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

Abstract

The Tamm–Dancoff Approximation (TDA) and Random Phase Approximation (RPA) many-body methods are applied to an effective Quantum Chromodynamics (QCD) 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 ([Formula: see text]) and a confining linear ([Formula: see text]) potential. 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, which in the RPA description is a highly collective state, is in 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.