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Effective interactions and long distance symmetries in the Nucleon-Nucleon system

Effective interactions, when defined in a coarse grained sense, such as Vlowk at the scale 450 MeV, display a remarkable symmetry pattern. Serber symmetry works with high accuracy for spin triplet states. Wigner SU(4) spin-isospin symmetry with nucleons in the fundamental representation works only for even partial waves exactly as predicted by large Nc limit of QCD with accuracy O(1/Nc^2). This suggests tailoring the very definition of effective interactions to provide a best possible fulfillment of long distance symmetries. With the Vlowk definition Wigner symmetry requires that chiral potentials have low cut-offs (450 MeV). Perturbative saturation of heavy mesonic resonances does not faithfully display the Serber symmetry pattern.