovery more challenging and may require novel search techniques.
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