Abstract
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\mathrm L}(N_f)\times SU_{\mathrm R}(N_f)$ and $U_{\mathrm A}(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal $n$-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.
Highlights
The idea of four-dimensional harmonic oscillator as a tool for universal description of the Regge spectrum of hadron masses was formulated long time ago by Feynman, Kislinger, and Ravndal [1] and later re-entered the discussion about quark confinement several times in various ways
The distinctive feature of the approach is that it links the concept of harmonic confinement and Regge character of hadron mass spectrum to the specific class of nonperturbative gluon configurations – almost everywhere homogeneous Abelianself-dual gluon fields
In all three cases one deals with the generalized Laguerre polynomials as characteristic for the radial meson excitations. Another interesting observation is that the form of Euclidean gluon and quark propagators in the presence of the Abelianself-dual background are in qualitative agreement with the decoupling scenario of the infra-red behaviour of the propagators in Dyson-Schwinger equations (DSE) and functional renormalization group (FRG) approaches and lattice QCD results for the Landau gauge propagators
Summary
The idea of four-dimensional harmonic oscillator as a tool for universal description of the Regge spectrum of hadron masses was formulated long time ago by Feynman, Kislinger, and Ravndal [1] and later re-entered the discussion about quark confinement several times in various ways. The reason for confinement of a single quark and Regge spectrum of mesons turned out to be the same – the analytic properties of quark and gluon propagators In this formalism any meson looks much more like a complicated collective excitation of a medium (QCD vacuum) involving quark, antiquark and gluon fields than a nonrelativistic quantum mechanical bound state of charged particles (quark and anti-quark) due to some potential interaction between them. In all three cases one deals with the generalized Laguerre polynomials as characteristic for the radial meson excitations Another interesting observation is that the form of Euclidean gluon and quark propagators in the presence of the Abelian (anti-)self-dual background are in qualitative agreement with the decoupling scenario of the infra-red behaviour of the propagators in Dyson-Schwinger equations (DSE) and functional renormalization group (FRG) approaches and lattice QCD results for the Landau gauge propagators.
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