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

在现实的超对称理论中，最重要的问题之一是理解超对称是如何被打破的，然后将其与低能物理联系起来。尽管最近超对称规范理论和超弦的理论有了很大的发展，但这个问题还没有得到令人满意的解决。然而，人们普遍认为，无论超对称破缺的起源是什么，在低能有效理论中都表现为软超对称破缺，因为软性是不破坏标准模型自然度问题的超对称解的理想性质。本研究的主要目的是找到与超对称破缺的具体性质无关的软超对称破缺项之间的关系，并在低能下做出明确的预测。本研究的主要结果如下：1)我们证明了在有效的N=1超重力中存在对称性，Alon…通过对汤川耦合的简单假设，得到了单边带参数之间的关系或求和规则。这些对称性是T-对偶，通常存在于四维超弦中。2)我们发现这些求和规则在微扰理论中是重整化群(RG)不变的，因此一旦它们在弦尺度上满足，它们也在弦尺度下满足。同时满足和规则的有限软超对称破缺项也属于重整化群不变关系的范畴。3)研究了和规则的低能结果，推导了最小超对称标准模型的超伙伴谱中的和规则。谱中的求和规则可以通过未来的实验直接检验，例如在LHC。从这些结果我们预计超对称大统一理论和超弦模型之间将会有密切的联系，我们希望沿着这条线的进一步研究可以对超对称破缺的理论本质产生更深的理解。较少

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