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

TL;DR

This paper develops a new resonating group method formalism for baryon-baryon interactions with unequal oscillator frequencies at the quark level, and applies it to the $N\Delta$ system within a chiral quark model, improving the description of such systems.

Contribution

A novel RGM formalism for baryon-baryon systems with unequal oscillator frequencies is introduced, enabling consistent analysis of bound states and scattering in these systems.

Findings

The new formalism accurately describes the $N\Delta$ interaction.

Comparison shows improvements over traditional equal-frequency approaches.

Results demonstrate the importance of considering unequal oscillator frequencies.

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 describing both single baryons and baryon-baryon interactions in a consistent framework. 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 $N\Delta$ system within a chiral SU(3) quark model, where the quark-quark interaction includes, in addition to the one-gluon exchange (OGE) 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 elucidated by comparing the results from the new formulation with those from traditional calculations.