Non-perturbative Renormalization Group and Dynamical Problems in Particle Physics

粒子物理学中的许多问题都归因于分层结构和/或参数的不自然大小。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坏参数。然而，分层参数可以通过大的辐射修正来实现。在本研究中，我主要从这个角度研究了粒子物理中具有层次参数的几个典型问题。对于这些研究，重整化群是一个非常有用的框架，我也旨在建立一种超对称场论的非摄动重整化群方程。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，我们发现了一种具有超共形场理论的超对称模型，可以在夸克和轻子超场中引入大的异常维数来实现上述质量结构。我们还指出，如果大统一理论具有超维时空，则超同步伙伴的预期质量结构可以自然实现。此外，利用超共形动力学的性质，考虑了一种求解超对称小层次问题的新情形。目前，这方面的研究仍在继续并进一步发展。

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.