Skyrmions in the presence of isospin chemical potential

TL;DR

This paper investigates how finite isospin chemical potential affects skyrmion solutions in the Skyrme model, revealing a critical chemical potential related to the pion mass where solutions disappear, with implications for understanding topological excitations in nuclear physics.

Contribution

It demonstrates the existence of a critical isospin chemical potential for skyrmions and clarifies its relation to the pion mass, challenging some previous findings.

Findings

Skyrmion solutions cease to exist above a critical isospin chemical potential.

The critical chemical potential is closely related to the pion mass.

Below the critical value, skyrmion mass and size are only mildly affected.

Abstract

We analyze the existence of localized finite energy topological excitations on top of the perturbative pion vacuum within the Skyrme model at finite isospin chemical potential and finite pion mass. We show that there is a critical isospin chemical potential $\mu_I^c$ above which such solutions cease to exist. We find that $\mu_I^c$ is closely related to the value of the pion mass. In particular for vanishing pion mass we obtain $\mu_I^c=0$ in contradiction with some results recently reported in the literature. We also find that below $\mui^c$ the skyrmion mass and baryon radius show, at least for the case of the hedgehog ansatz, only a mild dependence on the isospin chemical potential.