Extended Goldberger-Treiman relation obtained in a three-flavor parity doublet model

TL;DR

This paper develops an extended Goldberger-Treiman relation within a three-flavor parity doublet model, providing new insights into nucleon masses, decay widths, and chiral structure, with predictions testable by experiments or lattice QCD.

Contribution

It introduces an extended Goldberger-Treiman relation in a three-flavor parity doublet model, linking mass differences and pion couplings, and predicts decay width bounds and nucleon chiral components.

Findings

Derived an upper bound for the decay width of N(1440) → N(939) + π.

Predicted the chiral invariant mass of N(939) to be 500-800 MeV.

Estimated the N(939) nucleon composition as about 80% of a specific chiral representation.

Abstract

We study masses and decay widths of positive and negative parity nucleons using a three-flavor parity doublet model, in which we introduce three representations, $\left[({\bf 3} , \bar{{\bf 3}})\oplus (\bar{{\bf 3}} , {\bf 3})\right]$, $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$, and $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ of the chiral U$(3)_{\rm L}\times$U$(3)_{\rm R}$ symmetry. We find an extended version of the Goldberger-Treiman relation among the mass differences and the coupling constants for pionic transitions. This relation leads to an upper bound for the decay width of $N(1440) \rightarrow N(939) + \pi$ independently of the model parameters. We perform the numerical fitting of the model parameters and derive several predictions, which can be tested in future experiments or lattice QCD analysis. Furthermore, when we use the axial coupling of the excited nucleons obtained from lattice QCD analyses as inputs, we find that the ground state nucleon $N(939)$ consists of about 80% of $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$ component, and that the chiral invariant mass of $N(939)$ is roughly $500$ -- $800$MeV.