Effective interactions and long distance symmetries in the Nucleon-Nucleon system

TL;DR

This paper explores how effective nucleon-nucleon interactions exhibit long-distance symmetries, revealing that certain symmetries are accurately realized at specific energy scales and that tailoring interactions can enhance symmetry fulfillment.

Contribution

It demonstrates the scale-dependent realization of long-distance symmetries in effective interactions and suggests optimizing their definition for better symmetry representation.

Findings

Serber symmetry works with high accuracy for spin triplet states.

Wigner SU(4) symmetry holds for even partial waves at low cut-offs.

Heavy mesonic resonances do not reproduce Serber symmetry patterns.

Abstract

Effective interactions, when defined in a coarse grained sense, such as Vlowk at the scale 450 MeV, display a remarkable symmetry pattern. Serber symmetry works with high accuracy for spin triplet states. Wigner SU(4) spin-isospin symmetry with nucleons in the fundamental representation works only for even partial waves exactly as predicted by large Nc limit of QCD with accuracy O(1/Nc^2). This suggests tailoring the very definition of effective interactions to provide a best possible fulfillment of long distance symmetries. With the Vlowk definition Wigner symmetry requires that chiral potentials have low cut-offs (450 MeV). Perturbative saturation of heavy mesonic resonances does not faithfully display the Serber symmetry pattern.