Exploring Supersymmetry Breaking And Gauge Mediation

Any attempt to construct a supersymmetric model for explaining the experimental results must answer two important questions:one is how supersymmetry is broken, the other is how the supersymmetry breaking effect is transmitted into the minimal super-symmetric standard model. Dynamical supersymmetry breaking provides an elegant framework for breaking supersymmetry in terms of the dynamics of SQCD. Together with the gauge mediated supersymmetry breaking paradigm, we could analyze the su-persymmetric model in a unified and calculable framework. In this thesis, we provide some interesting examples in order to satisfy the recent experimental constraint from LHC. This thesis is roughly divided into three parts.In the first part, we present some basic introduction to supersymmetry which in-cludes the basic language of supersymmetry such as superspace and superfield. It also contains some relevant tool for exploring the model building of dynamical supersym-metry breaking.The generic existence of meta-stable supersymmetry is reviewed, es-pecially on the elegant ISS model. To transmit the supersymmetry breaking effect to minimal supersymmetric standard model, the calculable gauge mediated supersymme-try breaking is included. In addition, we also introduce the great method on computing the soft terms, i.e.,analytical continuation in superspace.In the second part, two different scenarios of supersymmetry breaking are con-sidered, one is the conventional dynamical supersymmetry breaking in flat spacetime, the other is greatly different from the former for constructing supersymmetry break-ing vacua in curved spacetime. In the first part, we investigate local supersymmetry-breaking vacua in s-confining theories with gauge group Sp(2N).By adapting the general recipe developed by Shadmi and Shirman, we construct a realistic model based on dynamics of SQCD coupled with singlets which allows a spontaneously broken su-pcrsymmclry. Since the chiral superfields in model have R-charges R=0and R=2only, the tedious computations of Coleman-Weinberg potential can be greatly alleviated from the lesson of David Shih. We observe that the pseudomoduli fields are stabilized at the origin of moduli space at one-loop order with calculability being preserved. In the second part, We study the questions of how supersymmetry is spontaneously bro-ken in Anti de-Sitter spacetime. We verify that the would-be R-symmetry in AdS4plays a central role for the existence of meta-stable supersymmetry breaking.To illustrate, some well-known models such as Poloyni models and O’Raifeartaigh models are in- vestigated in detail.Our calculations are reliable in flat spacetime limit and confirm us that meta-stable vacua are generic even though quantum corrections are taken into account.In the third part, We propose a small extension of the minimal gauge mediation through the combination of extended gauge mediation and conformal sequestering. We show that the focus point supersymmetry can be realized naturally, and the fine tuning is significantly reduced compared to the minimal gauge mediation and extended gauge mediation without focus point. The Higgs boson mass is around125GeV, the gauginos remain light, and the gluino is likely to be detected at the next run of the LHC. However, the multi-TeV squarks is out of the reach of the LHC. The numerical calculation for fine-tuning shows that this model remains natural.