Regge spectra of excited mesons, harmonic confinement, and QCD vacuum structure

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 briefly reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(N f ) × SUR(N f ) and UA(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. New systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Interrelation between the present approach, models based on ideas of soft wall AdS/QCD, light front holographic QCD, and the picture of harmonic confinement is outlined.

Finite Size Effects in the Free Energy Density for Abelian (Anti-)Self-Dual Gluon Field in SU(3) Gluodynamics

“…There exists certain evidence that physical QCD vacuum can be rather efficiently represented by the statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon field configurations. Indications come from study of QCD effective action by various methods [1][2][3][4][5][6][7] and application of the model of confinement, chiral symmetry breaking and hadronization in QCD, which is based on this representation of QCD vacuum, to calculation of hadron spectra, decay constants and formfactors [8][9][10][11][12]. In particular, study of the effective action demonstrated that homogeneous Abelian (anti-)self-dual field appears to be a good candidate for a global minimum of the effective action [1,7], and that there exist kink-like defects in the Abelian (anti-)self-dual homogeneous gluon background field [6] allowing one to explicitly represent general almost everywhere homogeneous Abelian (anti-)self-dual field configurations in the form of domain wall networks [13].…”

Excited scalar and pseudoscalar mesons in the extended linear sigma model

“…Excited mesons were a subject of interest already several decades ago [97,98]; to date, they have been considered in a wide range of approaches including QCD models / chiral Lagrangians [99][100][101][102][103][104], Lattice QCD [105][106][107][108][109][110], Bethe-Salpeter equation [111][112][113][114], NJL Model and its extensions [115][116][117][118][119][120][121][122][123][124][125], light-cone models [126], QCD string approaches [127] and QCD domain walls [128]. Chiral symmetry has also been suggested to become effectively restored in excited mesons [129,130] rendering their understanding even more important.…”

Electromagnetic couplings of radially excited light vector mesons from QCD sum rules

“…We found some estimates for F 1 (i.e. for F ρ ′ ) which lead to the following predictions: β ≈ 0.3 [78] (from a model of S-matrix unitarity for overlapping resonances); β 0.3 [79] (from contribution of ρ ′ to the electromagnetic pion mass difference); β ≈ 0.25 [80] (from a specific model of gluon vacuum); β ≈ 0.27 − 0.46 [81] (from a specific relativized potential quark model); β ≈ 0.59 (12) [82] (from finite energy QCD sum rules saturated by two resonances). It should be mentioned that the last estimate obtained with the help of the least square fitting method is consistent with the estimates which we will get in the present paper.…”