Glueball as a bound state in the self-dual homogeneous vacuum gluon field

Abstract

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex ${p}^{2}$ plane) and the weak coupling constant lead to the Regge behavior of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the self-dual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless ${0}^{++}$ two-gluon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass is 1765 MeV for ${\ensuremath{\alpha}}_{s}=0.33$ if the gluon condensate is $〈({\ensuremath{\alpha}}_{s}/\ensuremath{\pi})GG〉=0.012{\mathrm{GeV}}^{4}.$