QCD inspired relativistic bound state model and meson structures

TL;DR

This paper develops a QCD-inspired relativistic model for mesons, improving on previous models by incorporating angular momentum conservation, lattice QCD-based confinement, flavor mixing, and relativistic covariance, successfully describing meson spectra.

Contribution

The paper introduces a comprehensive relativistic meson model integrating angular momentum, confinement, flavor mixing, and covariance, advancing the understanding of meson structures and spectra.

Findings

Accurately describes spectra of 265 mesons with experimental data

Predicts masses and configurations for mesons with uncertain or unassigned quantum numbers

Provides insights connecting the model to low energy QCD and holographic approaches

Abstract

A QCD inspired relativistic effective Hamiltonian model for the bound states of mesons has been constructed, which integrates the advantages of several QCD effective Hamiltonian models. Based on light-front QCD effective Hamiltonian model, the squared invariant mass operator of meson is used as the effective Hamiltonian. The model has been improved significantly in four major aspects: i)it is proved that in center of mass frame and in internal coordinate Hilbert subspace, the total angular momentum $J$ of meson is conserved and the mass eigen equation can be expressed in total angular momentum representation and in terms of a set of coupled radial eigen equations for each $J$. ii)Based on lattice QCD results, a relativistic confining potential is introduced into the effective interaction and the excited states of mesons can be well described. iii)an SU(3) flavor mixing interaction is introduced phenomenologically to describe the flavor mixing mesons and the mass eigen equations contain the coupling among different flavor components. iv)the mass eigen equations are of relativistic covariance and the coupled radial mass eigen equations take full account of $L-S $ coupling and tensor interactions. The model has been applied to describe the whole meson spectra of about 265 mesons with available data. The agreement of the calculated masses, squared radii, and decay constants with data is quite well. For the mesons whose mass data have large experimental uncertainty, the model produces certain mass values for test. For some mesons whose total angular momenta and parity are not assigned experimentally, the model gives a prediction of the spectroscopic configuration$^{2S+1}L_J$. The connection between our model and the recent low energy QCD issues-the infrared conformal scaling invariance and holographic QCD hadron models is discussed.