Mirror versus naive assignment in chiral models for the nucleon

TL;DR

This paper compares naive and mirror chiral assignments for nucleons in chiral models, finding the mirror assignment with N(1650) as the chiral partner best matches experimental data on scattering lengths and decay widths.

Contribution

It evaluates low-energy nucleon properties in naive and mirror chiral models, identifying the mirror assignment with N(1650) as the most consistent with experimental results.

Findings

Naive assignment fails to reproduce isospin-odd scattering length.

Mirror assignment agrees well with experimental isospin-odd scattering length.

Both assignments struggle with isospin-even scattering length due to uncertain scalar sector.

Abstract

In the framework of chiral model(s) based on the linear realization of chiral symmetry, we investigate the low-energy phenomenological properties of the nucleon and its chiral partner (identified with either $N(1535)$ or $N(1650)$) in the naive assignment and compare the results with the ones obtained in the mirror assignment. We find that, within the naive assignment, we are not able to reproduce the experimental value of the isospin-odd scattering length, while the mirror assignment is in good agreement with it for both choices $N(1535)$ and $N(1650)$. The isospin-even scattering length is not yet conclusive in either assignment because it depends crucially on the poorly known scalar mesonic sector. The decay with $\Gamma_{N(1535)\rightarrow N\eta }$ turns out to be far too small in both the naive and mirror assignments, while $\Gamma_{N(1650)\rightarrow N\eta}$ is described correctly by both of them. In conclusions, the mirror assignment with $N(1650)$ as the chiral partner of the nucleon is the favored configuration.