Robustness of the Hedgehog Skyrmion

TL;DR

This paper analyzes the robustness of the hedgehog Skyrmion's radial profile in effective field theories of pions, showing it remains smooth and nearly universal across different EFT terms, assuming chiral symmetry.

Contribution

It demonstrates the stability and universality of the hedgehog Skyrmion profile in generic EFTs without pion mass terms, highlighting its robustness against higher derivative corrections.

Findings

The Skyrmion remains smooth with no singularities.

The profile function varies little across different EFT terms.

A universal profile function is proposed.

Abstract

We investigate the radial profile function of the hedgehog Skyrmion with unit baryon number in generic EFTs (effective field theories) of pions. The analysis assumes chiral symmetry and ignores the pion mass term. The Skyrmion is always smooth, because it has no point source at the origin, and terms in the EFT with higher numbers of pion derivatives do not result in uncontrolled large corrections or singularities there. The profile varies in quite a limited way as the terms in the EFT change, and a universal profile function is proposed.