Nucleon-nucleon Scattering And Non-perturbative Renormalization

A lot of investigations have been done on the interactions between nucleons, whose field theoretical foundation is known to be quantum chromodynamics(QCD). Beginning from 90's, employing the QCD-based effective field theory methods, Weinberg proposed to construct the potential of nucleon-nucleon interactions order by order from chiral perturbation theory and then calculate the T-matrix using Lippmann-Schwinger equation to obtain the phase shifts for nucleon-nucleon scattering.The ultraviolet divergence is non-perturbative in such Lippmann-Schwinger equation. The generally known renormalization programs only apply in perturbative context, it is hard to use them in non-perturbative regime. One must resort other means.From the Lippmann-Schwinger equation we obtained a non-perturbative parametrization of the T-matrix, where an important object (G) is introduced. Further analysis revealed that this object has a strong renormalization prescription dependence, in other words, it contains important information of the renormalization prescriptions as well as that of nucleon-nucleon potentials. Then we performed a phenomenological analysis of the renormalization prescription dependence of T matrix using the constructed potential and the Fade expansion of the introduced object G. Numerical results showed that such analysis is very useful and can enlighten the renormalization of T-matrix in non-perturbative regime.Then, basing on the analysis above, we tried a simplest approximation of the object G to analyze choice of reasonable renormalization approach. Comparing to the known results that are either numerical in nature or perturbative somehow, this strategy allows us to do more analytical treatments and further improvements in approximation, more over, it can be applied to any potential forms and partial wave channels.Similar problems also appear in other non-perturbative regime issues, where our discussions here might be helpful.