Electroweak symmetry breaking is the key ingredient of the standard model responsible for the generation of all elementary particle masses. The discovery of the Higgs boson is a major milestone towards understanding the mechanism of electroweak symmetry breaking but several important issues remain unexplained. Among them the key mystery is how to stabilize the electroweak symmetry scale, called the naturalness problem. To solve this problem, some new physics should be introduced to screen quantum corrections from higher energy scale. There are two classes of new physics theories: one is super symmetry model in which Higgs quadratic divergence is cancelled through the extended space-time symmetry between scalars and fermions. The other one is composite Higgs model in which the sensitivity to higher energy scale is reduced by the composite nature of Higgs. In super symmetry model, every field in standard model should have a super symmetric partner, which makes this theory very complicated. However, the composite Higgs models can address the naturalness problem in a very simple way. In this article we first review the Higgs mechanism in standard model and explain Higgs naturalness problem. Then we generally review the super symmetry model and its phenomenology. It is found that the tuning of this kind of model is worse than 1% when confronts experimental measurements. In the remaining parts we focus on discussing the composite Higgs model. We first review the structure of composite Higgs models and then discuss how to reduce Higgs mass through some symmetry collectively breaking or extra dimension mechanism. It is found that, in this kind of models, to produce a light Higgs the composite quarks canceling Higgs quadratic divergences should be relatively light, around 1 TeV. But the constraints from Large Hadron Collider (LHC) indicate that these fermions should be much heavier than 1 TeV, which results the difficulty in achieving a light Higgs. Moreover, to evade precise electroweak tests, the electroweak scale should be separated with Higgs confinement scale, called the Little Hierarchy, requiring more tuning in this model. In order to produce light Higgs while keeping composite quarks heavy, we plan to find a general principle to realize neutral naturalness mechanism in which Higgs quadratic divergences are cancelled by hidden sector. And then find the UV completion for this mechanism and fully study its phenomenology. In order to naturally solve Little Hierarchy, we plan to construct a mechanism to produce Higgs tree level or loop level self-quartic coupling, so that the big separation between electroweak and confinement scale can be achieved by adjusting properly this coupling without introducing any tuning. After solving above two problems, we combine these two mechanisms to construct the super-natural composite Higgs model which can successfully achieve electroweak symmetry breaking without any tuning.
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