An Analysis On The Chiral Effective Field Theory Of Nucleon-Nucleon Scattering

An effective field theory (EFT) is a simplified framework of quantum field theory that is constructed within a proper range of energy according to the symmetries of some underlying theory. In the low-energy chiral effective theories of quantum chormodynamics (QCD), being the bound states of quarks and gluons, the nucleons and mesons appear as ’elementary’ degrees of freedom, with the chiral symmetry breaking scale serving as the upper scale. Constrained by the QCD global chiral symmetry, the chiral effective theories have made remarkable achievements in pion scattering and many other areas of modest and low energy hadron physics. Beginning from Weinberg’s seminal suggestion in early 1990’s, chiral effective theories are employed to systematically derive and construct nuclear forces, marking the beginning of the EFT era of nuclear physics. However, the calculations must be performed in nonperturbative contexts due to the existence of large scattering lengths of nucleon systems, which hence brings about new issues and challenges. Actually, whenever the processes involving external baryons are calculated in chiral effective theories, the baryon masses as additional large scales always lead to coordination issues between chiral power counting and correct relativistic analytic behaviors. Our group has recently performed some primary analysis about the mapping between pionfull and pionless effective theories and revealed some subtle structures of the box diagram for nucleon-nucleon scattering, providing a novel perspective for looking at the issues of chiral effective theories for nuclear forces. Basing on the preceding researches, we will in this dissertation continue our study through analyzing all the one-loop pion-exchange diagrams for nucleon-nucleon scattering in the relativistic framework of chiral effective theory, namely, the football diagram, the triangle diagrams, the box diagram and the crossed diagram. With such calculation, we wish to further explore the structures of the chiral effective theory in order to contribute to the establishment of a satisfactory effective field theory for nuclear forces.