Implicit vs Explicit renormalization of the $NN$ force

TL;DR

This paper demonstrates that implicit and explicit renormalization methods for the two-nucleon force produce consistent results, using a toy model to compare flow equations and contact interactions across various cutoffs.

Contribution

It introduces a novel comparison between implicit and explicit renormalization in a two-nucleon system using a toy model, showing their equivalence over a range of cutoffs.

Findings

Implicit and explicit renormalizations produce matching contact strengths.

The flow equations effectively integrate out high-momentum components.

Fitted contact theories replicate the running of original contact strengths.

Abstract

We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.