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

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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