On the meson mass spectrum in the covariant confined quark model

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 αs calculated in an QCD-inspired approach.PACS numbers: 12.39. Ki,13.30.Eg,14.20.Jn,14.20.Mr Keywords: relativistic quark model, light and heavy mesons, mass spectrum and decay constants I IntroductionOne of the puzzles of hadron physics is the origin of the hadron masses. The Standard Model (SM) and, in particular, quantum chromodynamics (QCD) operate only with fundamental particles (quarks, leptons, neutrinos), gauge bosons and the Higgs. It is not yet clear how to explain the appearance of the multitude of observed hadrons and elucidate the generation of their masses. Therefore, the calculation of the hadron mass spectrum in a quality comparable to the precision of experimental data still remains one of the major problems in QCD.Actually, even before QCD was set up as the fundamental theory of strong interactions, it was understood that it is a difficult problem to describe a composite particle within quantum field theory as based on the relativistic S-matrix. The reason is that quantum field theory operates with free fields which are quantized by imposing commutator (anticommutator) relations between creation and annihilation operators. The asymptotic in-and out-states are constructed by means of these operators acting on the vacuum state. Physical processes are described by the elements of the Smatrix taken for the relevant in-and out-states. In perturbation theory, which originally has a mathematical meaning, the matrix elements are represented by a set of the Feynman diagrams which are the convolution of free Green functions (or propagators). The original Lagrangian describing free fields and their interactions requires renormalization, i.e. the transition from bare or unrenormalized quantities like mass, wave function, coupling constant to the physical or renormalized ones. In particular, the bare field is related to the dressed one by the ...

The fermi coupling, mass spectrum and decay properties of mesons within the covariant confined quark model

“…Up to now we have used only the compositeness condition in (3) to determine the renormalized Yukawa coupling g H as a function of meson mass and model parameters. In paper [3] we used the normalization condition (4) to investigate the dependence of the coupling G on physical meson masses.…”

“…Below we apply the CCQM to the meson mass problem [3]. We use the CC requirement to determine the renormalized Yukawa coupling g r as a function of model parameters and observed hadron masses m H .…”

Infrared Confinement: Mass-Scale Dependence of the Strong Effective Coupling, Leptonic Decay Constants and Spectrum of Mesons, the Lowest Glueball Mass

“…For the spectra of quark-antiquark and di-gluon bound states we solve BetheSalpeter type equations obtained in [3,4]. By omitting intermediate stages of calculation (see for details [5]) we rewrite the master equation determining the meson mass as follows: …”

“…These propagators are entire analytic functions in the Euclidean space. Note, another type of IR confinement applied to whole 'quarkantiquark' loop was applied in [8,9]. The analytic confinement disappears as Λ → 0.…”

“…Table 1. Estimated masses of conventional mesons M P and M V (in units of MeV) for new model parameters (8) compared to the recent experimental data [16]. Table 3.…”