Near-BPS Skyrmions

TL;DR

This paper studies near-BPS Skyrmions within a modified Skyrme model, using an epsilon-expansion to analyze corrections, stability, and bound states like the deuteron, providing a systematic approach to approximate solutions.

Contribution

It introduces a model with compacton BPS Skyrmions and applies epsilon-expansion to compute energies and bound states, advancing analytical methods in Skyrme theory.

Findings

Compact support BPS Skyrmions are stable solutions.

Epsilon-expansion accurately approximates energy corrections.

Bound state calculations match numerical results for the deuteron.

Abstract

We consider the Skyrme model in the near-BPS limit. The BPS part is made of the sextic term plus a potential and the deformation is made of the standard massive Skyrme model controlled by a small parameter $\epsilon\ll1$. In order to keep the perturbation under theoretical and computational control, we find a model for which BPS Skyrmions have compact support, henceforth denoted as compactons, and the spherically symmetric $B=1$ Skyrmion represents the most stable solution. We use the $\epsilon$-expansion scheme to systematically calculate the corrections to the energy and compare with the exact numerical computations in the $B=1$ sector. Finally, we use the $\epsilon$-expansion scheme to calculate the bound state of two $B=1$ Skyrmions and its binding energy, which corresponds, prior to quantization, to the deuteron in our model.