The Skyrme model and higher order terms

Baryonic sphere: A spherical domain wall carrying baryon number

“…The simplest possible extension is to add just a sixth-order derivative term to the action. For simplicity, we will only consider the type of higher-derivative terms that gives rise to a second-order equation of motion, along the lines of Marleau [21]. The action can be written as [15] with…”

Simulated annealing for generalized Skyrme models

“…Such a requirement was first proposed in [5]. In fact, the Skyrme model or any model made up of a linear combination of L 1 , L 2 and L 3 satisfy this condition so in a sense, the models we are interested in are their natural extensions.…”

“…Nowadays, this idea is partly supported by the 1/N c analysis [2,3], according to which the low-energy limit of QCD could be represented by an effective theory of infinitely many mesons fields whose derivatives appear to all-orders. Since little is known about the exact form of such a Lagrangian, significant efforts have been made to formulate in a simple way Skyrme-like effective Lagrangians [4,5]. It was then possible to improve the phenomenological predictions for the spherically symmetric skyrmion with unit topological charge (B = 1) [6,7] with higher order Lagrangians, whereas only a relative accord with experimental data was achieved with the original Skyrme model [8].…”

“…Since rational maps are conformal maps they preserved the relation a = c in which case only terms in the energy density which are at most linear in b survive and presumably this would correspond to an energically favoured configuration. So one might conjecture that the soliton solutions for the class of models defined in [5] are well represented by the rational map ansatz or that rational map solutions would remain well suited approximation for extended models as long as they belong to this particular class of models. This is the main motivation to compare rational maps inspired solutions with the exact numerical solutions for such models.…”

“…But even writing the most general higher-order Lagrangian rapidly becomes a cumbersome task as the number of terms increases with the number of derivatives let alone finding any solutions. In view of this difficulty, we choose to consider only a class of tractable models defined in [5]. The reason for such a choice will be explained in the next sections.…”