Low energy meson spectrum from a QCD approach based on many-body methods

TL;DR

This paper applies many-body methods to a QCD-inspired Hamiltonian to compute the low-energy meson spectrum, showing that TDA captures gross structures and RPA improves pion state predictions, with results compared to experiments.

Contribution

It introduces a QCD-motivated Hamiltonian approach using TDA and RPA methods to study the meson spectrum, incorporating gluon effects via an instantaneous interaction.

Findings

TDA reproduces gross meson structures

RPA yields better pion state agreement

Results are consistent with experimental data

Abstract

The TDA and RPA many-body methods are applied to a QCD motivated Hamiltonian in the Coulomb gauge. The gluon effects in the low energy domain are accounted for by the Instantaneous color-Coulomb Interaction between color-charge densities, approximated by the sum of a Coulomb and a confining linear potentials. We use the eigenfunctions of the harmonic oscillator as a basis for the quantization of the quark fields, and discuss how suitable this basis is in various steps of the calculation. We show that the TDA results already reproduce the gross-structure of the light flavored meson states. The pion-like state in the RPA description, which is a highly collective state, is in a better agreement with the experimental value. The results are related to other nonperturbative treatments and compared to experimental data. We discuss the advantages of the present approach.