Implicit and explicit renormalization: two complementary views of\n effective interactions

We analyze quantitatively the interplay between explicit and implicit\nrenormalization in Nuclear Physics. By explicit renormalization we mean to\nintegrate out higher energy modes below a given cutoff scale using the\nsimilarity renormalization group (SRG) with a block-diagonal evolution\ngenerator, which separates the total Hilbert-space into a model space and its\ncomplementary. In the implicit renormalization we impose given conditions at\nlow energies for a cutoff theory. In both cases we compare the outcoming\neffective interactions as functions of the cutoff scale. We carry out a\ncomprehensive analysis of a toy-model which captures the main features of the\nnucleon-nucleon (NN) S-wave interaction at low energies. We find a wide energy\nregion where both approaches overlap. This amounts to a great simplification in\nthe determination of the effective interaction. Actually, the outcoming scales\nare within the expected ones relevant for the physics of light nuclei.\n