Implicit vs Explicit Renormalization and Effective Interactions

TL;DR

This paper compares two methods of deriving effective interactions in nuclear physics, revealing a significant overlap in their results around relevant nuclear energy scales, which simplifies parameter determination.

Contribution

It provides a detailed comparison of implicit and explicit renormalization approaches, highlighting their agreement in a key energy region for light nuclei.

Findings

Both methods produce similar effective interactions around 200MeV.

The overlap simplifies the process of determining interaction parameters.

Explicit and implicit approaches are complementary in nuclear effective theories.

Abstract

Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the first method is numerically involved, the second one can be solved almost analytically. In both cases we compare the out coming effective interactions for the two nucleon system as functions of the cut-off scale and find a strikingly wide energy region where both approaches overlap, corresponding to relevant scales in light nuclei about 200MeV. This amounts to a great simplification in the determination of the effective interaction parameters.