Nonperturbative ’running’ Of EFT Couplings

With the discovery of Higgs bosons last year, the Standard Model of particle physics established. However, it is still very difficult to calculate hadron physics problems directly. Especially in nuclear physics, scientists have to use different kinds of empirical models that lack the basis of field theory to meet the needs of nuclear physics research so far. This is an irony for high-energy theory research and full with challenges. In the last four decades, inspired by the Wilson’s renormalization, the concepts and methods of effective field theory rose in the field of high energy physics and become the major research tools, which is more convenient and simpler than use the standard model directly. Effective field theory is a "simplified" quantum field theory built up within certain range of energy guided by the basic theory of symmetry using effective degrees of freedom. One of the most famous and successful cases is the chiral perturbation theory based on low-energy QCD chiral symmetry. However, the chiral perturbation theory is not suitable to use for low energy nucleon processes that is in nonperturbative regime. There is no complete unanimity concerning the correct treatment of this issue, controversies are constantly created. It is necessary for us to study the new content and features of renormalization in nonperturbative framework. In this thesis, we mainly focus on the functional relationship between the coupling constants and the renormalization parameters in low-energy nuclear effective field theory under nonperturbative approximation, which is also called the nonperturbative "running" behaviors. In low-energy the nuclear interaction is short-range and well represented by contact potential function. We can easily get the nucleon scattering transition T matrix in a closed form using a factorization method. Exploring the tight nonperturbative constraints imposed by the closed form T matrix, we can get the function relationship of nonperturbative coupling constant and renormalization parameters, and study the running behavior. We calculate the complex constraints introduced by nonperturbation of renormalization by the means of research on the T matrix of1s0reaction channel and3S1-3D1coupled reaction channel which is the most important in low-energy nuclear scattering. We explore the new features of the coupling constant running behavior under nonperturbative approximation which is different with the traditional perturbation, especially some parameters come from renormalization process become a physical parameters due to the nonperturbation constraints. These knowledge and achievements will explore new ideas for studying nucleon effective field theory, and could applied to other nonrelativistic short range interaction system.