Three-particle hyper-spherical harmonics and quark bound states

23rd International Conference on Integrable Systems and Quantum Symmetries

Salom, Igor^1 ; Dmitrainovi, V.^1

Institute of Physics, Belgrade University, Pregrevica 118, Beograd

11080, Serbia^1

关键词: Bound state;    Bound-state problems;    Effective potentials;    Hyperspherical harmonics;    Natural basis;    Spatial dimension;    Spherical harmonics;    Subalgebras;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012044/pdf
DOI  :  10.1088/1742-6596/670/1/012044

来源: IOP

【 摘 要 】

We construct the three-body permutation symmetric hyperspherical harmonics based on the subgroup chain S3⊗ SO (3)rot⊂ O(2) ⊗ SO (3)rot⊂ O(6) (and the subalgebra chain u(1) ⊗ so(3)rot⊂ u(3) ⊂ so(6)). These hyperspherical harmonics represent a natural basis for solving non-relativistic three-body Schrodinger equation in three spatial dimensions. In particular, we apply the calculated three-particle harmonics to the three-quark bound state problem. We consider confining Δ- and Y-string three-quark effective potentials, and then calculate the spectrum of low-lying (K