A Skyrme-type proposal for baryonic matter

Abstract

The Skyrme model is a low-energy effective field theory for QCD, where the baryons emerge as soliton solutions. It is, however, not so easy within the standard Skyrme model to reproduce the almost exact linear growth of the nuclear masses with the baryon number (topological charge), due to the lack of Bogomolny solutions in this model, which has also hindered analytical progress. Here we identify a submodel within the Skyrme-type low energy effective action which does have a Bogomolny bound and exact Bogomolny solutions, and therefore, at least at the classical level, reproduces the nuclear masses by construction. Due to its high symmetry, this model qualitatively reproduces the main features of the liquid droplet model of nuclei. Finally, we discuss under which circumstances the proposed sextic term, which is of an essentially geometric and topological nature, can be expected to give a reasonable description of properties of nuclei.Comment: 11 pages, 2 figures, latex. v3: Extended and revised version, some clarifications added. Some references and 2 figures added. v4: matches published versio

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.…”

“…In this paper, we consider a much more direct proposal, due to Adam, Sánchez-Guillén and Wereszczyński (henceforth ASW) [3]. Their idea is to consider an extended Skyrme model which includes both potential and sextic terms in its energy E(ϕ) = 1 2 R 3 c 0 U(ϕ) 2 + c 2 |dϕ| 2 + c 4 |ϕ * dµ| 2 + c 6 |ϕ * vol SU (2) | 2 =: c 0 E 0 + c 2 E 2 + c 4 E 4 + c 6 E 6…”

“…This proposal has been analyzed in detail in a sequence of papers by ASW and collaborators [3,4,2]. In [4], the BPS model with the usual pion mass potential is treated, a sequence of axially symmetric BPS skyrmions constructed and a rigid body semi-classical quantization of these performed to obtain phenomenological predictions of nuclear masses and radii.…”

“…In fact, every hedgehog skyrme field is restricted harmonic (though stability is an open question). By contrast, the axially symmetric BPS skyrmions ϕ B used in [3,4,2,11,10] are never restricted harmonic, for |B| > 1, so there certainly exist fields in their SDiff orbits with lower E 2 , which better approximate near-BPS skyrmions in the model E BP S + c 2 E 2 . Another natural family of skyrme fields, those within the rational map ansatz, can also be shown to have no restricted harmonic members with |B| > 1.…”

Solitons on Tori and Soliton Crystals

“…This is true whatever period lattice Λ we choose, no matter how crazy. Clearly, for a torus such as the one depicted in figure 1, the energy minimizers cannot meaningfully be interpreted as soliton crystals: they are an artifact of the choice of boundary conditions 1 . The choice of a cubic period lattice certainly looks more plausible.…”