Abstract
Radial vibrations of charge one hedgehog Skyrmions in the full Skyrme model are analysed. We investigate how the properties of the lowest resonance modes (quasi normal modes) — their frequencies and widths — depend on the form of the potential (value of the pion mass as well as the addition of further potentials) and on the inclusion of the sextic term. Then we consider the inverse problem, where certain values for the frequencies and widths are imposed, and the field theoretic Skyrme model potential giving rise to them is reconstructed. This latter method allows to reproduce the physical Roper resonances, as well as further physical properties of nucleons, with high precision.
Highlights
Modes of the classical solutions of the Skyrme model (Skyrmions) in a given topological sector one got access to fermionic excitations of this classically purely bosonic theory
For small, the resulting field theoretical potential is very peaked at the anti-vacuum, which corresponds to a significant concentration of the energy density at the origin. This unpleasant fact is cured if we increase the value of the coupling constant multiplying the sextic term, i.e., once we move the model towards the near-BPS Skyrme model [59, 60]
We investigated in detail the possibility to describe the Roper resonances within the context of the Skyrme model
Summary
We introduce the physical energy and length scales E = fπ/4e and leads to the following Lagrangian in Skyrme units (2.1) = 2/efπ. The potential is assumed to be a function of the scalar field ξ only. We want to consider how the charge one Skyrmion reacts under a spherically symmetric perturbation. Such a static stable B = 1 solution is given by the hedgehog ansatz ξ = ξ0(r), u tan θ 2 eiφ where the static profile ξ0 solves the following ODE (ξ0 ≡ (d/dr)ξ0). Function is a function of the radial coordinate and time ξ = ξ(r, t) This leads to the reduced Lagrangian d3x ξμξμ. This equation is the starting point for our further analysis
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