Chiral partner structure of light nucleons in an extended parity doublet model

TL;DR

This paper investigates the chiral partner structure of four light nucleons using an extended parity doublet model, fitting parameters to experimental and lattice data, and explores implications for chiral symmetry restoration in dense matter.

Contribution

It introduces a novel extended parity doublet model with four chiral representations to analyze nucleon chiral partners and distinguishes solution groups using axial-charge matrix elements.

Findings

Identified five solution groups with different chiral partner assignments.

Found small and large chiral invariant mass scenarios for nucleon partners.

Discussed mass changes during chiral symmetry restoration in high-density environments.

Abstract

We study chiral partner structure of four light nucleons, $N(939)$, $N(1440)$, $N(1535)$ and $N(1650)$ using an effective chiral model based on the parity doublet structure. In our model we introduce four chiral representations, $({\bf 1},{\bf 2})$, $({\bf 2},{\bf 1})$, $({\bf 2},{\bf 3})$ and $({\bf 3},{\bf 2})$ under ${\rm SU}(2)_{\rm L} \otimes {\rm SU}(2)_{\rm R}$ symmetry. We determine the model parameters by fitting them to available experimental values of masses, widths and the axial charge of $N(939)$ together with the axial charges of $N(1535)$ and $N(1650)$ by lattice analyses. We find five groups of solutions: In a group the chiral partner to $N(939)$ is $N(1440)$ having small chiral invariant mass. In another group, the chiral partner is a mixture of $N(1535)$ and $N(1650)$ having a large chiral invariant mass. We claim that off-diagonal elements of axial-charge matrix can be used for distinguishing these groups. We also discuss changes of masses associated with chiral symmetry restoration, which could emerge in high density matter.