Converging low energy expansion of nucleon-nucleon scattering based on the Wilsonian renormalization group analysis

In order to implement the power counting obtained in the Wilsonian renormalization group (WRG) analysis of nuclear effective field theory (NEFT) including pions, we propose a practical calculational scheme in which the short-distance part of one-pion exchange (S-OPE) is removed and represented as contact terms. A distinctive feature of our scheme is that two regularization schemes are used in combination. The dimensional regularization (DR) is used for diagrams consisting only of contact interactions and a momentum cutoff is implemented for diagrams con-taining the long-distance part of one pion exchange (L-OPE) by introducing a Gaussian damping factor(GDF). The sole purpose of the use of the dimensional regularization is that it considerably simplifies the treatment of nonperturbative part of the scattering amplitude. In the calculation the L-OPE is treated as perturbation and a part of the S-OPE is treated nonperturbatively along with a contact interaction without derivative nonperturbatively. We show the results of the next-To-next-to-leading order(NNLO) calculations for nucleon-nucleon elastic scattering in the S-waves that are fitted to Nijmegen partial wave analysis data.