Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Central Phases and the Deuteron

We analyze the renormalization of the NN interaction at low energies and the deuteron bound state through the Chiral Two Pion Exchange Potential assumed to be valid from zero to infinity. The short distance Van der Waals singularity structure of the potential as well as the requirement of orthogonality conditions on the wave functions determines that, after renormalization, in the 1S0 singlet channel and in the 3S1-3D1 triplet channel one can use the deuteron binding energy, the asymptotic D/S ratio and the S-wave scattering lengths as well as the chiral potential parameters as independent variables. We use then the asymptotic wave function normalization As of the deuteron and the singlet and triplet effective ranges to determine the chiral constants yielding c1, c3 and c4. The role of finite cut-off corrections, the loss of predictive power due to uncertainties in the input data and the connection to OPE distorted waves perturbative approaches is also discussed.