Approximate solutions for the single soliton in a Skyrmion-type model with a dilaton scalar field

Details Approximate solutions for the single soliton in a Skyrmion-type model with a dilaton scalar field Approximate solutions for the single soliton in a Skyrmion-type model with a dilaton scalar field

2004-05-26

arxiv.org/abs/hep-ph/0405258v2

Phys.Rev. C72 (2005) 065206

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 3 eps figures, version to be published in Phys.Rev.C

Scientific paper

10.1103/PhysRevC.72.065206

We consider the analytical properties of the single-soliton solution in a Skyrmion-type Lagrangian that incorporates the scaling properties of quantum chromodynamics (QCD) through the coupling of the chiral field to a scalar field interpreted as a bound state of gluons. The model was proposed in previous works to describe the Goldstone pions in a dense medium, being also useful for studying the properties of nuclear matter and the in-medium properties of mesons and nucleons. Guided by an asymptotic analysis of the Euler-Lagrange equations, we propose approximate analytical representations for the single soliton solution in terms of rational approximants exponentially localized. Following the Pad\'e method, we construct a sequence of approximants from the exact power series solutions near the origin. We find that the convergence of the approximate representations to the numerical solutions is considerably improved by taking the expansion coefficients as free parameters and then minimizing the mass of the Skyrmion using our ans\"atze for the fields. We also perform an analysis of convergence by computation of physical quantities showing that the proposed analytical representations are very useful useful for phenomenological calculations.

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