Hidden spin-isospin exchange symmetry

TL;DR

This paper explores an approximate spin-isospin exchange symmetry in nucleon interactions rooted in quantum chromodynamics, revealing it through averaging over spins and at a specific momentum scale, with implications for nuclear physics.

Contribution

It identifies the conditions under which the hidden large-$N_c$ spin-isospin symmetry becomes apparent and derives sum rules relevant for nuclear structure and interactions.

Findings

Symmetry emerges at a momentum scale of about 500 MeV.

Derived spin-isospin exchange sum rules.

Implications for nuclear forces and structure calculations.

Abstract

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $\Lambda_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $\Lambda_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of $^{30}$P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.