The chiral partner of the nucleon in the mirror assignment with global symmetry

TL;DR

This paper investigates the properties of nucleons within a globally symmetric linear sigma model, calculating scattering lengths and nucleon mass parameters, and compares results with lattice data to understand chiral symmetry effects.

Contribution

It introduces a calculation of pion-nucleon scattering lengths and nucleon mass parameters in a parity-doublet model with global symmetry, highlighting the need for additional scalar degrees of freedom.

Findings

The nucleon mass parameter $m_0$ is estimated to be 300-600 MeV.

The calculated $a_{0}^{(-)}$ agrees with experimental data.

The $a_{0}^{(+)}$ value is underestimated, suggesting missing scalar contributions.

Abstract

We calculate the pion-nucleon scattering lengths $a_{0}^{(\pm)}$ and the mass parameter $m_{0}$, which describes the nucleon mass in the chiral limit, at tree-level in the framework of a globally symmetric linear sigma model with parity-doubled nucleons. When recent lattice results [Takahashi] are used, we obtain $m_{0}\simeq300-600$ MeV. While $a_{0}^{(-)}$ is in fair agreement with experimental data, $a_{0}^{(+)}$ is too small because of the employed large scalar meson mass. This indicates the need to account for additional scalar degrees of freedom.