Singlet NN Regularization using a Boundary Condition for OPE and TPE potentials

Boundary conditions provide a simple and physically compelling Wilsonian renormalization method in coordinate space in the framework of effective field theory as applied to nucleon-nucleon interaction in the non perturbative regime, enabling to remove unphysical regularization cut-offs while keeping physical low energy threshold parameters such as the scattering length and effective range invariant. We illustrate how the method successfully works in the $^1S_0$ channel for the One Pion Exchange (OPE) and Two Pion Exchange (TPE) potentials