Comment on the Walliser-Weigel approach to exotic baryons in chiral soliton models

TL;DR

This paper critically examines Walliser and Weigel's approach to exotic baryons in chiral soliton models, highlighting issues with their methodology, nomenclature, and the validity of their phase shift calculations.

Contribution

It provides a detailed critique of the quantization methods and assumptions used in the original work, clarifying the proper interpretation of excitation energies in the model.

Findings

The identification of pentaquark excitation energy with small amplitude fluctuation frequency is incorrect.

The phase shift calculations in the original paper are not justified beyond leading order.

Misleading claims arise from nomenclature and ad hoc extensions in the original approach.

Abstract

This comment discusses a recent paper by Walliser and Weigel on the quantization of chiral soliton models in the context of exotic baryons. Claims made in that work are misleading due to unfortunate nomenclature. Moreover, attempts in that paper to go beyond the leading order calculations of the phase shifts are ad hoc and never justified. This comment also addresses a technical issue in that paper: the identification of the excitation energy of the pentaquark obtained via conventional rigid rotor quantization with a frequency obtained in the context of small amplitude fluctuations. The identification is erroneous: the small amplitude fluctuation result is based on a first-order perturbation computation of the frequency around a zero mode solution at a frequency far from zero and well away from the perturbative regime.