Abstract
An omega-meson extension of the Skyrme model — without the Skyrme term but including the pion mass — first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained energy minimisation problem within a natural geometric framework and studied analytically on compact domains, and numerically on Euclidean space. Using a constrained second-order Newton flow algorithm, classical energy minimisers are constructed for various values of the omegapion coupling. At high coupling, these Skyrmion solutions are qualitatively similar to the Skyrmions of the standard Skyrme model with massless pions. At sufficiently low coupling, they show similarities with those in the lightly bound Skyrme model: the Skyrmions of low baryon number dissociate into lightly bound clusters of distinct 1-Skyrmions, and the classical binding energies for baryon numbers 2 through 8 have realistic values.
Highlights
Hadronic physics, it is possible to include just one more particle into the theory to stabilise the topological solitons, namely the omega vector meson
We have found that a static field configuration φ(x1, x2, x3), ω0 = f (x1, x2, x3), ωi = 0, satisfies the Euler-Lagrange equations for the action (2.19) if and only if it is a critical point of the static energy functional
An appealing point about the ω-Skyrme theory that we study in this paper is that it only contains 2 physical parameters: m ∈ (0, ∞) and g ∈ (0, ∞). m is physically the ratio of the pion mass to the omega meson mass m mπ mω and g is a coupling constant β multiplied by the ratio of the omega meson mass and the pion decay constant g
Summary
We will find it convenient to give a coordinate free, geometric formulation of the field theory. Returning to the general case, the field equations are obtained by demanding that (φ, ω) is a formal critical point of S: for all smooth variations (φs, ωs) of (φ, ω) = (φs, ωs)|s=0 of compact support in M, d ds. C∞(X, N ) is an infinite dimensional manifold whose tangent space at a map φ is Γ(φ−1T N ), the vector space of smooth sections of the bundle φ−1T N This space carries a natural inner product called the L2 metric, so that, formally, C∞(X, N ) is a Riemannian manifold. E : C∞(X, N ) → R with respect to the L2 metric is grad Eφ φ) + (grad V ) ◦ φ + g ∗ (df ∧ Ξφ) Note that this is, at each fixed φ, a section of φ−1T N , and defines a vector field on C∞(X, N )
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