共振群方法用于具有不等振子频率的重子-重子相互作用及其在楚拉SU(3)夸克模型中NΔ系统的应用
Resonating group method for baryon-baryon interactions with unequal oscillator frequencies and its application to the $NΔ$ system in a chiral quark model
AI总结：
本文提出了一种适用于不等振子频率重子-重子相互作用的共振群方法，并应用于楚拉SU(3)夸克模型中的NΔ系统，考虑了标量和伪标量介子交换。
摘要：
共振群方法（RGM）被广泛用于研究重子-重子相互作用在夸克层面，通常假设参与的两个重子具有相同的谐振子频率。然而，在现实中，当给定一个特定的相互作用哈密顿量时，由于不同的量子数导致不同的相互作用势，不同的重子应具有不等的振子频率。在本工作中，我们开发了一种新的夸克层面RGM形式化方法，用于具有不等振子频率的重子-重子系统，目的是在一致的框架下描述单个重子和重子-重子相互作用。我们提出了解决束缚态和散射问题的形式化方法，特别强调构造具有不等振子频率的双重子系统的波函数。所提出的形式化方法随后应用于楚拉SU(3)夸克模型中的NΔ系统，其中夸克-夸克相互作用包括除了单胶子交换（OGE）和现象学束缚势之外，还包含由于楚拉SU(3)对称性的自发破缺而产生的非九标量和伪标量介子交换。通过将新方法的结果与传统计算结果进行比较，阐明了新发展的形式化方法的显著特征。
英文摘要：
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 (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 demonstrated by comparing the results from the new formulation with those from traditional calculations.
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