BS and DS equations in a Wilson loop context in QCD, effective mass operator, q-qbar spectrum

TL;DR

This paper explores the Bethe-Salpeter and Dyson-Schwinger equations in QCD to model the quark-antiquark spectrum, achieving good agreement with observed meson spectra through approximate diagonalization methods, with some limitations for light pseudoscalar states.

Contribution

It introduces an improved approach for calculating the q-qbar spectrum using a quadratic mass operator and center of mass Hamiltonian, enhancing previous models with a running coupling constant.

Findings

Successfully reproduces the meson spectrum for most states

Uses approximate diagonalization of H_{CM} and M^{2}

Requires parameter adjustments and a running coupling for accuracy

Abstract

We briefly discuss the quark-antiquark Bethe-Salpeter equation and the quark Dyson-Schwinger equation derived in preceding papers. We also consider the q-qbar quadratic mass operator M^{2} = (w_{1} + w_{2})^{2} + U obtained by three-dimensional reduction of the BS equation and the related approximate center of mass Hamiltonian or linear mass operator H_{CM} = M = w_{1} + w_{2} + V + ... We revue previous results on the spectrum and the Regge trajectories obtained by an approximate diagonalization of H_{CM} and report new results similarly obtained by an approximate diagonalization of H_{CM} and report new results similarly obtained for the original M^{2}. We show that in both cases we succeed to reproduce fairly well the entire meson spectrum in the cases in which the numerical calculations were actually practicable and with the exception of the light pseudoscalar states (related to the chiral symmetry problematic). A small rearrangement of the parameters and the use of a running coupling constant is necessary in the M^{2} case.