Nucleon-nucleon potential from instanton holonomies

TL;DR

This paper derives nucleon-nucleon interactions from the Skyrme model using instanton approximations, compares different skyrmion dynamics methods, and evaluates the resulting potentials against phenomenological models.

Contribution

It provides the first detailed comparison of classical potentials and metrics in skyrmion dynamics approximations and derives nucleon-nucleon potentials from these models.

Findings

Instanton approximation yields strong negative spin-orbit potentials.

Major disagreements found between different skyrmion approximations.

Results for other potentials are mixed due to zero pion mass limit.

Abstract

We derive the nucleon-nucleon interaction from the Skyrme model using the instanton and product approximations to skyrmion dynamics. In doing so, we also calculate the classical potential and metric for skyrmion dynamics in each of the approximations. This is the first time they have been compared in detail and the results show major disagreements between the approximations. We derive the eight low energy nucleon-nucleon interaction potentials and compare them with the Paris model. For the instanton approximation we find strong negative isoscalar and isovector spin-orbit potentials, matching phenomenological models and our geometric intuition. Results for the other potentials are mixed, in part due to the zero pion mass limit used in this approximation.