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Understanding the 1P and 2S nucleon resonances within the extended Lee-Friedrichs model

Yu-Hui Zhou1, Hui-Hua Zhong2, Zhi-Yong Zhou1,*, and Xian-Hui Zhong3,4,†

  • 1School of Physics, Southeast University, Nanjing 211189, People’s Republic of China
  • 2College of Aeronautics Mechanical and Electrical Engineering, Jiangxi Flight University, Nanchang 330088, People’s Republic of China
  • 3Department of Physics, Hunan Normal University, and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha 410081, People’s Republic of China
  • 4Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081, People’s Republic of China

  • *Contact author: zhouzhy@seu.edu.cn
  • †Contact author: zhongxh@hunnu.edu.cn
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Phys. Rev. D 113, 114028 – Published 15 June, 2026

DOI: https://doi.org/10.1103/h7dd-mgzz

Abstract

We present a unified description of the low-lying 1P- and 2S-wave nucleon resonance within the framework of an extended Lee-Friedrichs scheme. By incorporating the coupled-channel dynamics between bare quark-model states and the πN, πΔ and ηN meson-baryon continua, we examine the mass shifts and structural properties of these excited states. We demonstrate that when the model parameters are calibrated to match the 1P-wave spectrum and their widths, the pole associated with the bare 2S state is naturally shifted downward to the mass region of physical Roper resonance–N(1440), thereby offering a dynamical explanation for the long-standing level-inversion problem. An approximate analysis of compositeness and elementariness reveals that the Roper resonance contains a significant meson-baryon continuum states, consistent with the picture of a bare core heavily dressed by meson-baryon cloud. Simultaneously, the pole positions and properties of five 1P-wave resonances–N(1535), N(1650), N(1520), N(1700) and N(1675)—are successfully reproduced. Our results highlight the essential role of coupled-channel effects in shaping the nucleon spectrum and provide a consistent microscopic insight into the interplay between internal quark degrees of freedom and external hadronic fields.

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Phys. Rev. D 113, 114028– Published 15 June, 2026
  • Received 11 February 2026
  • Accepted 20 May 2026
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