Near-BPS baby Skyrmions with Gaussian tails

TL;DR

This paper investigates near-BPS baby Skyrmions with Gaussian tails by numerically analyzing a perturbed BPS model, revealing new solutions in the limit where the perturbation vanishes, which are not yet analytically understood.

Contribution

It introduces a numerical study of the perturbed baby Skyrme model approaching the BPS limit, discovering new nontrivial solutions with Gaussian tails.

Findings

Numerical solutions exist at the strict BPS limit ($psilon=0$).

Pions remain lighter than solitons for all small psilon.

New nontrivial BPS solutions with Gaussian tails are identified.

Abstract

We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient $\epsilon$ as well as the standard pion mass term, with coefficient $\epsilon m_1^2$. The pions remain lighter than the soliton for any $\epsilon$ and therefore the model is physically acceptable, even in the $\epsilon \to 0$ limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in the $\epsilon\to 0$ limit and even reach the strict $\epsilon=0$ case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.