Theoretical and phenomenological study of the sum rules of the soft supersymmetry breaking terms

现实超对称理论中最重要的问题之一是理解超对称是如何被破缺的，然后将其与低能物理联系起来。尽管近年来已有超对称规范理论和超弦理论的发展，但这一问题仍未得到满意的解决。然而，人们普遍认为，无论其起源如何，超对称破缺在低能有效理论中都表现为软超对称破缺（SSB）项，因为柔软性是不破坏标准模型自然性问题的超对称解的理想性质。本研究的主要目的是寻找与超对称破缺细节无关的SSB项之间的关系，并在低能量下做出明确的预测。本研究的主要结果如下：1)我们证明了有效的N = 1超引力中存在对称性，并且在简单的汤川耦合假设下，得到了SSB参数的关系或求和规则。这些对称性是T对偶性，通常存在于四维超弦中。2)我们发现这些和规则在微扰理论中是重整化群（RG）不变量，因此它们在弦尺度上被满足，在弦尺度下也被满足。有限软超对称破缺项也属于重整化群不变关系的范畴，它们也满足和规则。3)研究了和规则的低能量结果，并推导了最小超对称标准模型超伴谱中的和规则。谱中的和规则可以在未来的实验中直接测试，例如在大型强子对撞机上。根据这些结果，我们期望在超对称大统一理论和超弦模型之间有一个密切的联系，我们希望沿着这条线的进一步研究可能会对超对称破缺的理论本质有更深的理解。少

One of the most important issues in realistic supersymmetric theories is to understand how supersymmetry is broken and then to relate it with low energy physics. Though the recent exiting theoretical developments in supersymmetric gauge theories as well as superstrings, this problem has not been solved in a satisfactory fashion yet. It is however widely accepted that the supersymmetry breaking, whatever its origin is, appears as soft supersymmetry-breaking (SSB) terms in low energy effective theories, because the softness is a desirable property for not spoiling the supersymmetric solution of the naturalness problem of the standard model.The main purpose of the present research project is to find relations among the SSB terms that are independent of the detailed nature of supersymmetry breaking and to make definite predictions at low energies, The main results of the present study are the following:1) We showed that there exist symmetries in the effective N = 1 supergravity, which alon … More e with a simple assumption on Yukawa couplings lead to the relations or sum rules of the SSB parameters. These symmetries are T- dualities, which are usually present in four-dimensional superstrings.2) We found that these sum rules are renormalization group (RG) invariant in perturbation theory, so that once they are satisfied at the string scale, they are also satisfied below the string scale. Finite soft supersymmetry breaking terms, which also satisfy the sum rules, also fall into the class of the renormalization group invariant relations.3) We investigated the low energy consequences of the sum rules and derived the sum rules in the superpartner spectrum of the minimal supersymmetric standard model. The sum rules in the spectrum can be directly tested by future experiments, e.g., at LHC.From these result we expect that there will be a close connection between supersymmetric grand unified theories and superstring models, and we hope that further investigations along this line might yield deeper understandings of the theoretical nature of supersymmetry breaking. Less