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Study of pole trajectory within a bare state in the coupled channel model

Wei Hao1,*, Jia-Jun Wu2,3,†, and Jin-Lin Fu2,‡

  • *Contact author: haowei@nankai.edu.cn
  • †Contact author: wujiajun@ucas.ac.cn
  • ‡Contact author: jinlin.fu@ucas.ac.cn
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Phys. Rev. D 112, 056021 – Published 19 September, 2025

DOI: https://doi.org/10.1103/t4yt-p9q3

Abstract

We investigate two-particle scattering and two-particle scattering with a bare basis state using Hamiltonian effective field theory. We analyze the distribution of two-body scattering poles in the momentum and energy planes under relativistic conditions. Compared to the nonrelativistic case, there are significant differences in the distribution of bound state poles and resonance poles in the relativistic case, primarily due to the square root term in the relativistic formula. By considering pure two-particle scattering, we examine the relationship between the form factor and the number of poles. Additionally, we clearly elucidate the effects of attractive and repulsive interactions on the bound state poles and resonance poles. More importantly, we extend our model by including a bare state and explore the poles originating from the bare state or coupled channels through the trajectories of pole positions, as well as the compositeness of bound states.

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Phys. Rev. D 112, 056021– Published 19 September, 2025
  • Received 3 June 2025
  • Accepted 25 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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