A Solvable Model for Many Quark Systems in QCD Hamiltonians

TL;DR

This paper introduces an effective Hamiltonian model for multi-quark systems in QCD, utilizing BCS solutions and harmonic oscillator orbitals to explore constituent quark states and exact solutions.

Contribution

It presents a new solvable model for many-quark systems in QCD Hamiltonians using harmonic oscillator basis and combines analytical and numerical methods for solutions.

Findings

Exact solutions for restricted orbital states

Analytical and numerical methods for full orbital basis

BCS-type solutions representing constituent quarks

Abstract

Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single particle orbitals are chosen as 3-dimensional harmonic oscillators and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.