Roper resonances and quasi-normal modes of Skyrmions

TL;DR

This paper studies the radial vibrations of Skyrmions in the Skyrme model, analyzing how resonance properties depend on model parameters and reconstructing potentials to match physical Roper resonances.

Contribution

It introduces a method to reconstruct Skyrme model potentials from resonance data, enabling accurate reproduction of Roper resonances and nucleon properties.

Findings

Resonance frequencies and widths depend on potential form and sextic term inclusion.

Reconstructed potentials can precisely match physical Roper resonances.

Method enables tailored Skyrme models for nucleon phenomenology.

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.