A Study Of NN Scattering In Covariant Chiral Effective Field Theory At Two Loop Level

The applications of chiral effective theory in nuclear force and related area are began in 1990 with Weinberg's seminal suggestion:One first constructs the nucleon-nucleon(NN)potential according to chiral expansion rules in non-relativistic framework,then calculates the amplitudes or wave functions via Schrodingder equation.Subsequently,there appeared a lot of papers studying nuclear forces using chiral effective theories.However,there is an issue that remains unsatisfactory in field-theoretical contexts:the non-perturbative renormalization of the chiral effective field theory for nuclear force.Years ago,our group analyzed the one-loop diagrams for NN scattering using covariant chiral effective theory and found that,in the dominant box diagram,there are two kinds of contributions that violate chiral power counting rules:one is the local pieces due to nucleon mass,the other is a definite nonlocal piece.The local pieces could be readily removed by introducing local counterterms,while the definite piece could not be subtracted due to nonlocality,owning an 'anomalous' position.Obviously,the 'anomalous' contributions must be resumed up or treated non-perturbatively,while there is no more issue of non-perturbative renormalization due to its definiteness.In this way,the consistency of the chiral effective theory is ensured.This is the conclusion from one loop analysis.The present thesis is devoted to a continual study of NN scattering with covariant chiral effective theory.We will focus on the two-loop corrections to the box diagram.Two subtraction prescriptions will be employed for comparison,one the well-known (?),that is most frequently used in particle physics literature,the other is what is adopted in the one-loop case for removing the power counting violating terms,which,henceforth named as E(?),is in accordance with EOMS that is advanced for the studies of baryonic physics.Within (?),the loop amplitudes obtained possess terms that severely violate the chiral power counting,while within E(?),the results are totally chiral contributions except the nonlocal 'anomalous'ones that must be retained.Consequently,the conclusions drawn at one-loop level are verified to hold still at two-loop level and it is shown that there are more novel contents in the 'anomalous' contributions.These results imply that one must work with covariant formulation to account for the resummation or non-perturbative treatment of all the 'anomalous' contributions for NN scattering.In other words,we have shown in this thesis that one should work in covariant chiral effective theory aided with appropriate prescription to study nuclear force,where the 'anomalous'contributions should be properly resumed or non-perturbatively treated.These conclusions will provide very positive clues for finally establishing a satisfactory effective field theory for nuclear force.