Non-perturbative Renormalization Group and Dynamical Problems in Particle Physics

粒子物理学中的许多问题都是由于参数的层次结构和/或不自然的大小造成的。对于这类问题，最常用的方法是引入一些对称性来解释体结构及其合适的破缺参数。然而，分级参数可以实现通过大的辐射校正在长距离尺度。本研究主要从这个角度出发，研究了粒子物理中几个典型的具有层次参数的问题。在这些研究中，重整化群是一个非常有用的框架，我的目标也是发展一种非微扰重整化群方程的超对称场论。在许多问题中，我特别考虑了夸克和轻子质量矩阵的层次结构的动力学起源，以及在各种情况下超对称伙伴的普遍质量结构。通过多次合作，我们发现了一类超对称模型，超共形场论诱导夸克和轻子超场的大反常维度，以实现上述质量结构。我们还指出，如果大统一理论是在一个额外维的时空中给出的，那么超同步伙伴的预期质量结构就可以自然地实现。此外，我们考虑了一种新的类型的方案，解决超对称小层次问题，通过应用超共形动力学的性质。目前，这一方向的研究仍在继续并得到进一步发展。

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.