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

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, $\left[(3,\bar{3})\oplus (\bar{3},3)\right]$, $\left[(3,6)\oplus (6,3)\right]$, and $\left[(8,1)\oplus (1,8)\right]$ of the chiral U$(3{)}_{\mathrm{L}}\times$U$(3{)}_{\mathrm{R}}$ 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 $N(1440)\to N(939)+\pi$ 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 $\left[(3,6)\oplus (6,3)\right]$ component, and that the chiral invariant mass of $N(939)$ is roughly $500$ -- $800$MeV.

10 pages, 6 figures and 8 tables, version accepted for publication in Physical Review D

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• Chiral partner structure of light nucleons in an extended parity doublet model
• Influence of the axial anomaly on the decay $N(1535)\to N\eta$
• Baryon fields with $U_L(3)\times U_R(3)$ chiral symmetry V: Pion-Nucleon and Kaon-Nucleon $\Sigma$ Terms
• Comprehensive study of mass modifications of light mesons in nuclear matter in the three-flavor extended Linear Sigma Model
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