An Effective Field Theory Study Of Low-energy Nucleon-nucleon Scattering

In1990, Weinberg proposed that through systematic calculation of nucleon potentials using chiral perturbation theory, a non-relativistic effective field theory framework (via Lippmann-Schwinger equations, LSE) could be set up for investigation of nuclear forces and nucleon systems. The ensuing two decades people witnessed the remarkable achievements of effective field theory methods in the area of nuclear forces and nuclear physics. However, the renormalization of LSE equations proved very difficult due to the presence of nonperturbative divergences, esp. the treatment of divergences in nonperturbative regimes is complicated and incompatible with the effective field theory’s power counting rules. There have been many debates about this issue in the international community, many different attempts of solution have been made, with no complete consensus being reached yet. Therefore, further investigation along this line is worthwhile.In this thesis, we will explore nonperturbative renormalization and related issues through studying the rigorous solutions of LSE with contact nucleon-nucleon potentials, in order to provide novel perspectives and understanding of the issue. Our tricks are based on a general parametrization of divergences and factorization of the contact potentials that facilitate closed-form rigorous solutions of LSE, which in turn allow for lucid analysis of the novel aspects of renormalization in nonperturbative regimes. Then, through fitting to the lower ends of nucleon-nucleon scattering phase shifts in various channels, we study how a renormalization prescription affects physical quantities like phase shifts and calculate the contact couplings and the energy scales hidden there, so that one could better describe the physical behaviors of nucleons within the realm of pionless effective theory (contact nucleon interactions only). We will show via figures of phase shifts that low energy nucleon-nucleon scattering is controlled by the pion mass scale, i.e., governed by pion-exchange dynamics, not by much lower scales (which implies unknown dynamics, actually) as suggested by KSW and the like. To some extent, our study provides a valuable perspective for exploring the nonperturbative treatment of the more complicated pionfull effective theory.