On the meson mass spectrum in the covariant confined quark model

TL;DR

This paper investigates the meson mass spectrum using a covariant confined quark model, employing compositeness and mass function equations to relate meson properties to quark interactions, resulting in predictions consistent with experimental data.

Contribution

It introduces a novel application of the covariant confined quark model with compositeness conditions to derive meson mass spectra and compare Fermi coupling with QCD coupling.

Findings

Mass spectrum aligns well with experimental data

Fermi coupling varies smoothly with meson masses

Comparison shows Fermi coupling behavior similar to QCD coupling

Abstract

We provide a new insight into the problem of generating the hadron mass spectrum in the framework of the covariant confined quark model. One of the underlying principles of this model is the compositeness condition which means that the wave function renormalization constant of the elementary hadron is equal to zero. In particular, this equation allows to express the Yukawa coupling of the meson fields to the constituent quarks as a function of other model parameters. In addition to the compositeness condition we also employ a further equation which relates the meson mass function to the Fermi coupling. Both equations guarantee that the Yukawa-type theory is equivalent to the Fermi-type theory thereby providing an interpretation of the meson field as the bound state of its constituent fermions (quarks). We evaluate the Fermi-coupling as a function of meson (pseudoscalar and vector) masses and vary the values of the masses in such a way to obtain a smooth behavior for the resulting curve. The mass spectrum obtained in this manner is found to be in good agreement with the experimental data. We also compare the behavior of our Fermi-coupling with the strong QCD coupling alpha_s calculated in an QCD-inspired approach.