How to Use Renormalization Group Analysis in Lattice Nuclear Effective Field Theory

Abstract

We propose a new approach to Nuclear Effective Field Theory (NEFT) on a lattice on the basis of Renormalization Group (RG) analysis. In order to perform Markov-chain Monte Carlo lattice simulation of NEFT, we introduce auxiliary fields to integrate nucleon field so that its effects are represented as a determinant. The problem is that the determinant becomes complex and cannot be considered as a part of probability distribution function. We introduce a reweighting method, in which the reference determinant is chosen to be optimal in the RG analysis sense: the reference determinant contains only the relevant interactions and the closest to the original determinant. We calculate the standard deviation of the absolute value of the reweighting factor in a simple model, isospin-symmetric S-wave NLO NEFT without pions, and explain why our choice is optimal.