Exotic baryon resonances in the Skyrme model

TL;DR

This paper investigates exotic baryon resonances, specifically Theta+, within the Skyrme model, using analytical and numerical methods to analyze their properties and widths, and discusses the model's predictions and limitations.

Contribution

It demonstrates how the Skyrme model predicts the Theta+ resonance and analyzes its width using multiple methods, providing insights into the factors influencing the narrowness of the resonance.

Findings

Identifies a strong Theta+ resonance in kaon-Skyrmion scattering.

Shows the Skyrme model overestimates the width of Theta+.

Width can be estimated from the transition axial constant.

Abstract

We outline how one can understand the Skyrme model from the modern perspective. We review the quantization of the SU(3) rotations of the Skyrmion, leading to the exotic baryons that cannot be made of three quarks. It is shown that in the limit of large number of colours the lowest-mass exotic baryons can be studied from the kaon-Skyrmion scattering amplitudes, an approach known after Callan and Klebanov. We follow this approach and find, both analytically and numerically, a strong Theta+ resonance in the scattering amplitude that is traced to the rotational mode. The Skyrme model does predict an exotic resonance Theta+ but grossly overestimates the width. To understand better the factors affecting the width, it is computed by several methods giving, however, identical results. In particular, we show that insofar as the width is small, it can be found from the transition axial constant. The physics leading to a narrow Theta+ resonance is briefly reviewed and affirmed.