Exploring the generalized loosely bound Skyrme model

Sven Bjarke Gudnason

doi:10.1103/physrevd.98.096018

Abstract

The Skyrme model is extended with a sextic derivative term - called the BPS-Skyrme term - and a repulsive potential term - called the loosely bound potential. A large part of the model's parameter space is studied for the 4-Skyrmion which corresponds to the Helium-4 nucleus and emphasis is put on preserving as much of the platonic symmetries as possible whilst reducing the binding energies. We reach classical binding energies for Helium-4 as low as 0.2%, while retaining the cubic symmetry of the 4-Skyrmion, and after taking into account the quantum mass correction to the nucleon due to spin/isospin quantization, we get total binding energies as low as 3.6% - still with the cubic symmetry intact.

Highlights

The Skyrme model is an interesting approach to nuclear physics that is related to fundamental physics; i.e., it is a field theory [1,2]
We were able to use the relaxation method with a forward-time algorithm, but that turned out to be too slow for the generalized Skyrme model when including the BPS-Skyrme term
The full numerical calculations are necessary for detecting the symmetries of the Skyrmions, in particular, whether the 4-Skyrmion possesses the sought-for cubic symmetry or it loses it, becoming a tetrahedrally symmetric object of “point” particles

Summary

INTRODUCTION

The Skyrme model is an interesting approach to nuclear physics that is related to fundamental physics; i.e., it is a field theory [1,2]. The scope in this paper, will be to focus on reducing the classical binding energy of the Skyrmions under the constraint of preserving as much symmetry of the original Skyrmions as possible This is in the spirit of assuming that the fluctuation spectrum of the Skyrmions is weakly coupled and the classical mass is the largest contribution to the mass by far; the zero-mode quantization gives the most important quantum corrections, and the remaining modes give corrections to the mass of the order of magnitude of the zero-mode contributions or less. The model we study in this paper is the generalized Skyrme model—consisting of a kinetic term, the Skyrme term, and the BPS-Skyrme term—with a pion mass term and the so-called loosely bound potential. We will use m1 1⁄4 1=4 [19]

Observables

Symmetry

NUMERICAL RESULTS

DISCUSSION