Further Studies On Nucleon-Nucleon Scattering And Non-perturbative Renormalization

The applications of effective field theory method in nuclear systems began in early 1990s.In 1990,Weinberg proposed to handle the nonperturbative nucleon-nucleon scattering using Lippmann-Schwinger equation with the nucleon-nucleon potentials systematically constructed from chiral perturbation theory according to the chiral expansion power counting.Then in the following decades the EFT approach produced many significant results in nuclear forces, marked the advent of the EFT era of nuclear physics.However,there also appear nonperturbative divergences that are hard to tame within the perturbative programs of renormalization.Thus,ever since the beginning of EFT method in nuclear systems,the renormalization in nonperturbative regime has become an important theoretical topic.Through a proper transformation,we could turn the Lippmann-Schwinger equation into a nonperturbative parametrization of the T-matrix,where a crucial factor G of nonperturbative nature is introduced.Further analyses revealed that this very factor is nontrivially dependent upon renormalization prescriptions.In other words,this factor carries important information about renormalization as well as interactions.The presence of this factor implies that the perturbative renormalization wisdoms cease to apply here,as is recognized in recent literature. Unfortunately,there is no consensus about how to deal with nonperturbative divergences.Basing on rigorous solutions of T-matrix and numerical analysis of the ?)factor,we employed a nonperturbative scheme(via Pade approximant)to expand(?)to parametrize the nonperturbative prescription dependence.After separating out the partial wave factor 1/P²¹,we could numerically obtain physical observables in various partial waves,which in turn serve as test and evaluation of our parametrization scheme.The Pade coefficients are fitted to the low-energy ends of the partial wave phase shifts provided by Nijimegen and then employed to predict phase shifts at higher energies and other quantities.A new set of low energy constants for chiral perturbation theory is obtained through phenomenological analysis augmented by our nonperturbative renormalization treatment.Comparing to known numerical works and perturbative approaches,our present treatment is more accurate and applicable to wider ranges of potentials and partial wave channels.Our approach might be helpful to other nonperturbative issues,as well as to the conceptual issues of nonperturbative renormalization.