Near-BPS baby Skyrmions with Gaussian tails

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 ϵ as well as the standard pion mass term, with coefficient $$ \upepsilon {m}_1^2 $$ ϵ m 1 2 . The pions remain lighter than the soliton for any ϵ and therefore the model is physically acceptable, even in the ϵ → 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 ϵ → 0 limit and even reach the strict ϵ = 0 case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.

Near-BPS Skyrmions

“…In this work, we apply the successful techniques developed in refs. [21,22]. In particular, applying the perturbative scheme to the case of a single near-BPS Skyrmion, we find very good agreement with the exact full-numerical solution.…”

“…In the baby Skyrme model case, we were able to check the precision and validity of the -expansion scheme as a perturbative approach to near-BPS solitons by performing very large brute force numerical computations -only possible in the 2-dimensional case. We also found in the previous work, that the precision of the -expansion scheme is better in the case of compactons as compared to the solitons with tails [22]. Using this result as a guideline, in this paper we search for a viable BPS model with compactons.…”

“…with the kinetic, the Skyrme and the pion mass terms -all multiplied by a small control parameter, . This work is a continuation of the -expansion scheme that we have developed for the case of the baby Skyrme model in the case of compactons (Skyrmions with compact support in the BPS limit) [21] and in the case of baby Skyrmions with exponential (or rather Gaussian) tails [22]. In the baby Skyrme model case, we were able to check the precision and validity of the -expansion scheme as a perturbative approach to near-BPS solitons by performing very large brute force numerical computations -only possible in the 2-dimensional case.…”

“…Since the full numerical approach is extremely difficult, in this work we propose a semi-analytical method for exploring the near-BPS Skyrme model, building on the work of refs. [21,22]. The strategy is based on the expansion of the near-BPS field around a BPS solution, however, with respect to refs.…”

“…Moreover, without the possibility to perform numerical checks, it is even more difficult to establish when, and under what circumstances, a given approximation method could fail. To this end, instead of considering immediately the complicated 3D analysis, we previously performed our investigation in the 2D near-BPS baby Skyrme model [21,22]. For the 2D case, we were able to implement a new semi-analytical method for the near-BPS analysis and, simultaneously, check it with full numerics.…”