Non-perturbative Renormalization Group and Dynamical Problems in Particle Physics

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Many problems in the particle Physics are attribute to hierarchical structures and/or unnatural sizes of the parameters. The most frequently used approaches for this kind problem is to introduce some symmetries explaining the bulk structure and their suitable breaking parameters. However hierarchical parameters can be realized through large radiative corrections in the long range scales. In this research, I mainly study several typical problems in particle physics with hierarchical parameters from this point of view. For these studie, the renormalization group is a very useful framework and I also aimed to develop a kind of non-perturbative renormalization group equations for supersymmetric field theories.Among many problems, I considered especially the dynamical origins for the hierarchical structures of the quark and lepton mass matrices and also the universal structure of masses expected for the supersymmetric partners in various situations. Through many collaborations, we found a sort of supersymmetric models with superconformal field theories inducing large anomalous dimensions to the quark and lepton superfield to realize the above mass structures. We also pointed out that the expected mass structure for the supersynunetric partners can be naturally realized, if the grand unified theory is given with an extra-dimensional space-time. In addition, we considered a new type of scenarios for solving the supersymmetric little hierarchy problem by applying the nature of the superconformal dynamics. Studies of this direction are continued and developed further at present.