Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions

A non perturbative renormalization scheme for Nucleon-Nucleon interaction based on boundary conditions at short distances is presented and applied to the One Pion Exchange Potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation and allows to remove the short distance cut-off in a suitable way. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows to compute scattering phase shifts which are, by construction consistent with the effective range expansion to a given order in the C.M. momentum $p$. In the singlet $^1S_0$ and triplet $^3S_1- ^3D_1$ channels ultraviolet fixed points and limit cycles are obtained respectively for the threshold parameters. Data are described satisfactorily up to CM momenta of about $p \sim m_\pi$.