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

We present a simple and physically compelling boundary condition regularization scheme in the framework of effective field theory as applied to nucleon-nucleon interaction. It is free of off-shell ambiguities and ultraviolet divergences and provides finite results at any step of the calculation. 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 removed. This allows to compute scattering phase shifts which are, by construction consistent with effective range expansion to a given order in the CM momentum and are free from finite cut-off artifacts. We illustrate how the method works in the $^1S_0$ channel for the One Pion Exchange potential.