Near-BPS Skyrmions: Nonshell configurations and Coulomb effects

Abstract

The relatively small binding energy in nuclei suggests that they may be well represented by near-BPS Skyrmions since their mass is roughly proportional to the baryon number A. For that purpose, we propose a generalization of the Skyrme model with terms up to order six in derivatives of the pion fields and treat the nonlinear σ and Skyrme terms as small perturbations. For our special choice of mass term (or potential) V , we obtain well-behaved analytical BPS-type solutions with nonshell configurations for the baryon density, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme model . Along with static and (iso)rotational energies, we add to the mass of the nuclei the often neglected Coulomb energy and isospin breaking term. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.

Near BPS skyrmions and restricted harmonic maps

“…Consider now the case where R = R B : S 2 → S 2 , R B (θ, φ) = (θ, Bφ). Suspension maps of this form ϕ B (rn) = (cos f B (r), sin f B (r)R B (n)), (2.21) with profile function f B (r) = f (B −1/3 r) (with k = 1), occur frequently in studies of near BPS skyrmions [3,4,2,11,10]. Clearly such fields, for B > 1, have a string of conical singularities along the z-axis.…”

“…These problems were addressed in a pair of papers by Marleau and collaborators [11,10]. In [11] the model with a certain massless potential is studied.…”

“…In particular, ϕ should minimize E 2 within all fields in its SDiff(R 3 ) orbit. It is not hard to show that, for |B| > 1, the axially symmetric BPS skyrmions ϕ B used in [3,4,2,10,11] do not have this property, and that their failure to minimize E 2 gets worse as B grows. Recall that a function ϕ : (M, g) → (N, h) between Riemannian manifolds which locally extremizes the Dirichlet energy E 2 with respect to all smooth variations is called a harmonic map.…”

Some aspects of self-duality and generalised BPS theories

“…And, indeed, field theories based on versions of the above energy functional [7]- [15] are known to support both Bogomolnyi bounds and topological BPS solitons [10]- [15]. Among these BPS theories there are BPS submodels of some well-known and relevant non-linear field theories like, e.g., the Skyrme [16][17][18] and baby Skyrme [19][20][21][22][23] models or the abelian Higgs model, which makes them all the more interesting also from a phenomenological perspective (see, e.g., [24,25]). Given these results, one rather obvious question then arises -as to whether a version of the "deformation procedure" mentioned above generalises to the higher-dimensional theories, and whether this procedure can be used also in these cases to find soliton solutions of many different theories starting from a soliton of a certain "seed" theory.…”

“…This model defines a solvable sector of the full Skyrme theory and has found some applications in the context of the low energy limit of QCD [12,13,24,25]. We remark that models of this type should not be considered as complete field theories on their own.…”