Abstract
A relativistic quantum-field model based on analytic confinement is considered to study the two- quark and two-gluon bound states. For the spectra of two-particle bound states we solve the ladder Bethe-Salpeter equation. We provide a new, independent and analytic estimate of the lowest glueball mass and found it at 1660 MeV. The conventional mesons and the weak decay constants are described to extend the consideration. By using a few parameters (the quark masses, the coupling constant and the confinement scale) we obtain numerical results which are in reasonable agreement with experimental evidence in the wide range of energy scale from 140MeV up to 9 GeV. The model can serve a reasonable framework to describe simultaneously di erent sectors in low-energy particle physics.
Highlights
The calculations of hadron mass characteristics on the level of experimental data precision still remain among the unsolved problems in QCD due to some technical and conceptual difficulties related with the color confinement and spontaneous chiral symmetry breaking
The confinement and dynamical symmetry breaking are two crucial features of QCD, they correspond to different energy scales [2, 3]
The confinement is an explanation of the physics phenomenon that color charged particles are not observed, the quarks are confined with other quarks by the strong interaction to form bound states so that the net color is neutral
Summary
The calculations of hadron mass characteristics on the level of experimental data precision still remain among the unsolved problems in QCD due to some technical and conceptual difficulties related with the color confinement and spontaneous chiral symmetry breaking. One of the earliest suggestion in this direction is the Analytic Confinement (AC) based on the assumption that the QCD vacuum is realized by the self-dual vacuum gluon fields which are stable versus local quantum fluctuations and related to the confinement and chiral symmetry breaking [11]. It is shown that a ’toy’ model of interacting scalar ’quarks’ and ’gluons’ with AC could result in qualitatively reasonable description of the two- and three-particle bound states [18] and obtained analytic solutions to the ladder BSE lead to the Regge behaviors of meson spectra [19] This model was further modified in [20], applied to leptonic decay constants in [21] and used to simultaneously compute meson masses and estimate the mass of the lowest-lying glueball in [23]. We build a model describing hadrons as relativistic bound states of quarks and gluons and to calculate with reasonable accuracy the hadron important characteristics such as the lowest glueball mass, mass spectra of conventional mesons and the decay constants of light mesons
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