Block-diagonal similarity renormalization group and effective nucleon-nucleon interactions

Abstract

We apply the block-diagonal similarity renormalization group to a simple toy-model for the nucleon-nucleon (NN) interaction in the ¹ S ₀ channel, aiming to analyze the complementarity between the explicit and the implicit renormalization approaches in nuclear physics. By explicit renormalization we mean the methods based on the wilsonian renormalization group in which high-energy modes above a given cutoff scale are integrated out while their effects are replaced by scale dependent effective interactions consistently generated in the process. We call implicit renormalization the usual procedure of cutoff effective theories in which the high-energy modes above the cutoff scale are simply removed and their effects are included through parametrized cutoff dependent counterterms whose strengths are fixed by fitting low-energy data. We compare the effective interactions obtained in both schemes and find a wide range of cutoff scales where they overlap. We further analyze the role played by the one-pion exchange (OPE) considering a δ-shell plus OPE representation for the NN interaction.